December 2013
Intermediate to advanced
484 pages
14h 54m
English
Content preview from Nonlinear Option Pricing
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xiv Contents
10 McKean Nonlinear Stochastic Differential Equations 249
10.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
10.2 The particle method in a nutshell . . . . . . . . . . . . . . . 253
10.3 Propagation of chaos and convergence of the particle method 254
10.3.1 Building intuition: The BBGKY hierarchy . . . . . 254
10.3.2 Propagation of chaos and convergence of the particle
method . . . . . . . . . . . . . . . . . . . . . . . . . 259
10.3.3 The McKean-Vlasov SDE propagates the chaos . . 261
10.4 Exercise: Random matrices, Dyson Brownian motion, and
McKean SDEs . . . . . . . . . . . . . . . . . . . . . . . . . 265
10.A The Monge-Kantorovich distance and its financial
interpretation . . . . . . . . . . . . . . . . . . . .
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