The demand modeling for pure endowment life insurance in definite and stochastic modes

Pure Endowment life insurance is a type of life insurance in which the insurer makes a commitment to pay a sum of money to the insured in case he is alive in a predetermined date. It is distinctively designed for the people whose consumption in elderly years of their lives is more important than leaving a legacy for their heirs. In this theoretical paper, firstly, expected utility functions are defined and a wealth accumulation process constraint in deterministic as well as stochastic modes is implemented. Consequently, the utility functions have been optimized using definite optimal control techniques and ITO stochastic calculus. Our results exhibit that in definite mode interest rate affects demand for insurance positively, while factors like time preferences rate, degree of risk aversion, premium, propensity to consumption have a negative impact. However, although these results are similar in stochastic mode (that is, when the costumer has a risky asset to invest in), in this new setting the average returns of risky asset contributes positively to insurance demand. Keywords: Life insurance, pure endowment life insurance, risk, Ito stochastic calculus, CRRA utility function