HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 01 Mar 2021 07:35:29 GMT2021-03-01T07:35:29Z502281- On a Sparre Andersen risk model perturbed by a spectrally negative Lévy processhttp://hdl.handle.net/10722/186282Title: On a Sparre Andersen risk model perturbed by a spectrally negative Lévy process
Authors: Zhang, Z; Yang, H; Yang, H
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1862822013-01-01T00:00:00Z
- Insurance Risk Models: with and without Dividendshttp://hdl.handle.net/10722/241867Title: Insurance Risk Models: with and without Dividends
Authors: Yang, H
Description: Stream 5: Actuarial Science / Insurance Mathematics
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/2418672010-01-01T00:00:00Z
- Locally risk-minimizing hedging strategies for unit-linked life insurance contracts under a regime switching Lévy modelhttp://hdl.handle.net/10722/172489Title: Locally risk-minimizing hedging strategies for unit-linked life insurance contracts under a regime switching Lévy model
Authors: Qian, L; Yang, H; Wang, R
Abstract: This paper extends the model and analysis in that of Vandaele and Vanmaele [Insurance: Mathematics and Economics, 2008, 42: 1128-1137]. We assume that parameters of the Lévy process which models the dynamic of risky asset in the financial market depend on a finite state Markov chain. The state of the Markov chain can be interpreted as the state of the economy. Under the regime switching Lévy model, we obtain the locally risk-minimizing hedging strategies for some unit-linked life insurance products, including both the pure endowment policy and the term insurance contract. © 2011 Higher Education Press and Springer-Verlag Berlin Heidelberg.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1724892011-01-01T00:00:00Z
- Optimal portfolio in a continuous-time self-exciting threshold modelhttp://hdl.handle.net/10722/186279Title: Optimal portfolio in a continuous-time self-exciting threshold model
Authors: Meng, H; Yuen, FL; Siu, T.K; Yang, H
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1862792013-01-01T00:00:00Z
- Valuing T-year contingent optionshttp://hdl.handle.net/10722/165737Title: Valuing T-year contingent options
Authors: Yang, H; Gerber, HU; Shiu, ESW
Abstract: We consider the problem of valuing Guaranteed Minimum Death Benefits (GMDB) in various variable annuity and equity-indexed annuity contracts. We assume that the life contingent options will expire at a fixed time T. By using a discounted density function approach, we provide closed for expressions for the values of the contingent options. In particular we show that the results in Ulm (2008) can be obtained easily using our approach. This talk is based on a joint paper with Hans Gerber and Elias Shiu.
Description: Invited speaker
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1657372011-01-01T00:00:00Z
- Numerical methods for optimal dividend payment and investment strategies of regime-switching jump diffusion models with capital injectionshttp://hdl.handle.net/10722/198097Title: Numerical methods for optimal dividend payment and investment strategies of regime-switching jump diffusion models with capital injections
Authors: Jin, Z; Yang, H; Yin, GG
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1980972013-01-01T00:00:00Z
- Optimal dividends with debts and nonlinear insurance risk processeshttp://hdl.handle.net/10722/198098Title: Optimal dividends with debts and nonlinear insurance risk processes
Authors: Meng, H; Siu, TK; Yang, H
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1980982013-01-01T00:00:00Z
- Ruin problems for a discrete time risk model with random interest ratehttp://hdl.handle.net/10722/54356Title: Ruin problems for a discrete time risk model with random interest rate
Authors: Yang, H; Zhang, L
Abstract: In this paper, we study a discrete time risk model with random interest rate. The convergence of the discounted surplus process is proved by using martingale techniques, an expression of ruin probability is obtained, and bounds for ruin probability are included. In the second part of the paper, the distribution of surplus immediately after ruin, the distribution of surplus just before ruin, the joint distribution of the surplus immediately before and after ruin, and the distribution of ruin time are discussed.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/543562006-01-01T00:00:00Z
- The Omega model: from bankruptcy to occupation times in the redhttp://hdl.handle.net/10722/186276Title: The Omega model: from bankruptcy to occupation times in the red
Authors: Gerber, HU; Shiu, ESW; Yang, H
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1862762012-01-01T00:00:00Z
- Equilibruim approach of asset pricing under Lévy processhttp://hdl.handle.net/10722/172502Title: Equilibruim approach of asset pricing under Lévy process
Authors: Fu, J; Yang, H
