A convex duality method for optimal liquidation with participation constraints

Abstract

In spite of the growing consideration for optimal execution issues in the financial math- ematics literature, numerical approximations of optimal t rading curves are almost never discussed. In this article, we present a numerical method to approximate the optimal strat- egy of a trader willing to unwind a large portfolio. The metho d we propose is very general as it can be applied to multi-asset portfolios with any form o f execution costs, including a bid-ask spread component, even when participation constra ints are imposed. Our method, based on convex duality, only requires Hamiltonian functio ns to have C 1 , 1 regularity while classical methods require additional regularity and canno t be applied to all cases found in practice.no