Optimal Investment Strategy Under Time-inconsistency And Ambiguity Aversion

In this thesis we investigate three optimization problems: 1,Time-consistent reinsurance and investment strategies for mean-variance insurer under partial information;2,Optimal investment problem under robust mean-variance model in continuous-time case;3,Optimal investment problem under smooth ambiguity model in continuoustime case.For the problem of time-consistent reinsurance and investment strategies for mean-variance insurer under partial information,the surplus process of insurer is depicted by Cram?er-Lundberg model,stock's price follows hidden Markov model.Insurer's utility is characterized by mean-variance utility and risk aversion changes over time.The goal for the insurer is to maximize the mean-variance utility by investing in financial market and participating in reinsurance market.In this thesis,we get the timeconsistent investment and reinsurance strategy by solving an extended HJB equation.Then we compare results for optimal investment-reinsurance strategies given market state is unobservable and observable.Numerical results show that when market state is unobservable,insurer invests less in the stock and insurer's retention level becomes lower.For the optimal investment problem under robust mean-variance preference in continuous-time case,stock market consists of pure risky asset and ambiguity asset,investor is uncertain about the appreciate rate of the ambiguity asset.The same strategy will lead to different expected yields for different appreciate rates,investor's utility decreases as the difference between different expected yields becomes larger.The goal for the investor is maximizing the robust mean-variance utility by investing in risk free bond,pure risky asset and ambiguity asset.In this thesis,we use martingale method to find the optimal investment strategy and the corresponding value function.Numerical results show that as investor's ambiguity aversion becomes larger,investor will invest less in ambiguity asset and invest more in pure risky asset which is positively correlated with the ambiguity asset.For the optimal investment problem under smooth ambiguity preference in continuous-time case,financial market model also consists of three assets,but the objective function is the smooth ambiguity preference.we find that ambiguity averse investor's optimal investment strategy is the same as another ambiguity neutral investor's strategy by convex analysis method.Then martingale method is used to find the optimal final wealth distribution and optimal investment strategy.Numerical results show that 1,The effect of ambiguity aversion is equivalent to distorting investor's subjective probability for each scenario,ambiguity aversion leads to investor assigns smaller probability for the preferred scenario.2,As investor's ambiguity aversion becomes larger,risk aversion becomes smaller,investor assigns less probability for the preferred scenario.