Hamilton-Jacobi-Bellman equation of nonlinear optimal control problems with fractional discount rate

2022/11/21 by Gou Nishida, Nishida, Gou, Takamatsu Takahiro +3
Economics, Econometrics and Finance · Computer Science · #Economic theories and models #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2211.11196

Abstract

This paper derives the Hamilton-Jacobi-Bellman equation of nonlinear optimal control problems for cost functions with fractional discount rate from the Bellman's principle of optimality. The fractional discount rate is described by Mittag-Leffler function that can be considered as a generalized exponential function.

Related

• Dynamic programming principle and Hamilton-Jacobi-Bellman equations for fractional-order systems
• Classical solution to second-order Hamilton-Jacobi-Bellman equation and optimal feedback control for linear-convex problem
• Controlled Continuous Time Random Walks and fractional Hamilton Jacobi Bellman equations
• Analysis of the vanishing discount limit for optimal control problems in continuous and discrete time
• The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 2: Nonlinear coupling