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Presented By: Financial/Actuarial Mathematics Seminar - Department of Mathematics

Propagation of chaos for maxima of particle systems with mean-field drift interaction and applications in finance.

Nikos Kolliopoulos/ Carnegie Mellon

We study the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as those arising in an i.i.d system where each particle follows the associated McKean—Vlasov limiting dynamics. This allows for the asymptotic distribution of the normalized maxima to be determined by using results from standard Extreme—Value Theory. The proof uses a change of measure argument that depends on a delicate combinatorial analysis of the iterated stochastic integrals appearing in the chaos expansion of the Radon-Nikodym density. Our work is motivated by problems arising in stochastic portfolio theory, credit risk and mean-field games. Possible extensions to more complex settings are also discussed.

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January 25, 2023 (Wednesday) 3:00pm
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