An Introduction to Optimal Control of FBSDE with Incomplete Information by Guangchen Wang Zhen Wu & Jie Xiong

Author:Guangchen Wang, Zhen Wu & Jie Xiong
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

subject to

and a fully coupled FBSDE

(3.20)

For the monotonicity to be satisfied, we make the following assumptions on the constants: a 2 < 0, b 2 = −a 3, b 3 < 0, c 2 = −a 4, c 3 = −b 4, c 4 < 0, and e 1 > 0. Namely, for any , we can check that (H1.1)–(H1.3) are satisfied; then, (3.20) has a unique solution

In this situation, the adjoint equation is

(3.21)

Since (H1.1), (H1.2), and (H1.3)’ are applicable to (3.21), it admits a unique solution . Let

(3.22)

Clearly, u(⋅ ) is in . The Hamiltonian function is

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