Achieving A Given Financial Goal With Optimal Term Insurance Purchasing Policy

This paper researches the problem of purchasing m-year deferred nyear term life insurance or m-year deferred n-year term pure endowment in the context of financial planning to maximize the probability of achieving a given personal financial goal.Our paper firstly discusses the purchasing policy without stochastic factors,then we consider income,consumption and risky investment in the stochastic framework.In our problem,the term life insurance generates the time cutoff m and n which are different from the previous work.By establishing new controls,new "quasi-ideal value" and "ideal value",we solve the equations,and give the results.The main innovative point is extending the previous results of Bayrakta et al about reaching bequest goal by purchasing whole life insurance,and providing richer purchasing policies for investors.If m=0,n→∞,it’s equivalent to achieving the bequest goal by purchasing whole life insurance,the results are consistent with Bayraktar et al;if m>0,n→∞,we sheds light on reaching bequest goal by purchasing deferred whole life insurance;if m>0,n>0,that means purchasing deferred term life insurance;if m=0,n>0,it corresponds to the term life insurance.Finally,numerical analyses show that if the financial goal equals 1,and the initial wealth value is lower than 0.4,the maximum probability of purchasing deferred life insurance is higher than whole life insurance,but requires lower premium.Deferred term life insurance is a better choice for those who want to achieve their goals but are not financially sound.