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arXiv · 1301.3798

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

Paul Gassiat·Harald Oberhauser·Goncalo dos Reis
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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.

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Paul Gassiat, Harald Oberhauser, Goncalo dos Reis. 2014-09-15. Root's barrier, viscosity solutions of obstacle problems and reflected FBSDEs. https://arxiv.org/abs/1301.3798

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