Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same...

Recently, Chen (2011) studied the finite-time ruin probability in a discrete-time risk model in which the insurance and financial risks form a sequence of independent and identically distributed random pairs with common bivariate Farlie–Gumbel–Morgenstern (FGM) distribution. The parameter θ of the FGMdistribution governs the strength of dependence, with a smaller value of θ corresponding to a l...

We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a new technique to compute the quantity of interest for any initial value, and with any given precision. Rather than focusing on a particular model for risk proc...

Assume that the surplus of an insurer follows a jump­diffusion process and the insurer would invest its surplus in a risky asset, whose prices are modelled by a geometric Brow­ nian motion. The resulting surplus for the insurer is called as a jump­diffusion surplus process compounded by the geometric Brownian motion. In this resulting surplus process, ruin may be caused by a claim or by oscilla...

In this paper, we establish a simple asymptotic formula for the finite-time ruin probability of the compound Poisson model with constant interest force and subexponential claims in the case that the initial surplus is large. The formula is consistent with known results for the ultimate ruin probability and, in particular, is uniform for all time horizons when the claim size distribution is regu...

Recently, Albrecher and his coauthors have published a series of papers on the ruin probability of the Lévy insurance model under the so-called loss-carry-forward taxation, meaning that taxes are paid at a certain …xed rate immediately when the surplus of the company is at a running maximum. In this paper we assume periodic taxation under which the company pays tax at a …xed rate on its net inc...

Consider a discrete-time risk model in which the insurer is allowed to invest a proportion of its wealth in a risky stock and keep the rest in a risk-free bond. Assume that the claim amounts within individual periods follow an autoregressive process with heavy-tailed innovations and that the log-returns of the stock follow another autoregressive process, independent of the former one. We derive...

In this paper we consider an insurance company selling life insurance policies. New policies are sold at random points in time, and each policy stays active for a random amount of time, during which the policyholder pays premiums continuously at rate r. When the policy expires, the insurance company pays a claim of random size. The aim is to compute the probability of eventual ruin starting wit...