For the renewal risk model with subexponential claim sizes, we established for the finite time ruin probability a lower asymptotic estimate as initial surplus increases, subject to the demand that it should hold uniformly over all time horizons in an infinite interval. In the case of Poisson model, we also obtained the upper asymptotic formula so that an equivalent formula was derived. These ex...

This paper investigates the finite time ruin probability in the renewal risk model. Under some mild assumptions on the tail probabilities of the claim size and of the inter-occurrence time, a simple asymptotic relation is established as the initial surplus increases. In particular, this asymptotic relation is requested to hold uniformly for the horizon varying in a relevant infinite interval. T...

In this paper, we study ruin in a perturbed compound Poisson risk process under stochastic interest force and constant interest force. By using the technique of stochastic control, we show that the ruin probability in the perturbed risk model is always twice continuously differentiable provided that claim sizes have continuous density functions. In the perturbed risk model, ruin may be caused b...

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by ...

We describe a fast simulation framework for simulating small ruin probabilities in insurance risk processes with subexponential claims. Naive simulation is inefficient since the event of interest is rare, and special simulation techniques like importance sampling need to be used. An importance sampling change of measure known as sub-exponential twisting has been found useful for some rare event...

In this paper, we study the discounted free Gerber-Shiu function for the compound binomial risk model with by-claims and randomized dividend policy. Specifically, explicit expression for the discounted free Gerber-Shiu function is obtained. This result allows us to derive formulae for some useful insurance quantities, including the ruin probability, the probability function of the deficit at ru...

In this paper, we establish a simple asymptotic formula for the finite-time ruin probability of the renewal model with risky investment in the case that the claimsize is subexponentially distributed and the initial capital is large. The result is consistent with known results for the ultimate and finitetime ruin probability and, particularly, is inconsistent with the corresponding Poisson risk ...

In this paper, we consider some non-standard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim-size distribution belongs to some classes of heavy-tailed distributions and a constrai...

Consider the following stylized model for insurance business: X1,X2, ... the total sum of claims per period are iid nonnegative integer valued, c the total premium per period is a positive integer, and the initial surplus s is a non negative integer. The reserve R(t) of the company without dividend payment evolves as R(0) = s and R(t+ 1) = R(t) + c−Xt+1, t ≥ 0. Throughout the paper we assume th...

This paper investigates the ultimate ruin probability of a discrete time risk model with a positive constant interest rate. Under the assumption that the gross loss of the company within one year is subexponentially distributed, a simple asymptotic relation for the ruin probability is derived and compared to existing results.