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A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients

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  • Paul M. N. Feehan
  • Camelia Pop

Abstract

Motivated by applications to probability and mathematical finance, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable and which become degenerate along the boundary of the half-space. We establish existence and uniqueness of solutions in weighted Holder spaces which incorporate both the degeneracy at the boundary and the unboundedness of the coefficients. In our companion article [arXiv:1211.4636], we apply the main result of this article to show that the martingale problem associated with a degenerate-elliptic partial differential operator is well-posed in the sense of Stroock and Varadhan.

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  • Paul M. N. Feehan & Camelia Pop, 2011. "A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients," Papers 1112.4824, arXiv.org, revised Aug 2013.
    • Handle: RePEc:arx:papers:1112.4824
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    References listed on IDEAS

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Marc Atlan, 2006. "Localizing Volatilities," Papers math/0604316, arXiv.org.
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    Cited by:

    1. Annalena Mickel & Andreas Neuenkirch, 2021. "The Weak Convergence Rate of Two Semi-Exact Discretization Schemes for the Heston Model," Risks, MDPI, vol. 9(1), pages 1-38, January.

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