the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

In this paper, we study the perturbed risk model with a threshold dividend strategy and proportional investment. The insurance companies are allowed to invest their surplus in financial market consisting of risk-free asset risky fixed proportions; assets modeled by jump-diffusion process. Firstly, using theory stochastic process analysis, obtained integro-differential equations satisfied expect...

Most energy and commodity markets exhibit mean-reversion occasional distinctive price spikes, which result in demand for derivative products protect the holder against high prices. To this end, paper we present a few fast efficient methodologies exact simulation of spot dynamics modelled as exponential sum Gaussian Ornstein-Uhlenbeck process an independent pure jump process, where latter one is...

This paper studies the first passage times to flat boundaries for a double exponential jump diffusion process, which consists of a continuous part driven by a Brownian motion and a jump part with jump sizes having a double exponential distribution. Explicit solutions of the Laplace transforms, of both the distribution of the first passage times and the joint distribution of the process and its ...

In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructure...

We provide the option pricing formula of the SV-DEJ model as follows. Following the assumptions in Yu, Li and Wells (2011), we let γ (1) t = η svt and γ t = − 1 √ 1−ρ2 (ρη+ η v σv ) √ vt, where η s and η are the market prices of risk. Then there exists a risk-neutral measure Q under which W (1) t (Q) and W (2) t (Q) are standard Brownian motions: dW (i) t (Q) := dW (1) t + γ t dt, i = 1, 2 (Equ...

We derive closed formulas for the prices of European options andtheir sensitivities when the underlying asset follows a double-exponentialjump diffusion model, as considered by S. Kou in 2002. This author hasderived the option price by making use of double series where each termrequires the computation of a sequence of special functions, such thatthe implementation remains difficult for a large...

Calculations of noise-assisted jump rates and diffusion coefficients for diffusion of atoms adsorbed on a metal surface are presented and discussed, in the whole range of the damping strength, and with a direct numerical integration of the Langevin equation, by two different procedures: a mean first passage time calculation and by counting jumps with a given energy criterion. The results are co...