Optimal Investment,Consumption And Non-Life Insurance Decision Under Ambiguity

The resident is the most basic part of modern credit system and the smallest unit of the economy.Residential asset allocation plays an extremely important role to keep economic and social development stable and healthy.As population aging accelerates,the economy is under downward pressure and financial products continue to innovate,residents’wealth decisions are closely related to family living standards,risk management,and social efficiency.On the one hand,the reasonable residential finance contributes to share the social development achievements through investment return,commercial risk management.On the other hand,the resident’s wealth decision affect social welfare by the "multiplier effect"and promote the development of the financial market.As we all known,residential asset allocation is a hot topic.According to empirical analysis,scholars found that subjective survival beliefs affect personal decision.Specifically,young people overestimate their mortality rate so that lower savings and increase consumption.Conversely,the old underestimate their mortality rate,raise savings and lower the consumption.Meanwhile,split share,insider trading,financial fraud and so on make information opacity and investment strategy distortion.When researchers use data and various method to set up the model,if we ignore the influence of the above phenomena on residents,we may make the wrong setting of the model.As for personal decision making,classical expected utility theory and some behavioral economics such as subjective utility theory,prospect theory,cumulative prospect theory and so on are defined in the context of risk decision without considering uncertainty decision.Simultaneously,models about asset allocation,from fixed ratio model to risk parity model,have not focused on uncertainty.Admittedly,the model misspecification will be effectively calibrated by expanding data and improving statistical analysis techniques.However,it is hard to finish the above work thoroughly in a short period.To amend model misspecification,we study optimal strategy under ambiguity,which is a kind of decision under uncertainty,to close to the reality.The thesis focuses on three aspects of residential asset allocation:consumption,investment and insurance demand.And the thesis considers two kinds of ambiguity,namely ambiguity about the risky asset’s drift and mortality’s hazard rate.We determine the optimal robust strategy of a wage earner who seeks to maximize the utility of consumption and the final wealth.We solve three optimization problems under ambiguity.The first is to find the optimal robust consumption to maximize the goal.The second is maximize the utility while investing only in the stock market and consumption as normal.In the third problem,we allow the individual to purchase non-life insurance to transfer his/her risk.We use HamiltonJacobi-Bellman approach,Girsanov theorem,Radon-Nikodym derivative based on the dynamic programming principle to get analytical solutions.And numerical work is used to demonstrate these models by Matlab.We find that ambiguity results in consumption distortion,while the distortion will disappear rapidly as the terminal time approaches.Investing in risky assets revises the degree of consumption distortion effectively.In addition,ambiguous mortality has no effect on non-life insurance demand.Ambiguity about the risky asset’s drift squeezes the amount of investment.The thesis is organized by 7 chapters.Chapter 1 is the introduction.In chapter 2,we introduce the theory and the method of the thesis,especially the notion of ambiguity.In chapter 3,we study the optimal consumption problem for individuals with ambiguity aversion about their mortality.In chapter 4,I study the problem of how an individual should consume and invest their wealth in a risky financial market to maximize the utility of consumption and extra wealth in his/her retirement or death.In chapter 5,this study considers the optimal consumption and non-life insurance demand for an individual who concerns about the ambiguous hazard rate of her/his lifetime.In chapter 6,when the agent is ambiguity averse concerning the drift of the risky asset and risk-averse about uncertainty,she seeks the robust optimal investment and consumption strategy.Chapter 7 concludes the thesis and make recommendations for government,the insurer,the securities industry and the resident respectively.The contribution of this thesis is threefold.First,we study the individual optimal strategy using uncertain models that incorporate the ambiguous mortality and risky asset’s drift.The topic is rare in the individual’s decision.Second,we have comprehensive strategies for a wage earner including consumption,investment and non-life insurance.The comprehensive result is conductive to identify the interaction between different decisions.In addition,we obtain analytical solutions to four control problems from two perspectives,mortality hazard rate and risky asset’s drift.And numerical analysis with economic implications of our results is presented.