Model Tracking for Risk Problems

We assume that we have M candidate insurance models for describing a process. The models considered consist of a risk process driven by right-constant, finite-state spaces, jump processes. Based on observing the history of the risk process, we propose dynamics whose solutions indicate the likelihoods of each candidate model. 1. Introduction. Risk theory deals with stochastic models in insurance business, see, for example, Grandell [2]. Usually, in such models claims are described by point processes and the amounts claimed by policies holders are sequences of random variables. The profit, or the loss, of the company is the difference between premiums income and the claims. In this paper, we assume that we have M competing models, denoted by {H 1 ,...,H M }, describing the risk process, see Section 2. We are interested in ranking the candidate models based on their likelihood of being most appropriate for describing the risk process and some other processes driving the risk process. This problem as well as others fall within the category of Model Tracking or Detection problems as we are interested in tracking (or detecting) the most appropriate model for describing the proposed risk model, see, for example, Poor [5] and Snyder [6]. In the next section, we present the model of the paper. The main result of the paper is found in Section 3 where the likelihood that our model is best described by a certain candidate model is derived. In Section 4, a filtering problem is discussed.