We consider a financial market consisting of a nonrisky asset and a risky one. We study the minimal initial capital needed in order to super-replicate a given contingent claim under the Gamma constraint, i.e. a constraint on the unbounded variation part of the hedging porfolio. In the general...

In this paper, we define and study a new class of optimal stochastic control problems which is closely related to the theory of Backward SDE's and forward-backward SDE's. The controlled process takes values in RXR and a given initial data for X(O). Then, the control problem is to find the...

In order to get rid of the condition X=Y, we introduce an extension of the Dynkin game by allowing for an extended set of strategies, namely the set of mixed strategies. The main result of the paper is that the extended Dynkin game has a value when the processes X and Y are only restricted to be...

We study the problem of minimal initial capital needed in order to hedge a European contengent claim without risk. The financial market presents incompleteness arising from two sources: stochastic volatility and portfolio constraints described by a closed convex set. In contrast with previous...

In frictionless securities markets, the characterization of the no arbitrage condition by the existence of equivalent martingale measures in discrete time is known as the fundamental Theorem of Asset Pricing. In the presence of convex constraints on the trading strategies, we extend this theorem...