Description: This paper presents an approach in which a defective renewal equation is solved in terms of a related compound geometric distribution. The advantage of this approach is discussed. The authors then apply this approach to a defective renewal equation which involves the time of ruin, the surplus before ruin and the total deficit at the time of ruin. They show how to compute the moments of the time of ruin as well as the joint distribution of the surplus before ruin and the deficit at the time of ruin. Two important cases in terms of claim size distributions are considered in detail. First, the authors consider exponential claim size distributions. They then consider a combination of two exponentials. The moments of the time of ruin are given in both cases.

Description: In recent years, insurance companies have been introducing saving products whose returns are linked to equity market performance. Equity-indexed annuities [EIA's] are one of the products of this kind. This paper is a study on the recent introduction and popularity growth of equity-indexed annuities. An index is considered which provides a minimum interest guarantee and a participation in the increase in an index.

Description: Equity-indexed annuities [EIA's] are the fastest growing annuity products. An appealing feature of an EIA to its holder is that it contains path-dependent options which allow the policyholder to participate in favorable investment performance while maintaining a minimum guarantee on the benefit level. Studying the valuation problem of path-dependent options enables us to provide needed information to insurance companies on the costs of these options as well as investment strategy for their portfolios. The martingale approach by Gerber and Shiu [1994, 1996] enables us to solve some valuation problems in option pricing without knowing deep results in stochastic calculus such as the Reflection Principle and Girsanov Theorem. What is needed is the Laplace transform of certain distributions known by actuaries. This paper shows how to use Gerber and Shiu's approach to compute two defective density functions related to double barrier hitting probabilities of a geometric Brownian motion. The approach used here is simple and straightforward, and purely analytical. The authors then apply the formulas to value some exotic options whose payoffs are contingent on barrier hitting time.

Description: Random sum models with compound distributions are used extensively in modeling of insurance risks. Unfortunately, the compound distributions themselves are awkward to evaluate. Consequently, various numerical and analytical approximative techniques have been used. In this talk we derive various upper and lower bounds on the tails of compound distributions. Some notions in reliability theory are used.

Description: These are the abstract and reference of the paper 'Bounds on Multiple Contingent Claims'. Lo considered the problem on bounding a European option on a single asset. He obtained an upper bound on the payoff of the European call in terms of the mean and variance of the underlying asset. In this talk, we extend Lo's result to the multi-asset case. Unlike the one asset case, the correlations between the assets play an important role and have to be taken into consideration.

Description: This is the abstract of an article about the classical Lundberg inequality of insurance risk theory. From ACTUARIAL RESEARCH CLEARING HOUSE 1994 VOL. 1.