Abstract: This work considers the equilibrium approach of asset pricing for Lévy process. It derives the equity premium and pricing kernel analytically for the stock price process, obtains an equilibrium option pricing formula, and explains some empirical evidence such as the negative variance risk premium, implied volatility smirk, and negative skewness risk premium by comparing the physical and risk-neutral distributions of the log return. Different from most of the current studies in equilibrium pricing under jump diffusion models, this work models the underlying asset price as the exponential of a Lévy process and thus allows nearly an arbitrage distribution of the jump component. © 2012 Elsevier B.V. All rights reserved.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1725022012-01-01T00:00:00Z
- Actuarial education in the universitieshttp://hdl.handle.net/10722/165736Title: Actuarial education in the universities
Authors: Yang, H
Description: Invited speaker
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1657362011-01-01T00:00:00Z
- On the optimal dividend strategy in a regime-switching diffusion modelhttp://hdl.handle.net/10722/186284Title: On the optimal dividend strategy in a regime-switching diffusion model
Authors: Wei, J; Wang, R; Yang, H
Abstract: In this paper we consider the optimal dividend strategy under the diffusion model with regime switching. In contrast to the classical risk theory, the dividends can only be paid at the arrival times of a Poisson process. By solving an auxiliary optimal problem we show that the optimal strategy is the modulated barrier strategy. The value function can be obtained by iteration or by solving the system of differential equations. We also provide a numerical example to illustrate the effects of the restriction on the timing of the payment of dividends.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1862842012-01-01T00:00:00Z
- On a nonparametric estimator for ruin probability in the classical risk modelhttp://hdl.handle.net/10722/198105Title: On a nonparametric estimator for ruin probability in the classical risk model
Authors: Zhang, Z; Yang, H; Yang, H
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/1981052014-01-01T00:00:00Z
- Nonparametric estimate of the ruin probability in a pure-jump Lévy risk modelhttp://hdl.handle.net/10722/198099Title: Nonparametric estimate of the ruin probability in a pure-jump Lévy risk model
Authors: Zhang, Z; Yang, H
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1980992013-01-01T00:00:00Z
- Valuing equity-linked death benefits in jump diffusion modelshttp://hdl.handle.net/10722/198096Title: Valuing equity-linked death benefits in jump diffusion models
Authors: Gerber, HU; Shiu, ESW; Yang, H
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1980962013-01-01T00:00:00Z
- Cox risk model with variable premium rate and stochastic return on investmenthttp://hdl.handle.net/10722/198104Title: Cox risk model with variable premium rate and stochastic return on investment
Authors: Xu, L; Yang, H; Wang, R
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/1981042014-01-01T00:00:00Z
- Pricing options and equity-Indexed annuities in a Regime-switching Model by Trinomial Tree Methodhttp://hdl.handle.net/10722/159895Title: Pricing options and equity-Indexed annuities in a Regime-switching Model by Trinomial Tree Method
Authors: Yuen, FL; Yang, H
Abstract: In this paper we summarize the main idea and results of Yuen and Yang (2009, 2010a, 2010b) and provide some results on pricing of Parisian options under the Markov regime-switching model (MRSM). The MRSM allows the parameters of the market model depending on a Markovian process, and the model can reflect the information of the market environment which cannot be modeled solely by linear Gaussian process. However, when the parameters of the stock price model are not constant but governed by a Markovian process, the pricing of the options becomes complex. We present a fast and simple trinomial tree model to price options in MRSM. In recent years, the pricing of modern insurance products, such as Equity-Indexed annuity (EIA) and variable annuities (VAs), has become a popular topic. We show here that our trinomial tree model can been used to price EIA with strong path dependent exotic options in the regime switching model.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1598952011-01-01T00:00:00Z
- Optimal financing and dividend distribution in a general diffusion model with regime switchinghttp://hdl.handle.net/10722/231316Title: Optimal financing and dividend distribution in a general diffusion model with regime switching
Authors: Zhu, JX; Yang, H
