Root's barrier, viscosity solutions of obstacle problems and reflected FBSDEs

Abstract

We revisit work of Rost, Dupire and Cox--Wang on connections between Root's solution of the Skorokhod embedding problem and obstacle problems. We develop an approach based on viscosity sub- and supersolutions and an accompanying comparison principle. This gives a complete characterization of (reversed) Root barriers and leads to new proofs of existence as well as minimality of such barrier solutions by pure PDE methods. The approach is self-contained and general enough to cover martingale diffusions with degenerate elliptic or time-dependent volatility; it also provides insights about the dynamics of general Skorokhod embeddings.

References in corpus (5)

• The Skorokhod embedding problem and its offspring
• Optimal Transport and Skorokhod Embedding
• Embedding laws in diffusions by functions of time
• Parabolic comparison revisited and applications
• Distribution of the time to explosion for one-dimensional diffusions

Cited by in corpus (1)

• Optimal robust bounds for variance options