Optimal Time-Consistent Investment and Reinsurance Strategy Under Time Delay and Risk Dependent Model

Sheng Li,Yong He

doi:10.1155/2020/9368346

Abstract

In this paper, we consider the problem of investment and reinsurance with time delay under the compound Poisson model of two-dimensional dependent claims. Suppose an insurance company controls the claim risk of two kinds of dependent insurance businesses by purchasing proportional reinsurance and invests its wealth in a financial market composed of a risk-free asset and a risk asset. The risk asset price process obeys the geometric Brownian motion. By introducing the capital flow related to the historical performance of the insurer, the wealth process described by stochastic delay differential equation (SDDE) is obtained. The extended HJB equation is obtained by using the stochastic control theory under the framework of game theory. Under the reinsurance expected premium principle, optimal time-consistent investment and reinsurance strategy and the corresponding value function are obtained. Finally, the influence of model parameters on the optimal strategy is explained by numerical analysis.

Highlights

Since insurance companies have been allowed to enter the financial market for investing risk assets, the optimal investment strategy has become an important research topic in recent years
We study the optimal investment-reinsurance problem with delay and risk dependence under the meanvariance preference criterion
Considering the time-delay effect and risk dependence, we obtain the extended HJB equation with delay based on the time delay stochastic control framework and the equilibrium stochastic control method. e results show that the optimal time-consistent investment and reinsurance strategy will be affected by the time delay effect. e larger the capital flow related to the historical business performance, the greater the risk faced by the insurance company

Summary

Introduction

Since insurance companies have been allowed to enter the financial market for investing risk assets, the optimal investment strategy has become an important research topic in recent years. Browne [1] uses the surplus process given by the diffusion risk model to study the investment problem of maximizing the utility of the terminal wealth and minimizing the ruin probability of an enterprise and obtains the explicit optimal solution. Yuen et al [12], taking the expected utility maximization of the terminal wealth as the criterion, considered the optimal proportional reinsurance problem with multidimensional risk dependence by using the diffusion approach method.

The Model

Optimization Problem

Numerical Simulations

Conclusion