Abstract: We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model, where the drift and volatility coefficients are general functions of the level of surplus and the external environment regime. The environment regime is modeled by a Markov process. Both capital injection and dividend payments incur expenses. The objective is to maximize the expectation of the total discounted dividends minus the total cost of the capital injection. We prove that it is optimal to inject capital only when the surplus tends to fall below 0 and to pay out dividends at the maximal rate when the surplus is at or above the threshold, dependent on the environment regime.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2313162016-01-01T00:00:00Z
- On the probability of completeness for large marketshttp://hdl.handle.net/10722/159561Title: On the probability of completeness for large markets
Authors: Wright, JA; Yam, PSC; Yang, H
Abstract: We consider a family of discrete multiperiod multinomial market models F n, each of which contains n - 1 stocks and one bond. All the securities are allowed to be risky and we assume that the number of states in each period is finite. We let the securities' prices follow probability distributions that reflect the traders' view of the market. Under mild restrictions on the probability structure of F n, we show that the probability that a market, chosen at random from F n, is complete tends to one as n approaches infinity. © The JJIAM Publishing Committee and Springer 2011.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1595612011-01-01T00:00:00Z
- Optimal dynamic portfolio selection with earnings-at-riskhttp://hdl.handle.net/10722/54353Title: Optimal dynamic portfolio selection with earnings-at-risk
Authors: Li, ZF; Yang, H; Deng, XT
Abstract: In this paper we investigate a continuous-time portfolio selection problem. Instead of using the classical variance as usual, we use earnings-at-risk (EaR) of terminal wealth as a measure of risk. In the settings of Black-Scholes type financial markets and constantly-rebalanced portfolio (CRP) investment strategies, we obtain closed-form expressions for the best CRP investment strategy and the efficient frontier of the mean-EaR problem, and compare our mean-EaR analysis to the classical mean-variance analysis and to the mean-CaR (capital-at-risk) analysis. We also examine some economic implications arising from using the mean-EaR model. © 2007 Springer Science+Business Media, LLC.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/543532007-01-01T00:00:00Z
- Optimal asset allocation: a worst scenario expectation approachhttp://hdl.handle.net/10722/159899Title: Optimal asset allocation: a worst scenario expectation approach
Authors: Yuen, FL; Yang, H
Abstract: Mean-variance criterion has long been the main stream approach in the optimal portfolio theory. The investors try to balance the risk and the return on their portfolio. In this paper, the deviation of the asset return from the investor's expectation in the worst scenario is used as the measure of risk for portfolio selection. One important advantage of this approach is that the investors can base on their own knowledge, information, and preference on various risks, in addition to the asset's volatility, to adjust their exposure to various risks. It also pinpoints one main concern of the investors when they invest, the amount they lose in the worst situation. © 2011 Springer Science+Business Media, LLC.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1598992012-01-01T00:00:00Z
- Option pricing with tree model in view of hedginghttp://hdl.handle.net/10722/127198Title: Option pricing with tree model in view of hedging
Authors: Yuen, FL; Yang, H
Description: Session 5D Derivative Pricing
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1271982010-01-01T00:00:00Z
- An elementary approach to discrete models of dividend strategieshttp://hdl.handle.net/10722/125409Title: An elementary approach to discrete models of dividend strategies
Authors: Gerber, HU; Shiu, ESW; Yang, H
Abstract: The paper studies a discrete counterpart of Gerber et al. (2006). The surplus of an insurance company (before dividends) is modeled as a time-homogeneous Markov chain with possible changes of size + 1, 0, - 1, - 2, - 3, .... If a barrier strategy is applied for paying dividends, it is shown that the dividends-penalty identity holds. The identity expresses the expected present value of a penalty at ruin in terms of the expected discounted dividends until ruin and the expected present value of the penalty at ruin if no dividends are paid. For the problem of maximizing the difference between the expected discounted dividends until ruin and the expected present value of the penalty at ruin, barrier strategies play a prominent role. In some cases an optimal dividend barrier exists. The paper discusses in detail the special case where the distribution of the change in surplus does not depend on the current surplus (so that in the absence of dividends the surplus process has independent increments). A closed-form result for zero initial surplus is given, and it is shown how the relevant quantities can be calculated recursively. Finally, it is shown how optimal dividend strategies can be determined; typically, they are band strategies. © 2009 Elsevier B.V. All rights reserved.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1254092010-01-01T00:00:00Z
