We consider the problem of finding the minimal initial data of a controlled process which guarantees to reach a controlled target with a given probability of success or, more generally, with a givenâ€¦ (More)

We study a class of Markovian optimal stochastic control problems in which the controlled process Z is constrained to satisfy an a.s. constraint Z(T ) âˆˆ G âŠ‚ R P âˆ’ a.s. at some final time T > 0. Whenâ€¦ (More)

A Greek weight associated to a parameterized random variable Z(Î») is a random variable Ï€ such that âˆ‡Î»E [Ï† (Z(Î»))] = E [Ï† (Z(Î»)) Ï€] for any function Ï†. The importance of the set of Greek weights forâ€¦ (More)

The theory of Backward Stochastic Differential Equations (BSDEs for short) offers a large number of applications in the field of stochastic control or mathematical finance. Recently, Hu and Tang [4]â€¦ (More)

This paper provides a simple approach for the consideration of quadratic BSDEs with bounded terminal conditions. Using solely probabilistic arguments, we retrieve the existence and uniqueness resultâ€¦ (More)

In this paper, we study the discrete-time approximation of multi-dimensional reflected BSDEs of the type of those presented by Hu and Tang [16] and generalized by HamadÃ¨ne and Zhang [15]. Inâ€¦ (More)

We consider the infinite horizon optimal consumption-investment problem under the drawdown constraint, i.e. the wealth process never falls below a fixed fraction of its running maximum. We assumeâ€¦ (More)

The aim of this paper is to provide a survey on recent advances on probabilistic numerical methods for nonlinear PDEs, which serve as an alternative to classical deterministic schemes and allow toâ€¦ (More)

We introduce a new class of Backward Stochastic Differential Equations in which the T -terminal value YT of the solution (Y,Z) is not fixed as a random variable, but only satisfies a weak constraintâ€¦ (More)

This paper provides two different strong BSDE representations for optimal switching problems in the case where the dynamics of the underlying diffusion process depends on the current value of theâ€¦ (More)