Mild to Classical Solutions for XVA Equations Under Stochastic Volatility

Brigo, Damiano; Graceffa, Federico; Kalinin, Alexander

doi:10.2139/ssrn.3992507

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An Explicit Moment Estimate and Stability In First Moment1

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2021

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“…By using the negativity of the constant λl associated to the greatest power α l in the preceding condition, the announced exponential moment stability follows. Let us conclude with a specification of Example 3.11, which for m = 1 plays a major role in the volatility modelling in [9] and includes one-dimensional square-root diffusions. For this purpose, let U = u for some orthonormal matrix u ∈ R m×m .…”

Section: An Explicit Moment Estimate and Stability In First Momentmentioning

confidence: 99%

Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs: a multidimensional Yamada-Watanabe approach

Kalinin,

Meyer-Brandis,

Proske

2021

Preprint

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We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean-Vlasov equations with random coefficients, which are allowed to be non-Lipschitz continuous. In the case of deterministic coefficients we also obtain the existence of unique strong solutions. By using our approach, which is based on an extension of the Yamada-Watanabe ansatz to the multidimensional setting and which does not rely on the construction of Lyapunov functions, we prove first moment and pathwise α-exponential stability of solutions for α > 0. Furthermore, we are able to compute Lyapunov exponents explicitly.

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Section: An Explicit Moment Estimate and Stability In First Momentmentioning

confidence: 99%