- Markowitz's mean-variance asset-liability management with regime switching: A multi-period modelhttp://hdl.handle.net/10722/135508Title: Markowitz's mean-variance asset-liability management with regime switching: A multi-period model
Authors: Chen, P; Yang, H
Abstract: This paper considers an optimal portfolio selection problem under Markowitz's meanvariance portfolio selection problem in a multi-period regime-switching model. We assume that there are n + 1 securities in the market. Given an economic state which is modelled by a finite state Markov chain, the return of each security at a fixed time point is a random variable. The return random variables may be different if the economic state is changed even for the same security at the same time point. We start our analysis from the no-liability case, in the spirit of Li and Ng (2000), both the optimal investment strategy and the efficient frontier are derived. Then we add uncontrollable liability into the model. By direct comparison with the no-liability case, the optimal strategy can be derived explicitly. © 2011 Taylor & Francis.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1355082011-01-01T00:00:00Z
- On the absolute ruin in a MAP risk model with debit interesthttp://hdl.handle.net/10722/135501Title: On the absolute ruin in a MAP risk model with debit interest
Authors: Zhang, Z; Yang, H; Yang, H
Abstract: In this paper we consider a risk model where claims arrive according to a Markovian arrival process (MAP). When the surplus becomes negative or the insurer is in deficit, the insurer could borrow money at a constant debit interest rate to repay the claims. We derive the integro-differential equations satisfied by the discounted penalty functions and discuss the solutions. A matrix renewal equation is obtained for the discounted penalty function provided that the initial surplus is nonnegative. Based on this matrix renewal equation, we present some asymptotic formulae for the discounted penalty functions when the claim size distributions are heavy tailed. © Applied Probability Trust 2011.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1355012011-01-01T00:00:00Z
- On a multi-dimensional risk model with regime switchinghttp://hdl.handle.net/10722/231317Title: On a multi-dimensional risk model with regime switching
Authors: Wang, G; Wang, GJ; Yang, H
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2313172016-01-01T00:00:00Z
- Optimal debt ratio and dividend payment strategies with reinsurancehttp://hdl.handle.net/10722/231321Title: Optimal debt ratio and dividend payment strategies with reinsurance
Authors: Jin, Z; Yang, H; Yin, G
Abstract: This paper derives the optimal debt ratio and dividend payment strategies for an insurance company. Taking into account the impact of reinsurance policies and claims from the credit derivatives, the surplus process is stochastic that is jointly determined by the reinsurance strategies, debt levels, and unanticipated shocks. The objective is to maximize the total expected discounted utility of dividend payment until financial ruin. Using dynamic programming principle, the value function is the solution of a second-order nonlinear Hamilton–Jacobi–Bellman equation. The subsolution–supersolution method is used to verify the existence of classical solutions of the Hamilton–Jacobi–Bellman equation. The explicit solution of the value function is derived and the corresponding optimal debt ratio and dividend payment strategies are obtained in some special cases. An example is provided to illustrate the methodologies and some interesting economic insights.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2313212015-01-01T00:00:00Z
- Optimal retention for a stop-loss reinsurance with incomplete informationhttp://hdl.handle.net/10722/231320Title: Optimal retention for a stop-loss reinsurance with incomplete information
Authors: Hu, X; Yang, H; Zhang, L
Abstract: This paper considers the determination of optimal retention in a stop-loss reinsurance. Assume that we only have incomplete information on a risk XX for an insurer, we use an upper bound for the value at risk (VaR) of the total loss of an insurer after stop-loss reinsurance arrangement as a risk measure. The adopted method is a distribution-free approximation which allows to construct the extremal random variables with respect to the stochastic dominance order and the stop-loss order. We derive the optimal retention such that the risk measure used in this paper attains the minimum. We establish the sufficient and necessary conditions for the existence of the nontrivial optimal stop-loss reinsurance. For illustration purpose, some numerical examples are included and compared with the results yielded in Theorem 2.1 of Cai and Tan (2007).
