Related papers: Malliavin calculus and Clark-Ocone formula for fun…

Using the Malliavin calculus with respect to Gaussian processes and the multiple stochastic integrals we derive It\^{o}'s and Tanaka's formulas for the $d$-dimensional bifractional Brownian motion.

We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump type models have already been suggested, but none is suited to…

This paper is devoted to a study on SDEs with a bounded Borel drift b. We first remark that the original integration by parts formula due to P. Malliavin can be used to deal with derivatives with respect to space variables, then we obtain a…

In this paper we give easy-to-implement closed-form expressions for European and Asian Greeks for general L2-payoff functions and underlying assets in an exponential L\'evy process model with nonvanishing Brownian motion part. The results…

Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore classical methods, like dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that by using…

We consider a Poisson process $\eta$ on a measurable space $(\BY,\mathcal{Y})$ equipped with a partial ordering, assumed to be strict almost everwhwere with respect to the intensity measure $\lambda$ of $\eta$. We give a Clark-Ocone type…

In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation…

We construct optimal Markov couplings of L\'{e}vy processes, whose L\'evy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Brownian motions and the coupling of Brownian motions by…

For a L\'evy process $\xi=(\xi_t)_{t\geq0}$ drifting to $-\infty$, we define the so-called exponential functional as follows \[{\rm{I}}_{\xi}=\int_0^{\infty}e^{\xi_t} dt.\] Under mild conditions on $\xi$, we show that the following…

We study counterfactual stochastic optimization of conditional loss functionals under misspecified and noisy gradient information. The difficulty is that when the conditioning event has vanishing or zero probability, naive Monte Carlo…

We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of variations and we make Gaussian assumptions only…

The Malliavin derivative, divergence operator, and the Ornstein-Uhlenbeck operator are extended from the traditional Gaussian setting to generalized processes from the higher-order chaos spaces.

In this paper we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process, by using the Malliavin calculus. In analogy with the celebrated Black-Scholes formula, we aim at…

This paper provides a framework for investigations in fluctuation theory for L\'evy processes with matrix-exponential jumps. We present a matrix form of the components of the infinitely divisible factorization. Using this representation we…

Monotone L\'evy processes with additive increments are defined and studied. It is shown that these processes have a natural Markov structure and their Markov transition semigroups are characterized using the monotone L\'evy-Khintchine…

This work is devoted to deriving the Onsager-Machlup action functional for a class of stochastic differential equations with (non-Gaussian) L\'{e}vy process as well as Brownian motion in high dimensions. This is achieved by applying the…

We investigate some recursive procedures based on an exact or ``approximate'' Euler scheme with decreasing step in vue to computation of invariant measures of solutions to S.D.E. driven by a L\'evy process. Our results are valid for a large…

Let $(W,H,\mu)$ be the classical Wiener space on $\R^d$. Assume that $X=(X_t(x))$ is a diffusion process satisfying the stochastic differential equation with diffusion and drift coefficients $\sigma: \R^n\to \R^n\otimes \R^d$, $b: \R^n\to…

In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an…

In this paper, we establish existence, uniqueness, and regularity properties of the solutions to multi-dimensional backward stochastic Volterra integral equations (BSVIEs), whose (possibly random) generator reflects nonlinear dependence on…