We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear pricing equation. It holds in...

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....

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...

We consider a general multivariate financial market with transaction costs as in Kabanov and we analyse the stochastic control problems of maximizing the expected utility of the liquidation value of terminal wealth diminished by some random claim G for a utility function of exponential form.

In this paper, we prove a multidimensional extension of the so-called Bipolar Theorem proved in Brannath and Schachermayer (Séminaire de Probabilités, vol. XXX, 1999, p. 349), which says that the bipolar of a convex set of positive random variables is equal to its closed, solid convex hull....

We consider a continuous time multivariate financial market with proportionaltransaction costs and study the problem of finding the minimal initialcapital needed to hedge, without risk, European-type contingent claims. Themodel is similar to the one considered in Bouchard and Touzi (2000)...