Modeling of an insurance system and its large deviations analysis

Sezer A. D.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.235, no.3, pp.535-546, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 235 Issue: 3
  • Publication Date: 2010
  • Doi Number: 10.1016/
  • Page Numbers: pp.535-546


We model an insurance system consisting of one insurance company and one reinsurance company as a stochastic process in R(2). The claim sizes {X(i)} are an iid sequence with light tails. The interarrival times {tau(i)} between claims are also iid and exponentially distributed. There is a fixed premium rate cl that the customers pay; c < c(1) of this rate goes to the reinsurance company. If a claim size is greater than R the reinsurance company pays for the claim. We study the bankruptcy of this system before it is able to handle N number of claims. It is assumed that each company has initial reserves that grow linearly in N and that the reinsurance company has a larger reserve than the insurance company. If c and c(1) are chosen appropriately, the probability of bankruptcy decays exponentially in N. We use large deviations (LD) analysis to compute the exponential decay rate and approximate the bankruptcy probability. We find that the LD analysis of the system decouples: the LD decay rate gamma of the system is the minimum of the LD decay rates of the companies when they are considered independently and separately. An analytical and numerical study of gamma as a function of (c. R) is carried out. (C) 2010 Elsevier B.V. All rights reserved.