Optimal Investment-reinsurance Strategies With Multiple Risky Assets To Minimize The Probability Of Ruin Under Ambiguity Aversion

In this paper,we solve the optimization problem of minimizing the probability of ruin under ambiguity aversion for different subjects.We first determine the optimal robust investment problem for an individual who seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky assets(also called ambiguity aversion).We assume that the individual invests her wealth in a financial market consisting of a risk-free asset and n risky assets.According to stochastic control theories and the corresponding Hamilton-Jacobi-Bellman(HJB)equation,we obtain close-form expressions of the optimal investment and drift distor-tion,then we discuss their regularities which ensure these feedback forms satisfy the conditions of verification theorem.By defining "coffin state",the wealth process is extended to a process which include jumps.Using Ito's rule and regularities,we can finally complete the proof of verification theorem.According to the solutions under special parameters,we compare the optimal investment strategies of investor in some special cases.Inspired by the analysis of the case of ? = 0,we adjust the model and transit to the second optimization problem:optimal reinsurance and investment with multiple risky assets to minimize the probability of ruin under ambiguity aversion for insurance company.Using similar methods to solve corresponding HJB equation,we can get explicit expressions of optimal reinsurance and investment strategies.Also,we give regularities and the proof of verification theorem.Finally,we present some numerical illustrations to show the impact of some important parameters on value function.