Description: This presentation shows that, if the options or guarantees are exercisable only at the moment of death of the policyholder, the mathematics simplifies to an elementary calculus exercise.

Description: In classical collective risk theory, the aggregate claims process is assumed to be compound Poisson. In this paper the authors examine a more general model for the aggregate claims process: processes with independent, stationary and non-negative increments. From Actuarial Research Clearing House 1991, VOL. 1.

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.

Description: Presents some elementary and down-to-earth calculations for the optimal dividend strategy that maximizes the expectation of the discounted dividends until the possible ruin of a company.

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 shows that the Esscher transform is also 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. Two applications are presented, the first for valuing a European call option and the second for pricing derivative securities of multiple risky assets.