Let $X$ be an ${\Bbb R}^d$-valued special semimartingale on a probability space $(\Omega , {\cal F} , ({\cal F} _t)_{0 \leq t \leq T} ,P)$ with canonical decomposition $X=X_0+M+A$. Denote by $G_T(\Theta )$ the space of all random variables $(\theta \cdot X)_T$, where $\theta $ is a predictable...

In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity...

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...

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...