Modeling of unit-linked life insurance with exponential guarantee value and bonus.

The benefit provided by unit-linked life insurance depends on the future of the selected investment asset. Not only does it make the product attractive, but also riskier than the traditional life insurance. One way to make the product appealing is to set the guarantee asset value equal to the minimum benefits. In this paper, we propose a unit-linked life insurance product that provides bonus. In case the insured is still alive at the end of the period, e.g. at the end of year, and the price of the investment asset is higher than the guarantee asset value, the policy holder will receive a bonus which equals to the difference between those prices. Here we assume that the dynamics of the investment asset prices follow the Geometric Brownian Motion (GBM), so that the Black-Scholes-Merton formula can be applied to calculate the expected present value of the bonus. However, the simulation results show that by choosing a constant guarantee asset value, the premium paid by the policy holder gets higher and makes the product less engaging. To remedy this problem, we propose an exponential guarantee asset value, similar with the change caused by compounded interest rates. This is also relevant to the GBM assumptions about the price dynamics of investment asset prices. Simulation results show that the guarantee asset value makes the product more appealing because we can lower the premium paid by the policy. [ABSTRACT FROM AUTHOR]