Absolute Bankruptcy Of The Classical Risk Model With Interest Rates

In this paper we consider the absolute ruin in the risk processes with interest. The absolute ruin model is based on the compound poisson model, when the surplus is below zero or the insurer is on deficit, the insurer could borrow money at a debit interest rate to pay claims. The absolute ruin model has been studied in the literature form [1] to [4]. The absolute ruin probability with exponential claims has been studied in [2] using the martingale approach. In [4], Embrechts and Schmidli discussed the absolute ruin probability in a general insurance risk model using the theory of piecewise deterministic Markov processes. In this paper, we study the absolute ruin in risk process based on the literature [1] to obtain the expected discounted penalty function with two types of interest and the absolute ruin probability. We also study the absolute ruin in the perturbed compound poisson risk process under debit interest force. The thesis is divided into two chapters according to contents:In Chapter 1, we consider the Gerber-Shiu functions in the risk processes with two types of interest based on the literature [1]. In Section 2, we give some fundamental definitions for absolute ruin model; In Section 3, we derive a system of integro-differential equations for the Gerber-Shiu function; In Section 4, we give the absolute ruin probabilities for exponential claims.In Chapter 2, we study the absolute ruin in the perturbed compound poisson risk process under debit interest force based on the literature [10]. In this perturbed risk process, absolute ruin may occur in two different situations. In one situation, absolute ruin is caused by a claim and, in the other, absolute ruin is caused by oscillation. In Section 2, we give some fundamental definitions in the perturbed absolute ruin model; In Section 3, we derive a system of integro-differential equations for the absolute ruin probabilities; In Section 4, we derive explicit expressions for absolute ruin probabilities when claim sizes are exponential distributed.