Coarsening on a one-dimensional lattice is described by the voter model or equivalently by coalescing (or annihilating) random walks representing the evolving boundaries between regions of constant color and by backward (in time) coalescing random walks corresponding to color genealogies. Asympotics for large time and space on the lattice are described via a continuum space-time voter model who...

The aim of the paper is to develop pricing formulas for European type Asian options written on the exchange rate in a two currency economy. The exchange rate as well as the foreign and domestic zero coupon bond prices are assumed to follow geometric Brownian motions. As a special case of a discrete Asian option we analyse the delayed payment currency option and develop closed form pricing and h...

 This paper characterizes the trailing-stop strategy for stock trading and provides a simulation model to evaluate its validity. Based on a discrete time computational model, we perform probabilistic analyses of the risks, rewards and trade-offs of such a trading strategy. Numerical examples using real data from the S&P 500 and the Dow Jones Industrial Average indicate that the trailing-stop s...

We obtain the Laplace transform and integrability properties of the integral over R+ of the call quantity associated with geometric Brownian motion with negative drift, thus adding a new element to the list of already studied Brownian perpetuities.

The celebrated Black-Scholes formula which gives the price of a European option, may be expressed as the cumulative function of a last passage time of Brownian motion. A related result involving first passage times is also obtained.

We present a solution to an optimal stopping game for geometric Brownian motion with gain functions having the form of payoff functions of spread options. The method of proof is based on reducing the initial problem to a free-boundary problem and solving the latter by means of the smooth-fit principle. The derived result can be interpreted as pricing the (perpetual) spread game option in the Bl...

3 Stochastic Taylor expansions 5 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Brownian Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Exponential of a vector field . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.5 Li...

Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long-range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motio...

A Brownian time process is a Markov process subordinated to the absolute value of an independent one-dimensional Brownian motion. Its transition densities solve an initial value problem involving the square of the generator of the original Markov process. An apparently unrelated class of processes, emerging as the scaling limits of continuous time random walks, involves subordination to the inv...

The aim of this paper is to provide a semimartingale approximation of a fractional stochastic integration. This result leads us to approximate the fractional Black-Scholes model by a model driven by semimartingales, and a European option pricing formula is found. 2000 AMS Classification: 60H05, 65G15, 62P05.