HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 06 Jun 2023 21:57:46 GMT2023-06-06T21:57:46Z5031Optimal contract to induce continued efforthttp://hdl.handle.net/10722/307244Title: Optimal contract to induce continued effort
Authors: Sun, Peng; Tian, Feng
Abstract: We consider a basic model of a risk-neutral principal incentivizing a risk-neutral agent to exert effort to raise the arrival rate of a Poisson process. The effort is costly to the agent, is unobservable to the principal, and affects the instantaneous arrival rate. Each arrival yields a constant revenue to the principal. The principal, therefore, devises a mechanism involving payments and a potential stopping time to motivate the agent to always exert effort. We formulate this problem as a stochastic optimal control model with an incentive constraint in continuous time over an infinite horizon. Although we allow payments to take general forms contingent on past arrival times, the optimal contract has a simple and intuitive structure, which depends on whether the agent is as patient as or less patient than the principal toward future income.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/3072442018-01-01T00:00:00ZComment on “Optimal Contract to Induce Continued Effort”http://hdl.handle.net/10722/306621Title: Comment on “Optimal Contract to Induce Continued Effort”
Authors: Cao, P; Tian, F; Sun, P
Abstract: In this comment, we first use a counterexample to demonstrate that the optimal contract structure proposed in section 4 of the paper [Sun P, Tian F (2018) Optimal contract to induce continued effort. Management Sci. 64(9):4193–4217] can be wrong when the two players’ discount rates are different. We then specify correct optimal contract structures, which involve generalizing the contract space to allow random termination. Numerical study with a wide range of model parameters illustrates that such a random termination only occurs sparingly in optimal contracts. Moreover, the suboptimality gap, measured by the relative improvement of the optimal contract over the best contract without random termination, is extremely small.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10722/3066212021-01-01T00:00:00ZOptimal Contract for Machine Repair and Maintenancehttp://hdl.handle.net/10722/306433Title: Optimal Contract for Machine Repair and Maintenance
Authors: Tian, F; Sun, P; Duenyas, I
Abstract: A principal hires an agent to repair a machine when it is down and maintain it when it is up and earns a revenue flow when the machine is up. Both the up- and downtimes follow exponential distributions. If the agent exerts effort, the downtime is shortened, and uptime is prolonged. Effort, however, is costly to the agent and unobservable to the principal. We study optimal dynamic contracts that always induce the agent to exert effort while maximizing the principal’s profits. We formulate the contract design problem as a stochastic optimal control model with incentive constraints in continuous time over an infinite horizon. Although we consider the contract space that allows payments and potential contract termination time to take general forms, the optimal contracts demonstrate simple and intuitive structures, making them easy to describe and implement in practice.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10722/3064332021-01-01T00:00:00Z