Well-posedness of a system of SDEs driven by jump random measures

Ying Jiao () and Nikolaos Kolliopoulos
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Ying Jiao: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon, ISFA - Institut de Science Financière et d'Assurances

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Abstract: We establish well-posedness for a class of systems of SDEs with non-Lipschitz coefficients in the diffusion and jump terms and with two sources of interdependence: a monotone function of all the components in the drift of each SDE and the correlation between the driving Brownian motions and jump random measures. Pathwise uniqueness is derived by employing some standard techniques. Then, we use a comparison theorem along with our uniqueness result to construct non-negative, [Formula: see text]-integrable càdlàg solutions as monotone limits of solutions to approximating SDEs, allowing for time-inhomogeneous drift terms to be included. Our approach allows also for a comparison property to be established for the solutions to the systems we investigate. The applicability of certain systems in financial modeling is also discussed.

Date: 2023-05-13
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Published in Stochastics and Dynamics, 2023, 23 (04), ⟨10.1142/S0219493723500284⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04894084

DOI: 10.1142/S0219493723500284

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