Research On Optimal Investment And Consumption Problem Under Partial Information

Since the safe operation of insurance and pension funds is of great significance to the stability of the whole society,the optimal investment problem of insurance and pension funds is one of the popular topics in actuarial sciences,and has received extensive attention in both academia and industry.It should be pointed out that most scholars study optimization problems,assuming that the parameter information of the model is known.However,this assumption is inconsistent with actual situation.Therefore,in recent years,some researches have begun to discuss the optimal decision problem under the partial observation model.Since the research in this area has paid little attention and many problems have not been solved,this thesis studies the optimal investment problem of insurance companies and the optimal investment and consumption problem of pool annuities under partial information.The main research contents are as follows:First,this thesis studies the optimal investment problem of insurance companies under partial information.Assuming that both capital market and insurance market information is unobservable,and integrating this feature into the model framework,we get the optimal investment strategy by using Bayesian method and dynamic programming principle.At the same time,we also analyze that either some parameters in a capital market or in an insurance market are observable,and all parameters in two markets are known.Furthermore,we analyze and compare which market with unobservable information has a greater impact on the investment of insurance companies.By comparing the value functions,we find that it is better to use the partial information to deal with optimization problems,when the cognitive error of the model parameter information is large.Second,this thesis considers the optimal investment and consumption problem of pool annuity under partial information.It is assumed that the instantaneous rate of return in the stock market and the probability distribution information of death time are unknown.Different from other literature on investment and consumption problem of pool annuity,the background of their research is that pool members cannot exit the plan.But in order to reduce the risk of individuals,we allow all pool members to withdraw from the plan at a fixed time.As far as we know,this thesis is the first time to incorporate the unobservable death information of pool annuities into the model framework,and it is also the first time to study the investment and consumption problem of single-period pool annuities.In addition,filtering techniques and Hamilton-Jacobi-Bellman(HJB)equations are used to obtain explicit expressions of optimal consumption and investment strategies,and we examine the impacts of important parameters on the optimal investment and consumption strategies.Finally,this thesis considers the optimal investment and consumption problem of pooled annuities under partial information and ambiguity aversion.It is assumed that the instantaneous rate of return in the stock market and the probability distribution of death time are unobservable.Compared to the single-period pooled annuity problem,that is,pool members can only withdraw from the plan at a fixed time,the wealth of death individuals will be given to the living members during this period.In the paper,we allow pool members to withdraw from the pool annuity at any time.When the plan member dies or withdraws,he/she will leave a certain percentage of the amount to himself/herself or the beneficiary.Furthermore,by introducing ambiguity measure,using martingale measure transformation and HJB equation theory,we obtain the explicit expressions of optimal investment and consumption strategies,and describe the impact of the ambiguity aversion on investment and consumption strategies for pool annuity by numerical analysis.