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Optimal insurance control for insurers with jump-diffusion risk processes

Published online by Cambridge University Press:  16 July 2018

Linlin Tian  and
Lihua Bai
Linlin Tian
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China
Lihua Bai*
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China
*
*Correspondence to: Lihua Bai, School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China. E-mail: [email protected]
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Abstract

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.

Keywords

Compound Poisson processDiffusionHamilton-Jacobi-Bellman equationCompletion of squareStochastic maximum principle93E2091B30
Type
Paper
Information
Annals of Actuarial Science , Volume 13 , Issue 1 , March 2019 , pp. 198 - 213
Copyright
© Institute and Faculty of Actuaries 2018 

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