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2313202015-01-01T00:00:00Z
- Optimal asset allocation: Risk and information uncertaintyhttp://hdl.handle.net/10722/231318Title: Optimal asset allocation: Risk and information uncertainty
Authors: Yam, SCP; Yang, H; Yuen, FL
Abstract: In asset allocation problem, the distribution of the assets is usually assumed to be known in order to identify the optimal portfolio. In practice, we need to estimate their distribution. The estimations are not necessarily accurate and it is known as the uncertainty problem. Many researches show that most people are uncertainty aversion and this affects their investment strategy. In this article, we consider risk and information uncertainty under a common asset allocation framework. The effects of risk premium and covariance uncertainty are demonstrated by the worst scenario in a set of measures generated by a relative entropy constraint. The nature of the uncertainty and its impacts on the asset allocation are discussed.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2313182016-01-01T00:00:00Z
- Valuing equity-linked insurance productshttp://hdl.handle.net/10722/239157Title: Valuing equity-linked insurance products
Authors: Yang, H
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2391572016-01-01T00:00:00Z
- A constraint-free approach to optimal reinsurancehttp://hdl.handle.net/10722/239144Title: A constraint-free approach to optimal reinsurance
Authors: Yang, H; Gerber, HU; Shiu, ESW
Abstract: Reinsurance is available for a reinsurance premium that is determined according to a convex premium principle H. The first insurer selects the reinsurance coverage that maximizes his expected utility. No conditions are imposed on the reinsurer’s payment. The optimality condition involves the gradient of H. For several combinations of H and the first insurer’s utility function, closed form formulas for the optimal reinsurance are given. If H is a zero utility principle (for example, an exponential principle or an expectile principle), it can be shown, with results from Pareto optimal risk exchanges and the Theorem of Borch, that the optimal reinsurer’s payment satisfies the conditions that usually have to be imposed.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2391442016-01-01T00:00:00Z
- Valuing embedded options in insurance productshttp://hdl.handle.net/10722/239148Title: Valuing embedded options in insurance products
Authors: Yang, H
Abstract: In this talk, I shall provide an overview on equity-linked insurance products and present a valuation method. The problem is motivated by the Guaranteed Minimum Death Benefits in various deferred annuities. The payment of the products depends on the price of a stock at that time and possibly also on the history of the stock price. Because each time-until-death distribution can be approximated by a combination of exponential distributions, the analysis is made for the case where the time until death is exponentially distributed. The time-until-death random variable is assumed to be independent of the stock price process. The logarithm of the index process can be a Brownian motion, a jump-diffusion process or a random walk. We are able to obtain closed-form formulas for the contingent call and put options, for lookback options, and for barrier options. (This talk is based on joint papers with Hans U. Gerber and Elias S.W. Shiu).
Description: Plenary Talk 8
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2391482016-01-01T00:00:00Z
- Valuing embedded options under jump diffusion modelshttp://hdl.handle.net/10722/239147Title: Valuing embedded options under jump diffusion models
Authors: Yang, H
Abstract: We consider the valuation of various embedded options in equity-linked products. We are interested in modeling the stock price as the exponential of a Brownian motion plus an independent compound Poisson process. Results for exponential stopping of a Levy process are used to derive a series of closed-form formulas for a variety of contingent call and put options, lookback options, and barrier options with single or double barriers. This talk is based on join work with Hans Gerber and Elias Shiu.
Description: Invited Session-SA03-I09; Host: Lingnan (University) College, Sun Yat-Sen University & Business School, Sun Yat-Sen University
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2391472016-01-01T00:00:00Z
- Geometric Stopping of a Random Walk and Its Applications to Valuing Equity-linked Death Benefitshttp://hdl.handle.net/10722/239150Title: Geometric Stopping of a Random Walk and Its Applications to Valuing Equity-linked Death Benefits
Authors: Yang, H
Abstract: We study discrete-time models in which death bene ts can depend on a stock price index, the logarithm of which is modeled as a random walk. Examples of such benefit payments include put and call options, barrier options, and lookback options. Because the distribution of the curtate-future-lifetime can be approximated by a linear combination of geometric distributions, it su ces to consider curtate-future-lifetimes with a geometric distribution. In binomial and trinomial tree models, closed-form expressions for the expectations of the discounted bene t payment are obtained for a series of options. They are based on results concerning geometric stopping of a random walk, in particular also on a version of the
Wiener-Hopf factorization. This is a joint paper with Hans U. Gerber and Elias S.W. Shiu.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2391502016-01-01T00:00:00Z
- Valuing equity-linked death benefits under trinomial tree modelhttp://hdl.handle.net/10722/239153Title: Valuing equity-linked death benefits under trinomial tree model
