A general class, introduced in [7], of continuous time bond markets driven by a standard cylindrical Brownian motion <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\bar{W}$</EquationSource> </InlineEquation> in <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\ell^{2}$</EquationSource> </InlineEquation> is considered. We prove that there always exist non-hedgeable random variables in the space <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\textsf{D}_{0}=\cap_{p \geq 1}L^{p}$</EquationSource> </InlineEquation> and that <InlineEquation ID="Equ4"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

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...