The first passage time (FPT) problem is ubiquitous in many applications. In finance, we often have to deal with stochastic processes with jump-diffusion, so that the FTP problem is reducible to a stochastic differential equation with jump-diffusion. While the application of the conventional Monte-Carlo procedure is possible for the solution of the resulting model, it becomes computationally ine...

We consider the valuation of European and American-style options under jump-diffusion processes by variational methods. In particular, the value function is seen to satisfy a parabolic partial (spatial) integro-differential variational inequality. A theoretical framework is developed and an analysis of a Þnite element implementation presented. A key feature is the introduction of separate appro...

The first passage time problem has attracted considerable research interest in the field of stochastic processes. It concerns the estimation of the probability density of the time for a random process to cross a specified boundary level. Even though there are many theoretical advances in solving this problem, for many classes of random processes no analytical solution exists. The jumpdiffusion ...

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly...

At present, many cloud services are managed by using open source software, such as OpenStack and Eucalyptus, because of the unification management of data, cost reduction, quick delivery and work savings. The operation phase of cloud computing has a unique feature, such as the provisioning processes, the network-based operation and the diversity of data, because the operation phase of cloud com...

We investigate periodic solutions of regime-switching jump diffusions. first show the well-posedness to stochastic differential equations corresponding hybrid system. Then, we derive strong Feller property and irreducibility associated time-inhomogeneous semigroups. Finally, establish existence uniqueness solutions. Concrete examples are presented illustrate results.

In pricing and hedging with financial derivatives, term structure models with jump are particularly important [1], since ignoring jumps in financial prices may cause inaccurate pricing and hedging rates [2]. Solutions of term structure model under jump-diffusion processes are justified because of movements in interest rates displaying both continuous and discontinuous behaviors [3]. Moreover, t...

We consider the problem of valuation of certain Asian options in the geometric jump-diffusion models with continuously dividend-paying assets. With the sources of diffusion risks and two primitive tradeable assets, the market in this model is, in general, incomplete, and so, there are more than one equivalent martingale measures and no-arbitrage prices. For this jump-diffusion model, we adopt t...