Coupled FBSDEs with Measurable Coefficients and its Application to Parabolic PDEs

2021/10/09 by Nam, Kihun, Xu, Yunxi
#35K58 #60H10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2110.04641

Abstract

Using purely probabilistic methods, we prove the existence and the uniqueness of solutions fora system of coupled forward-backward stochastic differential equations (FBSDEs) with measurable, possibly discontinuous coefficients. As a corollary, we obtain the well-posedness of semilinear parabolic partial differential equations (PDEs) \beginaligned amp;L u(t,x)+F(t,x,u,∂_x u)=0; u(T,x)=h(x)
amp;L:=∂_t+(1)/(2)∑_i,j=1^m(σσ^\intercal)_ij(t,x)∂²_xixj \endaligned in the natural domain of the second-order linear parabolic operator L. We allow F and h to be discontinuous with respect to x. Finally, we apply the result to optimal policy-making for pandemics and pricing of carbon emission financial derivatives.

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