# American Institute of Mathematical Sciences

September  2020, 16(5): 2195-2211. doi: 10.3934/jimo.2019050

## Optimal investment-reinsurance policy with regime switching and value-at-risk constraint

 1 Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China 2 Department of Mathematical Sciences, University of Nevada, Las Vegas, NV89154, United States

*Corresponding author

Received  April 2018 Revised  October 2018 Published  September 2020 Early access  May 2019

Fund Project: This project was supported by Tianjin philosophy and social science planning project (TJGLQN18-005)

This paper studies an optimal investment-reinsurance problem for an insurance company which is subject to a dynamic Value-at-Risk (VaR) constraint in a Markovian regime-switching environment. Our goal is to minimize its ruin probability and control its market risk simultaneously. We formulate the problem as an infinite horizontal stochastic control problem with the constrained strategies. The dynamic programming technique is applied to derive the coupled Hamilton-Jacobi-Bellman (HJB) equations and the Lagrange multiplier method is used to tackle the dynamic VaR constraint. Furthermore, we propose an efficient numerical method to solve those HJB equations. Finally, we employ a practical example from the Korean market to verify the numerical method and analyze the optimal strategies under different VaR constraints.

Citation: Ming Yan, Hongtao Yang, Lei Zhang, Shuhua Zhang. Optimal investment-reinsurance policy with regime switching and value-at-risk constraint. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2195-2211. doi: 10.3934/jimo.2019050
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##### References:
$u_1^*(x)$ with different MVaR levels
$u_2^*(x)$ with different MVaR levels
$\pi_1^*(x)$ with different MVaR levels
$\pi_2^*(x)$ with different MVaR levels
$V_1(x)$ with different MVaR levels
$V_2(x)$ with different MVaR levels
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