Speaker: Emanuela Rosazza Gianin (University of Milano Bicocca)
Title: Measuring financial resilience using BSDEs
Abstract: We propose the resilience rate as a measure of financial resilience that captures the rate at which a dynamic risk measure 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) evaluated at stopping times.
These results reveal that our resilience rate can be represented as an expectation of the generator of a BSDE.
We also introduce resilience-acceptance sets and study their properties in relation to both the resilience rate and the dynamic risk measure.
The definition of the resilience rate is generalized from a Brownian filtration to the case of dynamic risk measures induced by BSDEs with jumps.
We illustrate our results in several examples.
Based on a joint work with Matteo Ferrari, Roger Laeven, and Marco Zullino.
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