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....

Let Zt,z[nu] be a -valued mixed diffusion process controlled by [nu] with initial condition Zt,z[nu](t)=z. In this paper, we characterize the set of initial conditions such that Zt,z[nu] can be driven above a given stochastic target at time T by proving that the corresponding value function is a...

We study the discrete-time approximation of the solution (Y,Z,K) of a reflected BSDE. As in Ma and Zhang [J. Ma, J. Zhang, Representations and regularities for solutions to BSDEs with reflections, Stochastic Processes and their Applications 115 (2005) 539-569], we consider a Markovian setting...

We study a discrete-time approximation for solutions of systems of decoupled Forward-Backward Stochastic Differential Equations (FBSDEs) with jumps. Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the scheme when the number of time steps n goes to infinity....

We suggest a discrete-time approximation for decoupled forward-backward stochastic differential equations. The Lp norm of the error is shown to be of the order of the time step. Given a simulation-based estimator of the conditional expectation operator, we then suggest a backward simulation...

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the...

We consider a class of production-investment models in discrete time with proportional transaction costs. For linear production functions, we study a natural extension of the no-arbitrage of the second kind condition introduced by M. Rasonyi [13]. We show that this condition implies the...

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...