Optimal Reinsurance and Derivative-Based Investment Decisions for Insurers with Mean-Variance Preference

Author:

Zhou Haiying1,Zhu Huainian2ORCID

Affiliation:

1. School of Port and Shipping Management, Guangzhou Maritime University, Guangzhou 510725, China

2. School of Economics, Guangdong University of Technology, Guangzhou 510520, China

Abstract

In our study, we investigate reinsurance issues and optimal investment related to derivatives trading for a mean-variance insurer, employing game theory. Our primary objective is to identify strategies that are time-consistent. In particular, the insurer has the flexibility to purchase insurance in proportion to its needs, explore new business, and engage in capital market investments. This is under the assumption that insurance companies’surplus capital adheres to the classical Cramér-Lundberg model. The capital market is made up of risk-free bonds, equities, and derivatives, with pricing dependent on the underlying stock’s basic price and volatility. To obtain the most profitable expressions and functions for the associated investment strategies and time guarantees, we solve a system of expanded Hamilton–Jacobi–Bellman equations. In addition, we delve into scenarios involving optimal investment and reinsurance issues with no derivatives trading. In the end, we present a few numerical instances to display our findings, demonstrating that the efficient frontier in the case of derivative trading surpasses that in scenarios where derivative trading is absent.

Funder

project of Basic and Applied Basic Research Foundation of Guangdong Province

Guangdong Province Key Construction Discipline Research Ability Improvement Project

Publisher

MDPI AG

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