Research On Family Life Insurance Issues Based On Stochastic Volatility And Deposit-loan Spreads

Forty years of reform and opening up,with the economic prosperity of people's life phi-losophy has also undergone a great transformation,from the beginning of not understanding life insurance to the current active purchase of life insurance.More families are aware of life in-surance against them now and The importance of future livelihood security,therefore,based on the dynamic continuous-time financial theory,this paper discusses the issue of life insurance de-mand,and analyzes the relationship between household consumption investment and insurance purchase.Combining life uncertainty with financial asset selection issues,using utility function maximization to build models,and using dynamic programming principles to find the optimal so-lution for the model,and thus obtain the optimal strategy for maximizing wealth utility,and based on the image Analyze the influence of related parameters on the optimal strategy.The main results obtained in this paper are as follows.First,we studied the family's optimal investment consumption and life insurance issues under stochastic volatility and inflation.Assume that households can invest in stocks,inflation index bonds,and banks,where the stock model is the Heston stochastic volatility model,using dynamic programming methods.The model is solved to obtain explicit equations and optimal strategies.Finally,numerical results are used to analyze the effect of stochastic volatility on the optimal strategy.Secondly,we studied the problem of optimal investment spending and life insurance under the deposit-loan spread.Assuming that the loan interest rate is higher than the deposit interest rate,households can invest in stocks,loans and bank deposits,and the income is random,in the power utility function(Under CRRA,the HJB equations that satisfy the optimal goal are deduced,and then the analytical solutions and optimal strategies of the equations are obtained.Finally,based on the obtained images,the related numerical analysis is discussed.Finally,we studied the optimal household investment and life insurance under the deposit and loan spreads and stochastic volatility.Assuming that the loan interest rate is higher than the deposit interest rate,households invest in loans,stocks and deposits.The stock model is The Heston model uses the dynamic programming method to derive the HJB equation that satisfies the optimal goal.The optimal strategy is obtained by solving the equation.Finally,the numerical analysis is performed based on the obtained image.