Authors: Yang, H
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2391532015-01-01T00:00:00Z
- Valuing equity-linked death benefit in jump diffusion modelshttp://hdl.handle.net/10722/239156Title: Valuing equity-linked death benefit in jump diffusion models
Authors: Yang, H
Abstract: We consider the valuation problem of Guaranteed Minimum Death Benefits in various equity-linked products. We are interested in modeling the stock price as the exponential of a Brownian motion plus an independent compound Poisson process. Results for exponential stopping of a Levy process are used to derive a series of closed-form formulas for a variety of contingent call and put options, lookback options, and barrier options with one or two barriers. This is a join paper with Hans U. Gerber and Elias S.W. Shiu.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2391562015-01-01T00:00:00Z
- Pension funding problem with regime-switching geometric brownian motion assets and liabilitieshttp://hdl.handle.net/10722/128527Title: Pension funding problem with regime-switching geometric brownian motion assets and liabilities
Authors: Ping, C; Yang, H
Abstract: This paper extends the pension funding model in (N. Am. Actuarial J. 2003; 7:37-51) to a regimeswitching case. The market mode is modeled by a continuous-time stationary Markov chain. The asset value process and liability value process are modeled by Markov-modulated geometric Brownian motions. We consider a pension funding plan in which the asset value is to be within a band that is proportional to the liability value. The pension plan sponsor is asked to provide sufficient funds to guarantee the asset value stays above the lower barrier of the band. The amount by which the asset value exceeds the upper barrier will be paid back to the sponsor. By applying differential equation approach, this paper calculates the expected present value of the payments to be made by the sponsor as well as that of the refunds to the sponsor. In addition, we study the effects of different barriers and regime switching on the results using some numerical examples. The optimal dividend problem is studied in our examples as an application of our theory. Copyright © 2009 John Wiley & Sons, Ltd.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1285272010-01-01T00:00:00Z
- Subjective risk measures: Bayesian predictive scenarios analysishttp://hdl.handle.net/10722/54357Title: Subjective risk measures: Bayesian predictive scenarios analysis
Authors: Siu, TK; Yang, H
Abstract: In this paper we study methods for measuring risk. First, we introduce a conditional risk measure and point out that it is a coherent risk measure. Using the Bayesian statistical idea a subjective risk measure is defined. In some special cases, closed form expressions for the risk measures can be obtained. The credibility theory can be used to relax the strong assumptions on the model and prior distributions, and to obtain approximated risk measure formulas. Applications in both finance and insurance are discussed. © 1999 Elsevier Science B.V.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10722/543571999-01-01T00:00:00Z
- Pricing options and equity-indexed annuities in a regime-switching model by trinomial tree methodhttp://hdl.handle.net/10722/127195Title: Pricing options and equity-indexed annuities in a regime-switching model by trinomial tree method
Authors: Yuen, FL; Yang, H
Abstract: In this paper we summarize the main idea and results of Yuen and Yang (2009, 2010a, 2010b). The Markov regime-switching model (MRSM) has recently become a popular model. The MRSM allows the parameters of the market model depending on a Markovian process, and the model can reflect the information of the market environment which cannot be modeled solely by linear Gaussian process. The Markovian process can ensure that the parameters change according to the market environment and at the same time preserves the simplicity of the model. It is also consistent with the efficient market hypothesis that all the effects of the information about the stock price would reflect on the stock price. However, when the parameters of the stock price model are not constant but governed by a Markovian process, the pricing of the options becomes complex. We present a fast and simple trinomial tree model to price options in MRSM. In recent years, the pricing of modern insurance products, such as Equity-Indexed annuity (EIA) and variable annuities (VAs), has become a popular topic. These products can be considered investment plans with associated life insurance benefits, a specified benchmark return, a guarantee of an annual minimum rate of return and a specified rule of the distribution of annual excess investment return above the guaranteed return. EIA usually has a long maturity time, hence it is not appropriate to assume that the interest rate and the volatility of the equity index are constants. One way to deal with this problem is to apply the regime switching model. However, the valuation of derivatives in such model is challenging when the number of states are large, especially for the strong path dependent options such as Asian options. Our trinomial tree model provides an efficient way to solve this problem.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1271952009-01-01T00:00:00Z
- Upper bounds for ruin probability under time series modelshttp://hdl.handle.net/10722/45340Title: Upper bounds for ruin probability under time series models
Authors: Chan, GKC; Yang, H
