Optimal position targeting with stochastic linear-quadratic costs

• Autorzy: Stefan Ankirchner , Thomas Kruse
• Języki publikacji: EN

Abstrakty

EN

We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linear-quadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T. We verify optimality of the candidate control by using a penalization argument. Special cases for which the problem has explicit solutions are discussed. Finally we illustrate our results in financial applications, where we derive optimal trading strategies for closing financial asset positions in markets with stochastic price impact and non-zero returns.

Kategorie tematyczne

• 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
• 93E20: Optimal stochastic control
• 60H10: Stochastic ordinary differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 104
• Numer: 1
• Strony: 9-24

Daty

wydano

2015

Twórcy

autor

Stefan Ankirchner

• Institut für Mathematik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany

autor

Thomas Kruse

• Laboratoire de Mathématiques et Modélisation d'Evry, Université d'Evry Val D'Essonne, 23 Boulevard de France, 91025 Evry Cedex, France

Identyfikatory

DOI

10.4064/bc104-0-1