Given a multi-dimensional Markov diffusion X, the Malliavin integration by parts formula provides a family of representations of the conditional expectation E[g(X <Subscript>2</Subscript>)|X<Subscript>1</Subscript>]. The different representations are determined by some localizing functions. We discuss the problem of variance reduction...</subscript></subscript>

We study the problem of finding the minimal price needed to dominate European-type contingent claims under proportional transaction costs in a continuous-time diffusion model. The result we prove has already been known in special cases - the minimal super-replicating strategy is the least...

We define (d,n)-coherent risk measures as set-valued maps from <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$L^\infty_d$</EquationSource> </InlineEquation> into <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\mathbb{R}^n$</EquationSource> </InlineEquation> satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the...</equationsource></inlineequation></equationsource></inlineequation>

This paper presents an original probabilistic method for the numerical computations of Greeks (i.e. price sensitivities) in finance. Our approach is based on the {\it integration-by-parts} formula, which lies at the core of the theory of variational stochastic calculus, as developed in the...