This problem, which I call the Scholes liquidation problem, is ubiquitous during unstable financial periods. Indeed, in the recent financial crisis, banks incurred large losses during the forced contraction of their balance sheets, as access to short-term financing through repo markets dried up (e.g., Adrian and Shin 2008; Brunnermeier 2009). A systemic deleveraging process propagated through t...

We consider a singular with state constraints version of the stochastic target problems studied in [22], [23] and more recently [6], among others. This provides a general framework for the pricing of contingent claims under risk constraints. Our extended version perfectly suits to market models with proportional transaction costs and to order book liquidation issues. Our main result is a direct...

We consider the problem of portfolio optimization in the presence of market impact, and derive optimal liquidation strategies. We discuss in detail the problem of finding the optimal portfolio under Expected Shortfall (ES) in the case of linear market impact. We show that, once market impact is taken into account, a regularized version of the usual optimization problem naturally emerges. We cha...

In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The model deals with both the permanent impact and the temporary impact in a regime s...