In a market with transaction costs, generally, there is no nontrivial portfolio that dominates a contingent claim. Therefore, in such a market, preferences have to be introduced in order to evaluate the prices of options. The main goal of this article is to quantify this dependence on...

We consider a financial market with costs as in Kabanov and Last (1999). Given a utility function defined on ${\mathbb R}$, we analyze the problem of maximizing the expected utility of the liquidation value of terminal wealth diminished by some random claim. We prove that, under the Reasonable...

We consider a singular version with state constraints of the stochastic target problems studied in Soner and Touzi (SIAM J. Control Optim. 41:404–424, <CitationRef CitationID="CR23">2002</CitationRef>; J. Eur. Math. Soc. 4:201–236, <CitationRef CitationID="CR24">2002</CitationRef>) and more recently Bouchard et al. (SIAM J. Control Optim. 48:3123–3150, <CitationRef CitationID="CR6">2009</CitationRef>), among others....</citationref></citationref></citationref>

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>

Motivated by an optimal investment problem under time horizon uncertainty and when default may occur, we study a general structure for an incomplete semimartingale model extending the classical terminal wealth utility maximization problem. This modelling leads to the formulation of a wealth-path...