We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula <p>\[F(\omega)=E[F]+\int_0^TE[D_tF|\F_t]\diamond W(t)dt\] <p>Here E[F] denotes the generalized expectation, $D_tF(\omega)={{dF}\over{d\omega}}$ is the...</p></p>

Let $X_1(t)$, $\cdots$, $X_n(t)$ be $n$ geometric Brownian motions, possibly correlated. We study the optimal stopping problem: Find a stopping time $\tau^*\infty$ such that \[ \sup_{\tau}{\Bbb E}^x\Big\{ X_1(\tau)-X_2(\tau)-\cdots -X_n(\tau)\Big\}={\Bbb E}^x \Big\{...

We study a problem of optimal consumption and portfolio selection in a market where the logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve pure-jump Lévy processes as driving noise instead of Brownian motion like in the Black and Scholes...

We consider an optimal portfolio-consumption problem which incorporates the notions of durability and intertemporal substitution. The logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve Lévy processes as driving noise instead of the more...