Description: We consider a class of compound renewal risk process with claim waiting times have a discrete Km distribution. The classical compound binomial risk model is a special case when m = 1. Both recursive and explicit formulas are derived for the expected discounted penalty function due at ruin, for the surplus before ruin and the deficit at ruin. Many ruin related quantities can be analyzed through the penalty function, e.g., ruin probability, the p.g.f. of the time of ruin, joint and marginal distributions of the surplus before ruin and the deficit at ruin, claim causing ruin, as well as their moments. Detailed discussions are given in two special cases: claim sizes are rationally distributed, or the claim sizes distribution have a finite support.

Description: Statistical properties of interest, annuity and insurance functions are examined when mortality and interest are treated as having a random component. Several special models of interest rate fluctuation are examined in detail. It is hoped that such theory will be useful in developing fluctuation reserves and premium margins. Presented at the 13th Annual Actuarial Research Conference, Ball State University, August 31st. September lst, 2nd. 1978.

Description: This paper discusses the binominal financial and insurance models. In addition, the paper expands the discussion to the martingale probabilities measures for insurances, annuities, endowment insurances, and equity-linked products.

Description: This is the abstract of the article 'A Proposed Unified Valuation System'. This article will briefly describe some analytical examples of a stochastic modeling of risk use to illustrate the S-curve approach to valuation, but more importantly describe key additional area of research and theory, which need to be developed. The focus of this presentation is an invitation for additional research to support a new approach to statutory valuation of life and health risk that can result in better management and regulatory information.

Description: This paper introduces a new direction for evaluating numerically survival probabilities pointed out by H. Seal in his book ‘Survival Probabilities: The goal of Risk Theory’. Some of special cases can be considered as a weighted Poisson process with an infinitely divisible mixing distribution. This property is well known for the negative binomial case [gamma mixing distribution].

Description: This paper presents a methodology of pricing the guaranteed minimum death benefit of a variable annuity in a market model with jumps. Recent developments in the stock market make variable annuities very attractive products from the insured point of view, but less attractive for insurers. The insured still has the possibility of investment benefits, while avoiding the risk of a stock market collapse. The insurer wants to minimize its risk and yet sell a competitive product. The financial market model consists of one riskless asset and one risky asset whose price jumps in proportions J at some random times T which correspond to the jump times of a Poisson process. The model describes incomplete markets and there is no perfect hedging. In the second part of the paper, we describe a possible method of risk analysis for binomial tree models.

Description: In this note, the asymptotic behavior of the probability of ruin is derived by means of infinitesimal generators and Laplace transforms. Using these same tools, it is shown that the probability of ruin has an algebraic decay rate if the insurance company invests its capital in a risky asset with a price which follows a geometric Brownian motion. The latter result is shown to be valid not only for exponentially distributed claim amounts, as in Frolova et al. 2002, but, more generally, for any claim amount distribution that has a moment generating function defined in a neighborhood of the origin.

Description: We propose asymptotically correct two-sided bounds for random sums where the number of summands has an arbitrary distribution which can be viewed as ruin probabilities or accumulated claim sizes in various risk processes. The bounds are fairly new and they reveal the real accuracy of some well-known and widely used asymptotic formulas. It turns out that this accuracy can be poor and the range where these formulas give appropriate approximations depends on the shape of the tail distribution of the summands. This dependence is examined in the research.

Description: An insurance company starts with an initial surplus, collects premium, pays claims to policyholders and pays dividends to stockholders. What remains is the following year’s surplus. The process continues. This paper describes how to calculate the distribution of surplus for any given year. With these distributions, one can make the calculations of premiums and dividends.

Description: In this paper we discuss some properties of the nth stop-loss order and their application in risk premium principles. We give a necessary condition and a sufficient condition for nth stop-loss orders. They are convenient tools to construct risk pairs with nth stop-loss orders. We show that exponential premium principles can diferentiate between losses more finely than the net premium principles under some conditions.