Solutions and Challenges in Computing FBSDEs with Large Jumps for Dam and Reservoir System Operation

EasyChair Preprint 6885

Abstract

Optimal control of Lévy jump-driven stochastic differential equations plays a central role in management of resource and environment. Problems involving large Lévy jumps are challenging due to their mathematical and computational complexities. We focus on numerical control of a real-scale dam and reservoir system from the viewpoint of forward-backward stochastic differential equations (FBSDEs): a new mathematical tool in this research area. The problem itself is simple but unique, and involves key challenges common to stochastic systems driven by large Lévy jumps. We firstly present an exactly-solvable linear-quadratic problem and numerically analyze convergence of different numerical schemes. Then, a more realistic problem with a hard constraint of state variables and a more complex objective function is analyzed, demonstrating that the relatively simple schemes perform well.

Keyphrases: Forward-backward stochastic differential equations, Resource and Environment, Stochastic maximum principle, Tempered stable subordinator, least-squares Monte Carlo

@booklet{EasyChair:6885,
  author    = {Hidekazu Yoshioka},
  title     = {Solutions and Challenges in Computing FBSDEs with Large Jumps for Dam and Reservoir System Operation},
  howpublished = {EasyChair Preprint 6885},
  year      = {EasyChair, 2021}}