Research On Reinsurance-investment Game With Bounded Memory

Reinsurance-investment optimization has always been a hot issue in the field of actuarial research.Reinsurance is a risk management method used by insurers to transfer part of their claim risks to the reinsurer through signing reinsurance contracts.Investment is an important method for insurers to maintain stable operation,because it can increase surplus and strengthen solvency.At present,most of the literature on the reinsurance-investment optimization problem focuses on a single insurer,and there are relatively few studies on the game between insurers and the game between the reinsurer and insurers in the insurance market.In addition,the reinsurer and insurers,as professional investment institutions in the financial market,their decision-making process should be related to their historical performance.Considering the bounded memory feature of wealth process,this paper studies several types of game phenomena in the insurance market,mainly including the research on reinsurance-investment non-zero-sum game between two insurers,the research on reinsurance-investment Stackelberg game between one reinsurer and one insurer,the research on reinsurance-investment multi-player game between one reinsurer and two insurers.Based on the risk theory,utility theory,stochastic control theory and game theory,this paper models these kinds of game phenomena and obtains the equilibrium strategy of each game model,which provides an important theoretical support for the company managers to make the optimal decision.Specifically,the main work of this paper is summarized as follows:Firstly,this paper studies the reinsurance-investment non-zero-sum game between two insurers considering the bounded memory feature of wealth processes under the asymmetric information of securities market.Both insurers can purchase proportional reinsurance contracts from the same reinsurer to spread their claims risk and can invest their wealth in a securities market that contains a risk-free asset and a risky asset.The goal of each insurer is not only to maximize the expected utility of its own terminal performance,but also to maximize the gap between its terminal performance and that of its competitor.The corresponding HJB equations are derived by means of measure transformation and dynamic programming principle.By solving the HJB equations of two insurers at the same time,we find the conditions for solving the game problem when considering the bounded memory feature and obtain the Nash equilibrium reinsurance-investment strategy and the value function.Furthermore,we analyze the influence of model parameters on the Nash equilibrium strategy,obtain the nature of the equilibrium strategy,and deepen the research conclusion.Through the simulation analysis,the influence of the model parameters on the equilibrium strategy is expressed intuitively and the corresponding economic explanation is given.Secondly,this paper studies the reinsurance-investment Stackelberg game between a reinsurer and an insurer when considering the bounded memory feature under the asymmetric information of securities market.Since any reinsurance contract is obviously a mutual agreement between the insurer and the reinsurer,a reinsurance strategy that only considers the interests of one party may be unacceptable to the other party.Therefore,this paper considers both the interests of the insurer and the reinsurer.In view of their unequal status in the insurance market,we regard the reinsurer and the insurer as the leader and the follower of the Stackelberg game,respectively.The objective of the reinsurer is to find the optimal reinsurance premium pricing strategy and investment strategy to maximize the CARA utility of its terminal performance.The objective of the insurer is to find the optimal reinsurance strategy and investment strategy such that its CARA utility of the relative performance is maximized.Based on measure transformation,the idea of backward induction and dynamic programming principle,the HJB equations are solved in turn.We obtain the equilibrium strategy and value function.Furthermore,we analyze the sensitivity of the equilibrium strategy to model parameters and intuitively present the relevant theoretical results through simulation experiments.Thirdly,under the framework of the Stackelberg game,this paper takes a reinsurer and an insurer as research objects,and includes a defaultable bond into their investment scope.We study the reinsurance-investment Stackelberg game problem when company managers are confronted with default risk.As the leader of the Stackelberg game,the reinsurer can determine the price of reinsurance premium and its own investment strategy.As the follower of the Stackelberg game,the insurer can determine the proportion of reinsurance and its investment strategy according to the price of reinsurance premium.Both the reinsurer and the insurer aim to maximize the expected utility of their terminal performance.We divide the Stackelberg game problem into two stages: the post-default stage and the pre-default stage.Based on the idea of backward induction and dynamic programming principle,we derive the equilibrium reinsurance-investment strategy and value function for each stage of the game by solving the optimization problems of the leader and the follower in turn.Then,we analyze the properties of the equilibrium strategy and the value function,and perform sensitivity analysis on the equilibrium strategy through numerical simulation to deepen the research conclusions.Finally,this paper considering one reinsurer and two insurers as research objects,studies the reinsurance-investment multi-player game with bounded memory,which includes the reinsurance-investment Stackelberg game problem between the reinsurer and two insurers and the reinsurance-investment non-zero-sum game problem between two insurers.The Stackelberg game describes the unequal status of the reinsurer and insurers in the insurance market.The non-zero-sum game describes the competitive relationship between insurers.The reinsurer,as the leader of the Stackelberg game,can price reinsurance premium and invest its wealth in a securities market to maximize the expected utility of its terminal performance.The two insurers,as the followers of the Stackelberg game,can purchase proportional reinsurance from the reinsurer and invest in the same securities market to maximize the expected utility of the relative performance relative to another insurer.Based on the idea of backward induction and the dynamic programming approach,we derive the equilibrium strategy and value functions explicitly by solving the optimization problems of the leader and followers in turn.Furthermore,we analyze the influence of competitive factors on the equilibrium strategy and the relationship between reinsurance demand and reinsurance premium price.Finally,through numerical analysis,we directly describe the influence of model parameters on the equilibrium strategy and give corresponding economic explanations.