Abstract: In this article, we consider an insurance risk model where the claim and premium processes follow some time series models. We first consider the model proposed in Cerber [2,3]; then a model with dependent structure between premium and claim processes modeled by using Granger's causal model is considered. By using some martingale arguments, Lundberg-type upper bounds for the ruin probabilities under both models are obtained. Some special cases are discussed. © 2006 Cambridge University Press.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/453402006-01-01T00:00:00Z
- Filtering a markov modulated random measurehttp://hdl.handle.net/10722/125411Title: Filtering a markov modulated random measure
Authors: Elliott, RJ; Siu, TK; Yang, H
Abstract: We develop a new exact filter when a hidden Markov chain influences both the sizes and times of a marked point process. An example would be an insurance claims process, where we assume that both the stochastic intensity of the claim arrivals and the distribution of the claim sizes depend on the states of an economy. We also develop the robust filter-based and smoother-based EM algorithms for the on-line recursive estimates of the unknown parameters in the Markov-modulated random measure. Our development is in the framework of modern theory of stochastic processes. © 2009 IEEE.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1254112010-01-01T00:00:00Z
- Bounds of Ruin Probability for Regime-switching Models Using Time Scale Separationhttp://hdl.handle.net/10722/224451Title: Bounds of Ruin Probability for Regime-switching Models Using Time Scale Separation
Authors: Yin, G; Liu, YJ; Yang, H
Abstract: This paper is concerned with regime-switching insurance risk models. The regime-switching is modeled by a continuous-time Markov chain. Owing to various modeling considerations, the state space is likely to be very large. A two-time-scale formulation is used to reduce the complexity. Under simple conditions, limits of ultimate survival probabilities and ultimate ruin probabilities are obtained. These results reveal that, for example, as a decision maker, one may ignore the detailed variations, and use the limit ultimate ruin probabilities to approximate that of the actual ones. Moreover, the differences of the original and limit ruin probabilities are examined. Error bounds are developed.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/2244512006-01-01T00:00:00Z
- Discrete-Time BSDEs with Random Terminal Horizonhttp://hdl.handle.net/10722/198106Title: Discrete-Time BSDEs with Random Terminal Horizon
Authors: Lin, Y; Yang, H
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/1981062014-01-01T00:00:00Z
- Lundberg-type bounds for the joint distribution of surplus immediately before and after ruin under a Markov-modulated risk modelhttp://hdl.handle.net/10722/82928Title: Lundberg-type bounds for the joint distribution of surplus immediately before and after ruin under a Markov-modulated risk model
Authors: Ng, CYA; Yang, H
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/829282005-01-01T00:00:00Z
- Ruin theory in a discrete time risk model with interest incomeshttp://hdl.handle.net/10722/82889Title: Ruin theory in a discrete time risk model with interest incomes
Authors: Sun, L; Yang, H
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/828892003-01-01T00:00:00Z
- Ruin probability under a threshold insurance risk modelhttp://hdl.handle.net/10722/82907Title: Ruin probability under a threshold insurance risk model
Authors: Kwan, KM; Yang, H
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/829072007-01-01T00:00:00Z
- An integrated risk management method: VaR Approachhttp://hdl.handle.net/10722/83034Title: An integrated risk management method: VaR Approach
Authors: Yang, H
Abstract: This article presents a simple methodology for computing Value at Risk (VaR) for a portfolio of financial instruments that is sensitive to market risk, rating change, and default risk. An integrated model for market and credit risks is developed. The Jarrow, Lando and Turnbull model (the Markov chain model) is used to represent the dynamics of the credit rating. Procedures for calculating VaR are presented. Numerical illustration results are included
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/830342000-01-01T00:00:00Z
- Premium calculation using the probability of ruinhttp://hdl.handle.net/10722/83035Title: Premium calculation using the probability of ruin
Authors: Yuen, KC; Yang, H; Chu, KL
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/830352001-01-01T00:00:00Z
- A PDE approach to risk measures of derivativeshttp://hdl.handle.net/10722/83031Title: A PDE approach to risk measures of derivatives
Authors: Siu, TK; Yang, H
Abstract: This paper proposes a partial differential equation (PDE) approach to calculate coherent risk measures for portfolios of derivatives under the Black-Scholes economy. It enables us to define the risk measures in a dynamic way and to deal with American options in a relatively effective way. Our risk measure is based on the representation form of coherent risk measures. Through the use of some earlier results the PDE satisfied by the risk measures are derived. The PDE resembles the standard Black-Scholes type PDE which can be solved using standard techniques from the mathematical finance literature. Indeed, these results reveal that the PDE approach can provide practitioners with a more applicable and flexible way to implement coherent risk measures for derivatives in the context of the Black-Scholes model.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/830312000-01-01T00:00:00Z
- Two-time-scale jump-diffusion models with markovian switching regimeshttp://hdl.handle.net/10722/82937Title: Two-time-scale jump-diffusion models with markovian switching regimes
Authors: Yin, G; Yang, H
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/829372004-01-01T00:00:00Z