Robust Optimal Reinsurance and Investment Strategy with Delay under Mean-variance Premium Principle
The problem of robust optimal reinsurance and investment strategies for insur-ance companies with time delay are investigated.By purchasing proportional reinsurance,insurance companies can transfer a portion of their claim risks and pay reinsurance premiums based on the general mean-variance premium principle.At the same time,insurance compa-nies invest their assets in a financial market consisting of a risk-free asset and a risky asset.Assume that the instantaneous expected return rate of the risky asset follows a mean-reverting Ornstein-Uhlenbeck(O-U)process.To maximize the exponential utility expectation of the in-surance company's terminal wealth,dynamic programming principles are applied.By solving the Hamilton-Jacobi-Bellman(HJB)equation,the optimal reinsurance-investment strategy and the corresponding explicit expression of the value function are obtained.Furthermore,numer-ical analysis shows the impact of the main parameters on the optimal strategy.The results reveal that reinsurance strategy is mainly affected by the parameters of the insurance market and risk-free asset models,rather than the risky asset model or expected return rate.Time delay and robustness factors have a significant impact on the optimal reinsurance-investment strategy.Considering time delay improves the stability of the company's wealth while incorpo-rating model uncertainty reduces the risk from inaccurate probability measures.
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