We consider a one-dimensional time-homogeneous regular diffusion between two constant elastic barriers as well as the special cases with pure absorbing and/or reflecting barriers. We derive the recurrence relations for moments of the first passage time. As examples, we consider several popular...

Let Xt be a standard d-dimensional Brownian motion with drift c started at a fixed X0, and let T be the hitting time for a sphere or concentric spherical shell. By using an appropriate martingale, a Laplace-Gegenbauer transform of the joint distribution of T and XT is determined.

We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model and then find the integro-differential equations...

In this paper, we consider the optimal dividend problem for the compound Poisson risk model. We assume that dividends are paid to the shareholders according to an admissible strategy with dividend rate bounded by a constant. Our objective is to find a dividend policy so as to maximize the...

In this paper we consider a modified version of the classical optimal dividend problem taking into account both expected dividends and the time value of ruin. We assume that the risk process is modeled by a general spectrally positive Lévy process before dividends are deducted. Using the...

This paper studies some asymptotic results for both finite and ultimate ruin probabilities in a discrete time risk model with nonconstant interest rates, under the assumptions that the individual net losses are bivariate upper-tail independent, identically distributed random variables having a...