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postgraduate thesis: Analysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model
Title | Analysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model |
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Authors | |
Issue Date | 2016 |
Publisher | The University of Hong Kong (Pokfulam, Hong Kong) |
Citation | Qi, X. [亓孝真]. (2016). Analysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5719475 |
Abstract | There is a vast literature in the analysis of the insurer's surplus process under the Sparre Andersen risk model. Since it is cumbersome to calculate distributions of ruin-related quantities in the continuous-time model, we shall consider the discrete-time model as a quick approximation to the corresponding ones in the continuous-time model. In this work, we consider the discrete-time setting of the Sparre Andersen risk model and use the generalized Gerber-Shiu function to study various ruin-related quantities associated with variables in the generalized Gerber-Shiu function such as the ladder height and the claim causing ruin.
First, the structural properties of the generalized Gerber-Shiu function are obtained and in turn, joint/marginal distributions of ruin-related quantities of our interest are derived.
Then we shall assume particular dependency structure for the claim sizes and the interclaim times.
In addition to the ordinary risk model, the delayed model has been receiving attention since the occurrence of the last claim before time zero is taken into account to model the process. Hence we shall investigate general results for the Gerber-Shiu function in the delayed model with time-dependent claim and also focus on its relationship with the ordinary model.
Finally the Farlie-Gumbel-Mogenstern (FGM) copula is considered to model dependency structure and distributions of the ruin-related quantities such as the claim causing ruin and the last ladder height. We will demonstrate the effects of dependency parameters, initial surpluses, discounting factors on the aforementioned distributions. Moreover, the probability functions of those quantities under the ordinary model and the delayed model are compared. |
Degree | Master of Philosophy |
Subject | Risk (Insurance) - Mathematical models |
Dept/Program | Statistics and Actuarial Science |
Persistent Identifier | http://hdl.handle.net/10722/223621 |
HKU Library Item ID | b5719475 |
DC Field | Value | Language |
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dc.contributor.author | Qi, Xiaozhen | - |
dc.contributor.author | 亓孝真 | - |
dc.date.accessioned | 2016-03-03T23:16:51Z | - |
dc.date.available | 2016-03-03T23:16:51Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Qi, X. [亓孝真]. (2016). Analysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5719475 | - |
dc.identifier.uri | http://hdl.handle.net/10722/223621 | - |
dc.description.abstract | There is a vast literature in the analysis of the insurer's surplus process under the Sparre Andersen risk model. Since it is cumbersome to calculate distributions of ruin-related quantities in the continuous-time model, we shall consider the discrete-time model as a quick approximation to the corresponding ones in the continuous-time model. In this work, we consider the discrete-time setting of the Sparre Andersen risk model and use the generalized Gerber-Shiu function to study various ruin-related quantities associated with variables in the generalized Gerber-Shiu function such as the ladder height and the claim causing ruin. First, the structural properties of the generalized Gerber-Shiu function are obtained and in turn, joint/marginal distributions of ruin-related quantities of our interest are derived. Then we shall assume particular dependency structure for the claim sizes and the interclaim times. In addition to the ordinary risk model, the delayed model has been receiving attention since the occurrence of the last claim before time zero is taken into account to model the process. Hence we shall investigate general results for the Gerber-Shiu function in the delayed model with time-dependent claim and also focus on its relationship with the ordinary model. Finally the Farlie-Gumbel-Mogenstern (FGM) copula is considered to model dependency structure and distributions of the ruin-related quantities such as the claim causing ruin and the last ladder height. We will demonstrate the effects of dependency parameters, initial surpluses, discounting factors on the aforementioned distributions. Moreover, the probability functions of those quantities under the ordinary model and the delayed model are compared. | - |
dc.language | eng | - |
dc.publisher | The University of Hong Kong (Pokfulam, Hong Kong) | - |
dc.relation.ispartof | HKU Theses Online (HKUTO) | - |
dc.rights | The author retains all proprietary rights, (such as patent rights) and the right to use in future works. | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject.lcsh | Risk (Insurance) - Mathematical models | - |
dc.title | Analysis of the generalized Gerber-Shiu function in discrete-time dependent Sparre Andersen model | - |
dc.type | PG_Thesis | - |
dc.identifier.hkul | b5719475 | - |
dc.description.thesisname | Master of Philosophy | - |
dc.description.thesislevel | Master | - |
dc.description.thesisdiscipline | Statistics and Actuarial Science | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.5353/th_b5719475 | - |
dc.identifier.mmsid | 991019122499703414 | - |