Abstract We study Malliavin differentiability of solutions to sub-critical singular parabolic stochastic partial differential equations (SPDEs) and we prove the existence densities for a class SPDEs. Both these results are implemented in setting regularity structures. For this construct renormalized models situations where some driving noises replaced by deterministic Cameron–Martin functions, ...

In this paper, Malliavin calculus is applied to arrive at exact formulas for the difference between volatility swap strike and zero vanna implied volatilities driven by fractional noise. To best of our knowledge, result first derive rigorous relationship strike. particular, we will see that a more accurate approximation than at-the-money volatility.

Abstract. This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on 3 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 L modulus of continuity for a 1-dimensional Brownian motion. (c) Ext...

Using Stein’s method and the Malliavin calculus of variations, we derive explicit estimates for the Gamma approximation of functionals of a Poisson measure. In particular, conditions are presented under which the distribution of a sequence of multiple Wiener-Itô stochastic integrals with respect to a compensated Poisson measure converges to a Gamma distribution. As an illustration, we present a...

Abstract In this paper, we prove the existence of strong solutions to an stochastic differential equation with a generalized drift driven by multidimensional fractional Brownian motion for small Hurst parameters $$H&lt;\frac{1}{2}.$$ H &lt; 1 2 </m...

We use Malliavin calculus and the Clark-Ocone formula to derive the hedging strategy of an arithmetic Asian Call option in general terms. Furthermore we derive an expression for the density of the integral over time of a geometric Brownian motion, which allows us to express hedging strategy and price of the Asian option as an analytic, that is closed form, expression. Numerical computations whi...

Abstract. We present various versions of the maximum principle for optimal control of forwardbackward stochastic differential equations (SDE) with jumps. Our study is motivated by risk minimization via g-expectations. We first prove a general sufficient maximum principle for optimal control with partial information of a stochastic system consisting of a forward and a backward SDE driven by Lévy...

In this paper, we extend Walsh’s stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous spatial correlation, in order to be able to integrate some random measure-valued processes. This extension turns out to be equivalent to Dalang’s one. Then we study existence and regularity of the density of the probability law for the real-valued mild solution to a gen...

This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the second order Edgeworth expansion for power variation of diffusion processes. Our methodology relies on martingale embedding, Malliavin calculus and stable central...