By means of Malliavin Calculus we see that the classical Hull and White formula for option pricing can be extended to the case where the noise driving the volatility process is correlated with the noise driving the stock prices. This extension will allow us to construct option pricing approximation formulas. Numerical examples are presented.

We consider a stochastic volatility model where the volatility process is a fractional Brownian motion. We estimate the memory parameter of the volatility from discrete observations of the price process. We use criteria based on Malliavin calculus in order to characterize the asymptotic normality of the estimators. 2000 AMS Classification Numbers: 60F05, 60H05, 60G18.

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the twoparameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity theory. Mathematics Subject Classification (2000): 60G15, G0H07, 60G35, 62M40

We consider the optimal selection of portfolios for utility maximizing investors under joint budget and shortfall risk constraints. The shortfall risk is measured in terms of the expected loss. Depending on the parameters of the risk constraint we show existence of an optimal solution and uniqueness of the corresponding Lagrange multipliers. Using Malliavin calculus we also provide the optimal ...

We establish an integration by parts formula in an abstract framework in order to study the regularity of the law for processes solution of stochastic differential equations with jumps, including equations with discontinuous coefficients for which the Malliavin calculus developed by Bismut and Bichteler, Gravereaux and Jacod fails. 2000 MSC. Primary: 60H07, Secondary 60G51

In this paper, we prove a central limit theorem for a sequence of multiple Skorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some applications to sequences of multiple stochastic integrals, and renormalized weighted quadratic variation of the fractional Brownian motion are discussed.

Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing limit laws, due to Nualart, Peccati and others.

In the first part of the paper, we obtain existence and characterizations of an optimal control for a linear quadratic control problem of linear stochastic Volterra equations. In the second part, using the Malliavin calculus approach, we deduce a general maximum principle for optimal control of general stochastic Volterra equations. AMS Subject Classification: Primary 60H15 Secondary 93E20, 35R60.

We deene an Euler type weak approximation for solutions of nonlinear diiusion processes. We nd the rate of convergence of this scheme in weak form. As in the diiusion case the weak rate of convergence is better than the strong one. The proof uses the integration by parts formula of Malliavin calculus.

We prove in nite-dimensional second order Poincaré inequalities on Wiener space, thus closing a circle of ideas linking limit theorems for functionals of Gaussian elds, Stein's method and Malliavin calculus. We provide two applications: (i) to a new second order characterization of CLTs on a xed Wiener chaos, and (ii) to linear functionals of Gaussian-subordinated elds.