REACHING A BEQUEST GOAL WITH LIFE INSURANCE: AMBIGUITY ABOUT THE RISKY ASSET'S DRIFT AND MORTALITY'S HAZARD RATE

Abstract

AbstractWe determine the optimal robust strategy of an individual who seeks to maximize the (penalized) probability of reaching a bequest goal when she is uncertain about the drift of the risky asset and her hazard rate of mortality. We assume the individual can invest in a Black–Scholes market. We solve two optimization problems with ambiguity. The first is to maximize the penalized probability of reaching a bequest goal without life insurance in the market. In the second problem, in addition to investing in the financial market, the individual is allowed to purchase term life insurance to help her reach her bequest goal. As the individual becomes more ambiguity averse concerning the drift of the risky asset, she becomes more conservative with her investment strategy. Also, as she becomes more ambiguity averse about her hazard rate of mortality, numerical work indicates she is more likely to buy life insurance when the ambiguity towards the return of the risky asset is not too large.