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Positivity of mild solution to stochastic evolution equations with an application to forward rates

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  • Carlo Marinelli

Abstract

We prove a maximum principle for mild solutions to stochastic evolution equations with (locally) Lipschitz coefficients and Wiener noise on weighted $L^2$ spaces. As an application, we provide sufficient conditions for the positivity of forward rates in the Heath-Jarrow-Morton model, considering the associated Musiela SPDE on a homogeneous weighted Sobolev space.

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  • Carlo Marinelli, 2019. "Positivity of mild solution to stochastic evolution equations with an application to forward rates," Papers 1912.12472, arXiv.org.
    • Handle: RePEc:arx:papers:1912.12472
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    File URL: http://arxiv.org/pdf/1912.12472
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    References listed on IDEAS

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    1. Assing, Sigurd, 1999. "Comparison of systems of stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 259-282, August.
    2. Denis, Laurent & Matoussi, Anis, 2013. "Maximum principle for quasilinear SPDE’s on a bounded domain without regularity assumptions," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1104-1137.
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    Cited by:

    1. Stefan Tappe, 2022. "Invariant cones for jump-diffusions in infinite dimensions," Papers 2206.13913, arXiv.org, revised Nov 2023.

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