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Optimal investment-reinsurance strategies with state dependent risk aversion and VaR constraints in correlated markets

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1-s2.0-S016766871830235X-main.pdf (1.02 MB)

Date

2019-03

Authors

Bi, Junna
Cai, Jun

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

In this paper, we investigate the optimal time-consistent investment–reinsurance strategies for an insurer with state dependent risk aversion and Value-at-Risk (VaR) constraints. The insurer can purchase proportional reinsurance to reduce its insurance risks and invest its wealth in a financial market consisting of one risk-free asset and one risky asset, whose price process follows a geometric Brownian motion. The surplus process of the insurer is approximated by a Brownian motion with drift. The two Brownian motions in the insurer’s surplus process and the risky asset’s price process are correlated, which describe the correlation or dependence between the insurance market and the financial market. We introduce the VaR control levels for the insurer to control its loss in investment–reinsurance strategies, which also represent the requirement of regulators on the insurer’s investment behavior. Under the mean–variance criterion, we formulate the optimal investment–reinsurance problem within a game theoretic framework. By using the technique of stochastic control theory and solving the corresponding extended Hamilton–Jacobi–Bellman (HJB) system of equations, we derive the closed-form expressions of the optimal investment–reinsurance strategies. In addition, we illustrate the optimal investment–reinsurance strategies by numerical examples and discuss the impact of the risk aversion, the correlation between the insurance market and the financial market, and the VaR control levels on the optimal strategies.

Description

The final publication is available at Elsevier via https://doi.org/10.1016/j.insmatheco.2018.11.007 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

optimization techniques, VaR constraint, equilibrium investment-reinsurance strategy, stochastic control, extended HJB system of equations, mean-variance criterion

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Citation

URI

https://doi.org/10.1016/j.insmatheco.2018.11.007
 http://hdl.handle.net/10012/14361

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Waterloo Research
Statistics and Actuarial Science