The surplus process of an insurance portfolio is defined as the wealth obtained by the premium payments minus the reimboursements made at the times of claims. When this process becomes negative (if ever), we say that ruin has occurred. The general setting is the Gambler’s Ruin Problem. In this paper we address the problem of estimating derivatives (sensitivities) of ruin probabilities with resp...

Abstract. In this work, we investigate a multi-risk model describing insurance business with two or more independent series of claim amounts. Each series of claim amounts consists of independent nonnegative random variables. Claims of each series occur periodically with some fixed inter-arrival time. Claim amounts occur until they can be compensated by a common premium rate and the initial insu...

We study a new technique for the asymptotic analysis of heavy-tailed systems conditioned on large deviations events. We illustrate our approach in the context of ruin events of multidimensional regularly varying random walks. Our approach is to study the Markov process described by the random walk conditioned on hitting a rare target set. We construct a Markov chain, whose transition kernel can...

The Expected Discounted Penalty Function (EDPF) was introduced in a series of now classical papers [Gerber, H.U., Shiu, E.S.W., 1997. The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. Insurance: Math. Econ. 21, 129–137; Gerber, H.U., Shiu, E.S.W., 1998a. On the time value of ruin. N. Am. Actuar. J. 2 (1), 48–78; Gerber, H.U., Shiu, E.S.W.,...

Based on Invariance Principle for Brownian Motion, we obtained a closed-form expression of the ruin probability Discrete-Time Risk Model with Random Premiums that was recently introduced by Korzeniowski [1]. We show in this model, given two strategies have same ultimate ruin, strategy larger initial capital and smaller loading factor is less risky than it lowers finite time horizon.

We determine the distribution of duration in the gambler’s ruin problem given that one specific player wins. In this version we allow ties in the single games. We present a unified approach which uses generating functions to prove and extend some results that were obtained in [Frederick Stern, Conditional expectation of the duration in the classical ruin problem, Math. Mag. 48 (4) (1975) 200–20...

We consider the capital of an insurance company that employs reinsurance. The reinsurer is assumed to have infinite sources of capital. The reinsurer covers part of the claims, but in return it receives a certain part of the income from premiums of the insurance company. In addition, the reinsurer receives some of the dividends that are withdrawn when a certain surplus level b is reached. A spe...

We consider a Markovian regime-switching risk model (also called the Markov-modulated risk model) with stochastic premium income, in which the premium income and the claim occurrence are driven by the Markovian regime-switching process. The purpose of this paper is to study the integral equations satisfied by the expected discounted penalty function. In particular, the discount interest force p...