In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to alpha-stable Levy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic...

In this paper we consider a jump-diffusion type approximation of the classical risk process by a gamma Levy process. We derive here the asymptotic behavior (lower and upper bounds) of the finite time ruin probability for any gamma Levy process.

In this article we derive formula for probability where Z={Z(t)} is a spectrally positive [alpha]-stable Lévy process with 0<[alpha]<=2 and .

Pickands constants appear in the asymptotic formulas for extremes of Gaussian processes. The explicit formula of Pickands constants does not exist. Moreover, in the literature there is no numerical approximation. In this paper we compute numerically Pickands constants by the use of change of...

In the paper we present a method of simulation of ruin probability over infinite horizon for fractional Brownian motion with parameter of self-similarity H ½. We derive some theoretical results which show how fast the method works. As an application of our method we numerically compute the...

In the paper we present a method of simulation of ruin probability over infinite horizon for fractional Brownian motion with parameter of self-similarity H ½. We derive some theoretical results which show how fast the method works. As an application of our method we numerically compute the...

In this paper we investigate asymptotic behavior of the tail probability for subordinated self-similar processes with regularly varying tail probability. We show that the tail probability of the one-dimensional distributions and the supremum tail probability are regularly varying with the...

In this article we quantify the bullwhip effect (the variance amplification in replenishment orders) when demands and lead times are predicted in a simple two-stage supply chain with one supplier and one retailer. In recent research the impact of stochastic order lead time on the bullwhip effect...