Séminaire du CIMMUL – Silvana Pesenti

Model modification and combination using Kullback-Leibler divergence and barycentre

Silvana Pesenti

University of Toronto

Résumé

In many settings, a modeler may have trained a model on data but that trained model is not consistent with their beliefs – e.g., the average time the process spends below some barrier is 10% from the estimated model, but their belief about the future evolution is that it should be 20%. Hence, they would like to modify this model in a minimal manner that respects their beliefs. Here we study such questions. More generally, given an n-dimensional stochastic process X driven by P-Brownian motions and Poisson random measures, we seek the probability measure Q, with minimal relative entropy to P, such that the Q-expectations of some terminal and running costs are constrained. We prove the existence and uniqueness of the optimal probability measure, derive the explicit form of the measure change, and characterise the optimal drift and compensator adjustments under the optimal measure. In a second part we look at model combinations, in particular how to combine different modellers / experts views using a barycentre approach. We further allow for the joint model to satisfy agreed upon constraints.

This talk will provide a high level view of how we solve this problem and several examples stemming from finance and insurance.

Bio : https://pesenti.utstat.utoronto.ca/?page_id=76

Le séminaire aura lieu au local PLT-2744 (pavillon Adrien-Pouliot) et en ligne.

Pour rejoindre la réunion Zoom :
https://ulaval.zoom.us/j/62680136430?pwd=eldBYjdNTG5QR2VxTTFqbVM4UGVRZz09

Meeting ID: 626 8013 6430
Passcode: 693150