考虑时滞效应与均值-方差效用的非零和投资与再保险博弈

doi:10.15960/j.cnki.issn.1007-6093.2021.02.003

Abstract

Abstract:

This paper investigates a non-zero-sum stochastic differential investment and reinsurance game with delay effect between two competitive insurers, who aim to maximize the mean-variance utility of his terminal wealth relative to that of his competitor. By applying stochastic control theory, corresponding extended Hamilton-Jacobi-Bellman (HJB) system of equations are established. Furthermore, closed-form expressions for the Nash equilibrium investment and reinsurance strategies and the corresponding value functions are derived both in the classical risk model and its diffusion approximation. Finally, some numerical examples are conducted to illustrate the influence of model parameters on the equilibrium investment and reinsurance strategies and draw some economic interpretations from these results.

Key words: investment and reinsurance, non-zero-sum game, delay effect, meanvariance utility, extended Hamilton-Jacobi-Bellman equation

CLC Number:

F830.59
F224

Huainian ZHU, Hui ZHONG, Ning BIN. Non-zero-sum investment and reinsurance game with delay effect and mean-variance utility[J]. Operations Research Transactions, 2021, 25(2): 35-54.

Figures/Tables 5

References 45

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保险公司1的参数		保险公司2的参数
λ₁	3	λ₂	4
μ₁	2	μ₂	2.500
σ₁	2	σ₂	3
η₁	0.400	η₂	0.800
δ₁	0.050	δ₂	0.030
h₁	2	h₂	3
ω₁	0.200	ω₂	0.244
κ₁	0.300	κ₂	0.700
γ₁	0.200	γ₂	0.900

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Non-zero-sum investment and reinsurance game with delay effect and mean-variance utility

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