Optimal Variational Principle for Backward Stochastic Control Systems Associated with Lévy Processes

2010/10/22 by Maoning Tang, Qi Zhang, Tang, Maoning +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC

paper · pdf · doi:10.48550/arxiv.1010.4744

openalex publication_date 2010/10/22 · arxiv created 2011/01/08 · arxiv updated 2011/01/11 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/02

Abstract

The paper is concerned with optimal control of backward stochastic differential equation (BSDE) driven by Teugel's martingales and an independent multi-dimensional Brownian motion, where Teugel's martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes (see Nualart and Schoutens \citeNuSc). We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria (called backward linear-quadratic problem, or BLQ problem for short) is discussed and characterized by stochastic Hamilton system.

Citations

• Conjugate convex functions in optimal stochastic control

Related

• Linear-Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations with Jumps
• Stochastic Evolution Equation Driven by Teugels Martingale and Its Optimal Control
• A Class of Forward-Backward Stochastic Differential Equations Driven by Lévy Processes and Application to LQ Problems
• Partial Information Stochastic Differential Games for Backward Stochastic Systems Driven By Lévy Processes
• Linear-Quadratic Optimal Control for Backward Stochastic Differential Equations with Random Coefficients