Robust Investment And Reinsurance Game Under Markov Regime Switching Model

With the rapid economic development of our country in recent decades,people are facing more and more realistic and potential risks while their wealth is increasing.It is a reasonable way to purchase insurance to transfer losses.As a special financial enterprise that manages the risk of insurance applicants,insurance companies have become people's concerns about their ability to sustainably and healthy operations and development.Insurance companies need to manage their surplus and insurance claims scientifically and rationally for sustainable and healthy development.In recent years,academia has conducted many researches on the investment and reinsurance of insurance companies.Most of the existing literature on the investment and reinsurance of insurance companies assumes that the state of the financial and insurance markets is single and unchanging.Therefore,this paper studies the investment reinsurance of insurance companies under the change of the state of the financial and insurance markets,enrich the existing theoretical research,and provide a theoretical basis for insurance companies' decision-making.This paper uses Markov chains in a continuous-time finite state to characterize the changes in the financial and insurance markets.The main research contents are as follows.1.Study the robust non-zero-sum game of which reinsurance and investment strategies should be chosen by two ambiguity aversion insurance companies under the changing conditions of the financial and insurance markets.Suppose that two insurance companies invest part of their surplus in the same risk-free asset and the same risk asset,and the two companies purchase proportional reinsurance from the reinsurance company based on the amount of the claim.The robust strategy is used to solve the uncertainty problem of the reference model caused by statistical errors,and the investment reinsurance model under the reference probability measure is converted to the robust investment reinsurance problem under the alternative probability measure according to the Girsanov's theorem.What the two insurance companies pursue is to maximize the expected utility of the terminal relative to wealth in the worst case of the alternative probability measurement.Then a minimum-maximization objective function with ambiguity aversion under robust control is established.With the help of exponential utility maximization criterion,a robust HJB equation is established.Through a verification theorem,the solution of the HJB equation is the robust equilibrium Strategy and value function of the insurance company.2.Study the problem of the consistent and robust investment reinsurance game of two insurance companies under the Markov regime switching model.The two insurance companies purchase proportional reinsurance from the reinsurance company based on the amount of the claim,and invest part of the surplus funds into the same risk-free Assets and the same kind of risky assets.The company's risk process is Brownian motion with drift,and the two companies that are ambiguity aversion are worried about the uncertainty of the model due to statistical errors.The goal of the two companies is to maximize the terminal relative wealth expectation while minimizing the terminal relative wealth variance in the worst case.Establish an objective function with ambiguity aversion parameters under robust control,use the mean variance utility function to establish a robust extended HJB equation,and obtain the solution of the extended HJB equation through a verification theorem is the insurance company's robust equilibrium strategy and value function.The theoretical results found that the equilibrium investment reinsurance strategy is only related to the current financial and insurance market conditions,but the transition probability has an impact on the value function,and investment and reinsurance strategies are independent of each other.The ambiguity aversion parameter is inversely proportional to the amount of investment and proportional to the amount of reinsurance.The competition coefficient is directly proportional to the amount of investment and inversely proportional to the amount of reinsurance.Therefore,changes in the financial and insurance markets have an impact on the investment and reinsurance strategies of insurance companies.Insurance companies should increase the amount of investment and reduce the amount of reinsurance when the rate of return on risky assets is high and competition is fierce.