Optimal Leisure,Consumption,Investment And Life Insurance Purchase Strategy Considering Labor Income

In recent years,China’s financial market has developed rapidly,and residents’awareness of investment has gradually increased.As a result,more and more attention has been paid to asset allocation.Furthermore,in the stage of high-quality development,the awareness of insurance in the whole society has been continuously improved,so that insurance products,especially life insurance,have gradually become an important part of the asset allocation of individuals and families.On the basis of investment and consumption,the purchase of life insurance has gradually become the choice of more individuals and families.In addition,with the improvement of living standard and development quality,the government and society pay more and more attention to individual’s income and life quality.Taking variables related to income and labor-leisure choice into consideration and discussing their impact on total utility conform with the needs of model improvement and real life situation.Based on the background above,this paper constructs a stochastic optimal control model including four control variables,which are leisure,consumption,investment and life insurance purchase.In this model,leisure and consumption can enhance individual’s utility.Investment,consumption,wage and purchase of life insurance products will affect the total wealth of individual,and then affect the expected utility.Individual can be dead at random moment.If they die before retirement,the life insurance payout will be included in the terminal wealth.With this model,this paper aims to maximize expected utility,and obtain the optimal strategy and corresponding value function under exponential utility and power utility by solving HamiltonJacobi-Bellman(HJB)equation under the assumption of fixed volatility.Furthermore,this paper adopts the stochastic volatility model which is closer to the real market,and solves the optimal strategy and value function under the exponential utility based on this assumption.In order to directly present the influence of parameters related to market,wage,life insurance,wealth and utility on the optimal strategies,we conduct numerical simulation.The simulation and analysis results show that the influence of model parameters on the optimal strategies is consistent with the actual market situation.This paper also puts forward a series of suggestions on individual’s asset management strategy and labor-leisure choice based on the results of numerical simulation.This paper has three main contributions.First,we comprehensively consider the influence of four control variables on individual’s utility.Compared with the existing work,this model is more complete and the strategies are more abundant.Secondly,our model improves the way of determining wage level which is influential on the wealth process.Leisure is used to describe labor intensity indirectly,and wage is the product of labor intensity and wage coefficient,and the constant wage coefficient in existing works is improved to a function of time.Thirdly,this paper introduces the stochastic volatility model proposed by Heston into the existing model,in order to make the model more suitable for the actual situation of financial market.