Optimal Stopping Without Snell Envelopes

Pennanen, Teemu und Perkkiö, Ari-Pekka (2020): Optimal Stopping Without Snell Envelopes. In: Proceedings of the American Mathematical Society, Bd. 152, Nr. 4

Abstract

This paper proves the existence of optimal stopping times via elementary functional analytic arguments. The problem is first relaxed into a convex optimization problem over a closed convex subset of the unit ball of the dual of a Banach space. The existence of optimal solutions then follows from the Banach-Alaoglu compactness theorem and the Krein-Millman theorem on extreme points of convex sets. This approach seems to give the most general existence results known to date. Applying convex duality to the relaxed problem gives a dual problem and optimality conditions in terms of martingales that dominate the reward process.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch