Research On Optimal Control Strategy To Minimize The Probability Of Drawdown Under Ambiguity Aversion

In this thesis,stochastic control theory and dynamic programming principle are used to study the drawdown probability minimization problem of investment consumption portfolio and multi-asset risk model.When individuals or insurance companies lack confidence in the reference model,they hope to find an alternative model with equivalent measure,and use penalty function to punish the deviation between the reference model and the alternative model.Therefore,this thesis focuses on individuals or insurance companies with ambiguity aversion attitude to study the robust optimal investment strategy and reinsurance strategy.This thesis is divided into two parts:the first part studies the optimal investment problem for individuals/fund managers with ambiguity aversion attitude to minimize drawdown probability.Individuals or fund managers can invest in the risk-free asset and risky asset,consumption as an uncertain function,the HJB equation satisfied by the value function is derived by using Ito formula,and find the optimal investment strategy.Then the influence of the ambiguity aversion coefficient on the drawdown probability and the optimal investment strategy is analyzed.The second part studies the optimal reinsurance strategy for insurance companies with ambiguity aversion attitude in the multiasset risk model to minimize drawdown probability.Insurance companies can invest in a risk-free asset and n risk assets,by buying proportional reinsurance to transfer risk.The expression of minimizing drawdown probability,the optimal investment strategy and the retention ratio of reinsurance are obtained by using the dynamic programming principle,then analyze the influence of ambiguity aversion coefficient for them.