Optimal Time-Consistent Investment and Premium Control Strategies for Insurers with Constraint under the Heston Model

Zilan Liu, Yijun Wang, Ya Huang and Jieming Zhou
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Zilan Liu: School of Business, Hunan Normal University, Changsha 410081, China
Yijun Wang: Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
Ya Huang: School of Business, Hunan Normal University, Changsha 410081, China
Jieming Zhou: Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China

Mathematics, 2022, vol. 10, issue 7, 1-22

Abstract: In this work, we study the optimal investment and premium control problem with the short-selling constraint under the mean-variance criterion. The claim process is assumed to follow the non-homogeneous compound Poisson process. The insurer invests the surplus in one risk-free asset and one risky asset described by the Heston model. Under these, we consider an optimization objective that maximizes the return (the expectation of terminal wealth) and minimizes the risk (the variance of terminal wealth). By constructing the extended Hamilton–Jacobi–Bellman (HJB) system with the dynamic programming method, the time-consistent strategies and the corresponding value function are obtained. Furthermore, we provide numerical examples to illustrate the effects of the model parameters on the optimal policies.

Keywords: investment; premium control; short-selling constraint; mean-variance criterion; the extended HJB system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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