In this paper, we apply a single barrier strategy to optimise dividend payments in the situation where there is a time lag d0 between decision and implementation. Using a classical surplus process with exponentially distributed jumps, we obtain the optimal barrier b* which maximises the expected...

Although the square-root process has long been used as an alternative to the Black-Scholes geometric Brownian motion model for option valuation, the pricing of Asian options on this diffusion model has never been studied analytically. However, the additivity property of the square-root process...

This paper provides a survey of results on the quantiles of a Brownian motion with drift as well as a general Lévy process. The motivation is to calculate the price of related financial options. At the end of the paper some new results on variability orderings between various quantities...

In this paper, we apply the single barrier strategy to optimize the dividend payment in the situation where there is a time lag d 0 between decision and implementation. Using a Brownian motion with drift as the surplus process, we obtain the optimal barrier b* which maximises the expected...

In this paper, we extend the concept of ruin in risk theory to the Parisian type of ruin. For this to occur, the surplus process must fall below zero and stay negative for a continuous time interval of specified length. Working with a classical surplus process with exponential jump size, we...

Applying piecewise deterministic Markov processes theory, the probability generating function of a Cox process, incorporating with shot noise process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise process at claim jump times, using...

Although the square-root process has long been used as an alternative to the Black-Scholes geometric Brownian motion model for option valuation, the pricing of Asian options on this diffusion model has never been studied analytically. However, the additivity property of the square-root process...

In this paper, we extend the concept of ruin in risk theory to the Parisian type of ruin. For this to occur, the surplus process must fall below zero and stay negative for a continuous time interval of specified length. We obtain the probability of ruin in the infinite horizon for the case when...

We use the Cox process (or a doubly stochastic Poisson process) to model the claim arrival process for catastrophic events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic...

In this paper we look at pricing stop-loss reinsurance contracts using an approximation technique similar to that of Basu (Ph.D. Thesis, London, 1999) and Rogers and Shi [Journal of Applied Probability 32 (4) (1995) 1077–1088] for processes with constant claims and the underlying stochastic...