Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations

2012/08/31 by Paul M. N. Feehan, Camelia A. Pop · 1 citation
Mathematics · Economics, Econometrics and Finance · #math.AP #math.PR #q-fin.CP #q-fin.PR #msc:35J70 #msc:49J40 #msc:35R45 #msc:60J60

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published as Advances in Differential Equations 20 (2015), no. 3/4, 361-432 · 55 pages, 1 figure. To appear in Advances in Differential Equations. Incorporates final galley proof corrections corresponding to published version

arxiv created 2014/11/13 · arxiv updated 2015/02/03

Abstract

We establish higher-order weighted Sobolev and Holder regularity for solutions to variational equations defined by the elliptic Heston operator, a linear second-order degenerate-elliptic operator arising in mathematical finance. Furthermore, given C^∞-smooth data, we prove C^∞-regularity of solutions up to the portion of the boundary where the operator is degenerate. In mathematical finance, solutions to obstacle problems for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset.

Cited by

• On regularity of finite-maturity American put options in the Heston model

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