2020/05/31 by Chaman Kumar, Kumar, Chaman, Neelima Neelima +5 · 7 citations
Economics, Econometrics and Finance · Social Sciences · #Stochastic processes and financial applications #Financial Markets and Investment Strategies #Insurance, Mortality, Demography, Risk Management
paper · pdf · doi:10.48550/arxiv.2006.00463
In this paper, we first establish well-posedness of McKean-Vlasov stochastic\ndifferential equations (McKean-Vlasov SDEs) with common noise, possibly with\ncoefficients having super-linear growth in the state variable. Second, we\npresent stable time-stepping schemes for this class of McKean-Vlasov SDEs.\nSpecifically, we propose an explicit tamed Euler and tamed Milstein scheme for\nan interacting particle system associated with the McKean-Vlasov equation. We\nprove stability and strong convergence of order 1/2 and 1, respectively. To\nobtain our main results, we employ techniques from calculus on the Wasserstein\nspace. The proof for the strong convergence of the tamed Milstein scheme only\nrequires the coefficients to be once continuously differentiable in the state\nand measure component. To demonstrate our theoretical findings, we present\nseveral numerical examples, including mean-field versions of the stochastic\n3/2 volatility model and the stochastic double well dynamics with\nmultiplicative noise.\n