Title: Well-posedness and tamed schemes for McKean-Vlasov Stochastic Differential Equations with Common Noise
Speaker: Chaman Kumar (IIT Roorkee)
Date: 02 September 2020
Time: 3 pm
Venue: Microsoft Teams (online)
We prove well-posedness of McKean–Vlasov stochastic differential equations (McKean–Vlasov SDEs) with common noise,
possibly with coefficients having super-linear growth in the state variable. We propose (moment) stable numerical
schemes for this class of McKean–Vlasov SDEs, namely tamed Euler and tamed Milstein schemes. Further, their rates
of convergence in strong sense are shown to be 1/2 and 1 respectively. We employ the notion of measure derivative
introduced by P.-L. Lions in his lectures delivered at the College de France. The strong convergence of the tamed
Milstein scheme is established under mild regularity assumptions on the coefficients. To demonstrate our theoretical
findings, we perform several numerical simulations on popular models such as mean-field versions of stochastic 3/2
volatility models and stochastic double well dynamics with multiplicative noise.
The talk is based on my recent joint works with Neelima (Delhi University), Christoph Reisinger (Oxford University)
and Wolfgang Stockinger (Oxford University).