We formulate the generalized master equation for a class of continuous-time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean-f...

We obtain lower and upper bounds on option prices in one-dimensional jump-diffusion markets with point process components. Our proofs rely in general on the classical Kolmogorov equation argument and on the propagation of convexity property for Markov semigroups, but the bounds on intensities and jump sizes formulated in our hypotheses are different from the ones already found in the literature...

Abstract. Calculation of Greeks by Malliavin weights has proved to be a numerically satisfactory procedure for usual Ito-diffusions. In this article we prove existence of Malliavin weights for jump diffusions under Hörmander conditions and hypotheses on the invertibility of the linkage operators. The main result – in the hypo-ellitpic case – is the invertibility of the covariance matrix, which ...

A theoretical analysis tool, iterated optimal stopping, has been used as the basis of a numerical algorithm for American options under regime switching [19]. Similar methods have also been proposed for American options under jump diffusion [3] and Asian options under jump diffusion [4]. We show that a re-arrangement of the numerical algorithm in the form of local policy iteration [21, 17] has p...

Jump frequencies of Cd tracer atoms in In3La were measured via nuclear quadrupole relaxation caused by stochastic reorientation of the electric field gradient using the method of perturbed angular correlation of gamma rays. Activation enthalpies of 0.53(1) and 0.81(1) eV were found at the two phase boundaries, which differ in composition by only about 0.1 at. %. The jump frequency was found to ...

The fair price for an American option where the underlying asset follows a jump diffusion process can be formulated as a partial integral differential linear complementarity problem. We develop an implicit discretization method for pricing such American options. The jump diffusion correlation integral term is computed using an iterative method coupled with an FFT while the American constraint i...