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 consider a multi-asset continuous-time model of a financial market with transaction costs and prove that, for a strongly risk-averse investor, the reservation price of a contingent claim approaches the super-replication price increased by the liquidation value of the initial endowment.

The Bachelier Society for Mathematical Finance, founded in 1996, held its 1st World Congress in Paris on June 28 to July 1, 2000, thus coinciding in time with the centenary of the thesis defence of Louis Bachelier. In his thesis Bachelier introduced Brownian motion as a tool for the analysis of...

We discuss the no-arbitrage conditions in a general framework for discrete-time models of financial markets with proportional transaction costs and general information structure. We extend the results of Kabanov et al. (Finance Stoch 6(3):371–382, 2002; Finance Stoch 7(3):403–411, 2003) and...

In this note, we consider a general discrete time ¯nancial market with pro- portional transaction costs as in Kabanov and Stricker [4], Kabanov et al. [5], Kabanov et al. [6] and Schachermayer [10]. We provide a dual formulation for the set of initial endowments which allow to super-hedge some...

We introduce a new class of control problems in which the gain depends on the solu- tion of a stochastic differential equation (SDE) reflected at the boundary of a bounded domain, along directions which are controlled by a bounded variation process. We provide a PDE characterization of the...

We study the problem of finding the minimal initial capital needed in order to hedge without risk a barrier option when the vector of proportions of wealth invested in each risky asset is constrained to lie in a closed convex domain. In the context of a Brownian diffusion model, we provide a...

We consider a continuous time multivariate financial market with proportional transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in Bouchard and Touzi [B....