Geometric BSDEs

2024/05/15 by Roger J. A. Laeven, Laeven, Roger J. A., Emanuela Rosazza Gianin +3 · 1 citation
Computer Science · #60H10 #60H30 #62P05 #91B06 #91B30 #Advanced Database Systems and Queries #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Risk Management (q-fin.RM)

paper · pdf · doi:10.48550/arxiv.2405.09260

openalex publication_date 2024/05/15 · openalex created_date 2024/05/17 · openalex updated_date 2026/07/28

Abstract

We introduce and develop the concepts of Geometric Backward Stochastic Differential Equations (GBSDEs, for short) and two-driver BSDEs. We demonstrate their natural suitability for modeling continuous-time dynamic return risk measures. We characterize a broad spectrum of associated, auxiliary ordinary BSDEs with drivers exhibiting growth rates involving terms of the form y|ln(y)|+|z|²/y. We establish the existence, regularity, uniqueness, and stability of solutions to this rich class of ordinary BSDEs, considering both bounded and unbounded coefficients and terminal conditions. We exploit these results to obtain corresponding results for the original two-driver BSDEs. Finally, we apply our findings within a GBSDE framework for representing the dynamics of return and star-shaped risk measures including (robust) L^p-norms, and analyze functional properties.

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• Measuring Financial Resilience Using Backward Stochastic Differential Equations

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