Optimal insurance control for insurers with jump-diffusion risk processes

In this paper, we model the surplus process as a compound Poisson process perturbed by diffusion and allow the insurer to ask its customers for input to minimize the distance from some prescribed target path and the total discounted cost on a fixed interval. The problem is reduced to a version of a...

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Bibliographic Details
Published in:Annals of actuarial science 2019-03, Vol.13 (1), p.198-213
Main Authors: Tian, Linlin, Bai, Lihua
Format: Article
Language:English
Subjects:
Actuarial science
Brownian motion
Dynamic programming
Economic models
Equality
Insurance
Optimization
Partial differential equations
Poisson distribution
Queuing theory
Random variables
Stochastic control theory
Utility functions
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Summary:In this paper, we model the surplus process as a compound Poisson process perturbed by diffusion and allow the insurer to ask its customers for input to minimize the distance from some prescribed target path and the total discounted cost on a fixed interval. The problem is reduced to a version of a linear quadratic regulator under jump-diffusion processes. It is treated using three methods: dynamic programming, completion of square and the stochastic maximum principle. The analytic solutions to the optimal control and the corresponding optimal value function are obtained.
ISSN:1748-4995
1748-5002
DOI:10.1017/S1748499518000192