Optimal Consumption Investment And Life Insurance

The problem of optimal consumption and investment is an important research content of financial mathematics.Investors' assets are allocated between consumption and investment to achieve the goal of maximizing expected utility within a specific time interval.With the development of China 's economy and the strengthening of residents 'financial management consciousness,many changes have occurred in the structure of residents' financial assets.In addition to bank deposits and securities assets,more and more residents are considering purchasing life insurance.Therefore,when studying the issue of optimal consumption and investment,Taking life insurance into account is of practical significance.The life of life insurance is usually relatively long.Over a long period of time,the interest rate faced by investors is uncertain.In addition,investors will also face the impact of price changes on assets and consumption.Therefore,this article is studying the optimal The two aspects of consumer investment and life insurance are taken into account.First of all,life insurance is introduced into the classic consumer investment problem.Investor assets are allocated between consumer investment and purchase of life insurance.The HJB equation corresponding to the control problem is obtained through the principle of dynamic programming,and the HJB equation is solved.Secondly,considering the impact of interest rates and inflation,it is assumed that the interest rate follows the Vasicek interest rate model,and the price level follows the general Ito process.The actual wealth owned by the investor is obtained after the investor 's nominal wealth is adjusted according to the price level.The investor 's assets are consumed during consumption.Distribution between investment and life insurance,in addition to investing in stocks,investors also invest in inflation index bonds to hedge against inflation risks.The HJB equation corresponding to the control problem is obtained through the principle of dynamic programming,and the HJB equation is solved in the form of a stochastic differential utility function.Finally,through Matlab numerical simulation,the effects of interest rates,expected inflation rates,and relative risk aversion coefficients on the optimal consumer investment and life insurance strategies are analyzed.The results show that with the increase of interest rates,investors should increase consumption,reduce the proportion of stock investment,and increase the proportion of inflation index bond investment;as the expected inflation rate increases,investors should increase consumption,reduce the proportion of stock investment,and increase inflation Index bond investment ratio;as the relative risk aversion coefficient rises,investors should reduce consumption when young,increase consumption when old,reduce the proportion of stock investment,increase the proportion of inflation index bond investment,increase the proportion of life insurance purchases as a proportion of wealth;The proportion of the investor's life insurance purchase amount to wealth has nothing to do with interest rates and expected inflation rates.When the ratio of life insurance premium to mortality is low,investors should purchase life insurance.Compared with the existing literature,the contribution of this paper is to consider the impact of price in the optimal consumer investment and life insurance issues.Assuming that the price level is random,an investor's optimal strategy considering inflation is given,which is more in line with reality.