Measuring Financial Resilience Using Backward Stochastic Differential Equations

Roger Laeven, Matteo Ferrari, Emanuela Rosazza Gianin and Marco Zullino

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Abstract: We propose the resilience rate as a measure of financial resilience. It captures the expected rate at which a dynamic risk evaluation recovers, i.e., bounces back, after the risk-acceptance set is breached. We develop the corresponding stochastic calculus by establishing representation theorems for 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 a BSDE. We analyze the properties of the resilience rate. 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.

Date: 2025-05, Revised 2025-11
New Economics Papers: this item is included in nep-rmg
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