Research On Household Asset Allocation Problems

This thesis studies household financial behaviors including investment,consumption,life insurance and housing purchase in the stochastic financial market model.Theoretical methods include the optimal stopping-time theory,stochastic optimal control theory,the method for solving the Lagrange dynamic problem and the martingale method.The following five problems are considered.(?)Investment,consumption and life insurance decision-making problem based on consumption habit formation and inflation risk.(?)Optimal portfolio selection with life insurance under subjective survival belief and consumption habit formation.(?)Dynamic asset allocation for the pension based on bequest motivation and minimum performance demand.(?)Investment and consumption problem for owning a house.(?)Housing,consumption and investment decision-making based on consumption habit formation.The details are described below.Firstly,this thesis studies the decision-making behaviors of an agent,involving investment,consumption and life-insurance purchase under inflation risk and mortality risk.The consumption habit formation of the agent is considered.In the model,it is assumed that agent can invest in a risky asset,an index bond and a stock.Life insurance hedges the mortality risk,and the index bond hedges the inflation risk.The goal of the agent is to maximize the expected utility of consumption,benefit and terminal wealth,in which the utility from consumption is the part of consumption exceeding the minimum consumption level,and the minimum consumption level is determined by the habit level,In particular,we find that the effects of the expected inflation rate and consumption habit on the optimal strategy interact with each other;increasing the mortality force will increase the demand for life insurance;increasing mortality force will increase the demand for life insurance;The effects of other parameters on the optimal strategy are also constrained by the consumption habit and mortality force change.Secondly,the above model is extended in two aspects.On the one hand,the agent's "money illusion" in the formation of habit is considered,that is,nominal consumption is mistaken for actual consumption.Thus,two habit formation types are set up,namely,nominal habit formation and real habit formation.Under these two habit formation types,the real habit levels are given respectively.On the other hand,the concept of subjective survival belief is introduced to describe the agent's optimistic or pessimistic attitude towards longevity risk.Finally,the analytical solution of the optimization problem is obtained.The numerical results show that subjective survival belief and habit formation types play an important role in agents'financial behaviors.In particular,the existence of subjective survival belief,habit formation and relative risk aversion coefficient have the impact on the demand for life insurance.Thirdly,in the context of family members participating in the DC pension plan,this thesis studies the asset allocation problem,which involves the bequest motivation of the plan participant' the wage flow before retirement,the minimum living security after retirement and the minimum performance demand of the fund manager.This setting not only considers the interests of the pension plan participant,but also takes into account the basic performance requirement of the fund manager.In the model,the pension fund can be invested in a risk-free asset,an index bond and a stock.The goal of the fund manager is to maximize the expected utility of terminal surplus(that is,the part of the terminal wealth of the pension account that exceeds the minimum living security of the participant);At the same time,the optimal investment strategies and wealth process are obtained by using martingale method.On this basis,numerical examples are given to highlight the influence of some important parameters on the optimal investment strategies.The results show that the bequest level,the minimum performance level,the initial contribution value,the initial minimum living security value and the initial wealth value all affect the fund managers' judgment for economic environment states,and then affect his/her investment behaviors.Fourthly,this thesis studies an investment,consumption and housing purchase problem.In the model,the household has random income from non-financial market,can invest in a risky asset and a risk-free asset,and plans to buy a house for living.When buying a house,the household is required to pay a part of the total housing value as a down payment,and the rest can be financed by loans.The household's utility comes from consumption before buying a house,and from consumption and housing after buying a house.The goal of the household is to maximize the expected discounted utility,to find the optimal consumption and investment strategies before and after buying a house,the optimal purchase time and the optimal housing units.In the process of solving the problem,we transform the goal problem into a mixed problem of optimal control problem and optimal stopping time problem.On this basis,we obtain the solution of the problem,at the same time,we find that human capital provides fund for consumption and investment,loan repayment reduces the demand for consumption and investment,and increasing down payment ratio reduces the consumption demand before buying a house and enhances the consumption demand after buying a house.Finally,based on the consumption habit formation for a household,this thesis studies a problem involving investment,consumption and housing.In the model,the household can invest in a risk-free asset and a risky asset.The price of the risky asset follows a geometric Brownian motion.By the dynamic programming method,the value function and consumption investment strategies buying a house are obtained,and then the optimal housing units are.On this basis,the problem is transformed into a hybrid problem of the optimal control and optimal stopping time problems.The corresponding variation inequality is solved.The optimal investment and consumption strategies,the value function before buying a house,and the price threshold are obtained.The results show that time preference,consumption preference and consumption habit formation play important roles in the financial behaviors of the household.