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

2021/02/07 by Ying Jiao, Jiao, Ying, Nikolaos Kolliopoulos +1
Decision Sciences · Economics, Econometrics and Finance · #34F05 #60G57 #60H10 #60J76 #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2102.03918

openalex publication_date 2021/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, L¹-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.

Citations

• Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling

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