An iterated Azéma-Yor type embedding for finitely many marginals

Journal article

We consider here an n-marginal Skorokhod embedding problem (SEP). We construct an explicit solution which has desirable optimal properties. The classical (one-marginal) SEP consists in finding a stopping time τ such that a given stochastic process (Xt) stopped at τ has a given distribution µ. For the solution to be useful (and non-trivial) one further requires τ to be minimal (cf. Ob l´oj (21, Sec. 8)). When X is a continuous local martingale and µ is centred in X0, this is equivalent to (Xt∧τ : t ≥ 0) being a uniformly integrable martingale. The problem dates back to the original work in Skorokhod (25) and has remained an active field of research since. New solutions often either considered new classes of processes X or focused on finding stopping times τ with additional optimal properties. This paper contributes to the latter category. We are motivated, as was the case for several earlier works in the field, by questions arising in mathematical finance which we highlight below.

Authors: Obloj, J; Spoida, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Institute of Mathematical Statistics
• Journal: Annals of Probability
• Volume: 45
• Issue: 4
• Pages: 2210-2247
• Publication date: 2017-08-11
• Acceptance date: 2016-04-13
• DOI: 10.1214/16-AOP1110
• ISSN: 0091-1798
• Keywords: Skorokhod embedding problem; maximum process; Azéma-Yor embedding; marginal constraints; continuous martingale; martingale optimal transport