Regularity of solutions to the parabolic fractional obstacle problem

By Luis Caffarelli, Alessio Figalli. 2011

124 citations recorded by the source corpus.

In this paper we study a parabolic version of the fractional obstacle problem, proving almost optimal regularity for the solution. This problem is motivated by an American option model proposed by Menton which introduces, into the theory of option evaluation, discontinuous paths in the dynamics of the stock's prices.

Subfields: Applied Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/14765a82ec7182bd42a02f8003e8c99ae7d2b47c

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Citations in the corpus

Global regularity for the free boundary in the obstacle problem for the fractional Laplacian (2015, methodology): “We refer to [12, Chapter 6,D] for a description of the model in the case of Brownian motion, and to the book [10] for an exhaustive discussion in the case of jump processes (see also [18, 6] for some regularity results in the case of finite expiration date).”
Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem (2013, background): “itten as u(x0;t) ’(x0) 0; (( x0)s+ @ t)u0; (u(x0;t) ’(x0))(( x0)s+ @ t)u= 0 in Rn 1 (0;T) with the initial condition u(x0;0) = ’(x0): This problem has been recently studied by Caarelli and Figalli [CF12]. We emphasize that, although their time-independent versions are locally equivalent, the problem”
On the regularity of the non-dynamic parabolic fractional obstacle problem (2016, background): “For the proof, see for instance [2] when γ = 0 or [9] for −1 < γ < 1.”
Obstacle problems for integro-differential operators: Higher regularity of free boundaries (2019, background): “, the higher order version of the blow-up technique from [31], and the proof of (7)) open the road to the study of the higher regularity of free boundaries in other obstacle problems that until now seemed out of reach, such as nonlocal operators with drift [15, 18, 27], or even the parabolic obstacl”
Optimal results for the fractional heat equation involving the Hardy potential (2014, background): “– Appendix A includes a Hölder regularity result, that can be seen as the translation to the bounded domain case of some results in [15].”