Abstract: During the past and this decade, a new generation of continuous-time financial models has been intensively investigated in a quest to incorporate the so-called stylized empirical features of asset prices like fat-tails, high kurtosis, volatility clustering, and leverage. Modeling driven by “memoryless homogeneous” jump processes (Lévy processes) constitutes one of the most plausible d...

The energetics of Ni vacancy jumps in the intermetallic compound NiAl are studied by combining embedded-atom and first-principles calculations. The embedded-atom potential used in this work is fit to both experimental and first-principles data and provides an accurate description of point defect energies and vacancy jump barriers in NiAl. Some of the embedded-atom results reported here, are ind...

In this paper we consider discontinuous Galerkin (DG) finite element approximations of a model scalar linear hyperbolic equation. We show that in order to ensure continuous stabilization of the method it suffices to add a jump-penalty-term to the discretized equation. In particular, the method does not require upwinding in the usual sense. For a specific value of the penalty parameter we recove...

Keywords: Fractional calculus Anomalous diffusion Continuous time random walk Central limit theory Operator stable law a b s t r a c t In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW is coupled if the waiting time and the subsequent jump are dependent random variables. The CTRW is used in physics to model diffusing particles. Its scaling limit ...

In this paper we consider two processes driven by diffusions and jumps. We consider both finite activity and infinite activity jump components. Given discrete observations we disentangle the covariation between the two diffusion parts from the co-jumps. A commonly used approach to estimate the diffusion covariation part is to take the sum of the cross products of the two processes increments; h...

General theorems for existence and uniqueness of viscosity solutions for HamiltonJacobi-Bellman quasi-variational inequalities (HJBQVI) with integral term are established. Such nonlinear partial integro-differential equations (PIDE) arise in the study of combined impulse and stochastic control for jump-diffusion processes. The HJBQVI consists of an HJB part (for stochastic control) combined wit...

We consider a Markov process X which is the solution of a stochastic differential equation driven by a Lévy process Z and an independent Wiener process W . Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Lévy density of Z outside any neighborhood of the origin, we obtain a small-time secondorder polynomi...

We derive results similar to Bo et al. (2010), but in the case of dynamics of the FX rate driven by a general Merton jump-diffusion process. The main results of our paper are as follows: 1) formulas for the Esscher transform parameters which ensure that the martingale condition for the discounted foreign exchange rate is a martingale for a general Merton jump-diffusion process are derived; usin...

In this paper, we present an unbiased Monte Carlo estimator for lookback options in jumpdiffusion models. Lookback options are difficult to price in jump-diffusion models, as their pay-off depends on the maximum of the share price over a particular time interval. In general, closed form solutions for prices of lookback options are not available but even simulating the pay-off of such an option ...

We present a closed form solution to the perpetual American double barrier call option problem in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial irregular optimal stopping problem to an integro-differential free-boundary problem and solving the latter by using continuous and smooth fit. The obtained...