Description: This paper gives analytic approximations for the distribution of a stochastic life annuity.

Description: This is the abstract for the presentation on option pricing with stochastic volatility: applying Parseval's theorem.

Description: This paper addresses the extension of the theory of life contingencies to a stochastic interest environment and its application to solvency valuation and surplus. A discussion of the paper follows. From Transactions of Society of Actuaries 1990, Vol. 42.

Description: This paper focuses on two aspects of SFAS 87. The first is the availability of the discount rate, and its consequences. The second is the corridor approach to gains and losses amortization. From Actuarial Research Clearing House 1993, VOL. 2.

Description: This presentation considers the pricing of European derivatives in a Black-Scholes model with stochastic volatility. The presentation shows how Parseval’s theorem may be used to express those prices as Fourier integrals. This is a significant improvement over Monte Carlo simulation in many cases. The main ingredient in this presentation's method is the Laplace transform of the ordinary [constant volatility] price of a put or call in the Black-Scholes model, where the transform is taken with respect to maturity [T]. The presentation derives these formulas and then applies them to the case where volatility is modelled as a Markov chain in continuous time, the so-called 'Markov regime switching model'. This model has been used previously in stochastic volatility modelling, but mostly with only N=2 states. The presentation shows how to use N=3 states without difficulty, and how larger number of states can be handled. Numerical illustrations are given, including the volatility smile in a three-state model.

Description: Contains two separate articles, called notes. The first note, “A note on correlation in mean variance portfolio theory,” is an elementary discussion of how negative correlation coefficients can be, given any set of N random variables. The second note, “Two essential formulas in actuarial science and financial mathematics,” gives a more or less self-contained introduction to Jensen’s inequality and to another formula, which the author decided to call the “survival function expectation formula.”

Description: This is a stochastic model used to find the distribution of the discounted value of all future cash-flows.

Description: Research paper assessing how contributions and fund levels are affected when the rates of return of the plans' assets form an i.i.d. sequence of random variables.

Description: This paper studies the variability of pension costs and fund levels under various funding methods. From Actuarial Research Clearing House 1990, Vol. 1.

Description: This paper is part of The research project dealing with pension accounting, more precisely with Statement of Financial Accounting Standards No. 87 [or FAS 87]. The goal of the project is to study the variability of pension accounting costs under FAS 87. In this paper, the author addresses only one specific point, namely the behavior of experience gains and losses over time. This is directly related to the corridor approach to amortization of gains and losses. However, what is said also applies to experience gains and losses in other areas, particularly in pension funding and insurance. From Actuarial Research Clearing House 1993, Vol. 1.