Can I read Coupled FBSDEs with Measurable Coefficients and its Application to Parabolic PDEs on EtoBox?

Coupled FBSDEs with Measurable Coefficients and its Application to Parabolic PDEs by Nam, Kihun; Xu, Yunxi is a scholarly article available to read on EtoBox.

What is Coupled FBSDEs with Measurable Coefficients and its Application to Parabolic PDEs about?

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) $$ \begin{aligned} &\mathcal{L} u(t,x)+F(t,x,u,\partial_x u)=0;\qquad u(T,x)=h(x)\\ &\mathcal{L}:=\partial_t+\frac{1}{2}\sum_{i,j=1}^m(\sigma\sigma^\intercal)_{ij}(t,x)\partial^2_{x_ix_j} \end{aligned} $$ in the natural domain of the second-order linear parabolic operator $\mathcal{L}$. 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.

Author

Nam, Kihun; Xu, Yunxi

Published

2021

Language

EN