The Robust Optimal Investment-reinsurance Strategy Towards Joint Interests Of The Insurer And The Reinsurer

The asset allocation problem of insurance company is the hot topic in actuarial studies. It includes reinsurance, investment, dividend and so on. How to choice a rational reinsurance-investment strategy to share risk, keep stability and enhance corporate strength is a important issue for scholars. In the past several decades, the study based on parameters certainty and considering only the insurer ’s interest. In recent years, with the development of stochastic control theory and the increase of interdisciplinary communication, the research for asset allocation problem of insurance company has enter the diversity stage. In this paper, aiming at the investment and reinsurance problem of insurance company, we get essence from behavioral finance and stochastic control theory to set robust optimal model which gives consideration to both insurance company and reinsurance company. It has theory value and practical significance for enriching risk theory.Since model uncertainty influence the model building and object solving, inspired by the thought in behavioral finance, we consider insurer and reinsurer as “ambiguity aversion” decision-makers to quantify model uncertainty. Then the ordinary investment-reinsurance problem is translated to a robust optimal investment and reinsurance problem. Since the reinsurance treaty contain both insurer and reinsurer, we try to study systematically the joint optimal asset allocation problem under various price process of the risky asset.First, we build the surplus process model of the insurer and reinsurer under the Black-Scholes model. The insurer can purchase proportional reinsurance form the reinsurer and both the insurer and the reinsurer can invest in a risk-free asset and a risky asset. Besides, owing to the model specification error concern the general insurance company’s manager is ambiguity averse, he will search for a robust optimal investment and reinsurance strategy. The optimal strategy is to maximize the minimal expected exponential utility of the weighted sum surplus process of the insurer and reinsurer. By using techniques of stochastic control theory, we derive the optimal reinsurance and investment strategies for the insurer and the reinsurer, respectively. Finally, we present numerical examples to illustrate the effects of model parameters on the optimal investment and reinsurance strategies.Due to the fact that the return rate of risky asset is time-variable instead of invariable, we assume the risky asset is described by the Heston model with stochastic volatility in Chapter 4. Using dynamic programming principle, we study the robust optimal investment and reinsurance problem for the insurer and reinsurer and drive the optimal investment and reinsurance strategies for them. Finally, we present numerical examples to illustrate the effects of model parameters on the optimal investment and reinsurance strategies.Usually, optimization objective function of the joint optimal investmentreinsurance problem is set up through maximizing the expected utility of terminal weighted sum surplus process which is took into account the interests of both the insurer and the reinsurer. We try to study the problem from a new perspective. That is to study the asset allocation problem with maximizing the terminal wealth under expected product exponential utility function.Sometimes the mean-variance portfolio problem and the optimization problem under expected utility will produce some time inconsistency problem. Through defining the equilibrium strategy and equilibrium value function which is inspired by game theory, we set up the robust optimization objective of joint asset allocation problem when both insurance company and reinsurance company invest in financial market. Then we derive the HJB equations for the surplus processes of insurance company and reinsurance company, get the solution of the equations and verify it. Finally, we give numerical examples to deepen the results.