Description: Equity-indexed annuities [EIAs] can be viewed as mutual funds wrapped around with various guarantees. A recent paper derived a closed form formula for pricing this dynamic guarantee if early withdrawal from the fund [before maturity] is not permitted. This paper studies the pricing of dynamic protection without a maturity date, i.e., the investor chooses the date to cash in the fund accumulation.

Description: This paper studies the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. The classical model is generalized by discounting with respect to the time of ruin. The authors show how to calculate an expected discounted penalty, which is due at ruin, and may depend on the deficit at ruin and the surplus immediately before ruin.

Description: This paper shows that the Esscher transform is an efficient technique for valuing derivative securities if the logarithms of the prices of the primitive securities are governed by certain stochastic processes with stationary and independent increments. From the Transactions of Society of Actuaries 1994, Vol. 46.