The particular entropy method proposed by Hoch et al. [7] for the computation of NMR complex spectra allows an elegant application of the concepts of duality theory. Correspondingly, duality theory casts new light on their choice of entropy. The purpose of this paper is to present the relevant...

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...

We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we allow for nonsmooth utility functions, so as to include the...

This paper presents a general theory that works out the relation between coherent risk measures, valuation bounds, and certain classes of portfolio optimization problems. It is economically general in the sense that it works for any cash stream spaces, be it in dynamic trading settings, one-step...

An investor faced with a contingent claim may eliminate risk by (super-)hedging in a financial market. As this is often quite expensive, we study partial hedges, which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal...

This paper presents a general theory that works out the relation between coherent risk measures, valuation bounds, and certain classes of portfolio optimization problems. It is economically general in the sense that it works for any cash stream spaces, be it in dynamic trading settings, one-step...

An investor faced with a contingent claim may eliminate risk by (super-)hedging in a financial market. As this is often quite expensive, we study partial hedges, which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal...

The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps [HK79]. In the context of optimal portfolio selection with expected utility preferences this question has been the focus of considerable attention over...

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Follmer and Schied (2002). The dynamic optimization problem of finding a self-financing...

The paper studies the problem of minimizing coherent risk measures of shortfall for general discrete-time financial models with cone-constrained trading strategies, as developed by Pham and Touzi. It is shown that the optimal strategy is obtained by super-hedging a contingent claim, which is...