Annual Losses for Straight Deductible Coverage

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A practical mathematical development of a probabilistic model for annual loss amounts is developed. A simulation is used to validate the hypothesis that under general conditions, the Gaussian (normal) probability model is appropriate for annual loss amounts when straight deductible insurance is purchased. Formulae for deriving the parameters of the Gaussian model are provided and a numerical example is given. Summary simular output is provided. Straight deductible limits are a feature of many insurance coverages. Monte Carlo simulation has provided one of the few generalized approaches to expressing such coverages on a fiscal period basis instead of a per incident basis [3, p. 504]. In this paper an attractive alternative approach to Monte Carlo simulation is suggested for a class of frequently discussed models for loss frequency and loss amounts (the Poisson and lognormal distributions, respectively) [6, pp. 699-704]. The methodology discussed in the present paper provides a direct method of describing the mean and variance of annual loss amounts for given deductible limits. Furthermore, evidence is offered in support of the thesis that annual loss amounts can be reflected by the common Gaussian (normal) probability distribution when expected loss frequency is about eight or more a year. RANDOM VARIABLES AND THEIR PARAMETERS Definitions and Notation X = A random variable representing the amount of loss associated with a single fortuitous event. In the present paper the assumption is that X is lognormally distributed. Stated differently, it is assumed that logeX is normally (Gaussian) distributed. fX(x) = ( exP0(1/2a2)(1og x 2]for x > 0, 0 for x < 0. Note the parameters of f (x): 1 and a2. Brian Schott is Associate Professor of Quantitative Methods, Georgia State University. He holds the Ph.D. degree and the A.S.A. designation. He is coauthor of SIMQ: A Business Simulation Game for Decision Science Students and author of RISKM: A Risk Management! Financial Management Model. He has served as an advisor to Anistics, a subsidiary of Alexander and Alexander, Inc. Research support for this work was provided by the College of Business Administration Research Council, Georgia State University.