The purpose of this paper is to introduce and construct a state dependent counting and persistent random walk. Persistence is imbedded in a Markov chain for predicting insured claims based on their current and past period claim. We calculate for such a process, the probability generating...

A mutual insurance firm is a firm whose stockholders are the bearers of the insurance contracts. Insurance is then viewed as a collective (pooled) process of persons paying a fixed (or variable, contingent) amount monthly (the premium) and seeking protection against claims that may occur to any...

A dispatching problem with random availability of vehicles and options to send rented vehicles is considered. We assume passenger arrivals to be described by a pure-birth process. Such a problem is analytically attractive and is shown to have practical applications in vehicle dispatching models....

We consider a retailer who orders products before the price for them becomes known. The price is an outcome of perfect competition in a complete market. Since the demand is price sensitive, the uncertainty in prices induces uncertain profits and associated risks. In this paper we show that if...