We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and ”payoff” functions depending on the process at multiple future times. In the spirit of Fournié et al [14] and Davis and Johansson [10] this can improve Monte Carlo numerics for stochastic volatility models with jumps. To this end one needs so-called Malliavin weights and we give explicit formulae valid in presence of...

Using elementary arguments, we show how to derive Lp-error bounds for the approximation of frictionless wealth process in markets with proportional transaction costs. For utilities bounded risk aversion, these estimates yield lower frictional value function, which pave way its asymptotic analysis using stability results viscosity solutions. tools from Malliavin calculus, also simple sufficient ...

Although introduced in the case of Poisson random measures (cf [2], [3]), the lent particle method applies as well in other situations. We study here the case of marked point processes. In this case the Malliavin calculus (here in the sense of Dirichlet forms) operates on the marks and the point process doesn’t need to be Poisson. The proof of the method is even much simpler than in the case of...

We consider a general class of SPDEs in R driven by a Gaussian spatially homogeneous noise which is white in time. We provide sufficient conditions on the coefficients and the spectral measure associated to the noise ensuring that the density of the corresponding mild solution admits an upper estimate of Gaussian type. The proof is based on the formula for the density arising from the integrati...

Abstract. We develop a stochastic calculus for processes which are built by convoluting a pure jump, zero expectation Lévy process with a Volterra-type kernel. This class of processes contains, for example, fractional Lévy processes as studied in Marquardt (2006b). The integral which we introduce is a Skorohod integral. Nonetheless we avoid the technicalities from Malliavin calculus and white n...

In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDEs). The scheme has convergence order 1. In order to establish the scheme, we prove an infinitedimensional Itô formula for “tame” functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires...

This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on three closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, where the limit law is an intricate Gaussian mixture. (b) Central limit theorems for the projections of L2 modulus of continuity for a one-dimensional Brownian motion. (c) Extens...