Recursive Stochastic Linear-Quadratic Control with Indefinite Weights for Jump-Diffusion Systems with Random Coefficients
Abstract
We study finite-horizon stochastic linear-quadratic (LQ) control for finite-activity jump diffusions with bounded random coefficients, indefinite weights and a linear recursive cost. The cost is defined by a backward stochastic differential equation (BSDE) whose generator has bounded deterministic coefficients multiplying the Brownian and jump integrands. A Brownian-Poisson change of measure and an integrating factor reduce the criterion to a nonrecursive LQ functional. On the intersection of the physical and transformed square-integrable control spaces, we establish recursive evaluation for L^1 quadratic data under the transformed measure and equality with the full transformed value. Under transformed uniform convexity and invertibility of the uncontrolled jump map, we identify the stochastic Riccati equation from the nonrecursive value kernel. Conditional energy estimates justify transferring its martingale coefficients to the physical measure. Completion of squares gives feedback representation, comparison and uniqueness in the feedback-admissible class. For each initial pair, the recursive value is attained exactly when the transformed optimizer has finite physical control energy. Analytical examples illustrate nonzero feedback and uniform convexity with a negative control weight.
Related
- Stochastic Riccati equations with jumps for indefinite linear-quadratic control: A stochastic value-flow approach
- General Leader-Follower Linear-Quadratic Stochastic Graphon Games with Indefinite Control Weights
- Turnpike Properties for Exploratory Stochastic Linear-Quadratic Optimal Control with Indefinite Cost Functionals
- Infinite-Horizon Stochastic Recursive Differential Games with Jumps: Nonautonomous Coefficients and Nonzero Terminal Values
- Ergodic Linear-Quadratic Optimal Control with Stochastic Coefficients
BibTeX
@misc{ma2026recursive,
title = {{Recursive Stochastic Linear-Quadratic Control with Indefinite Weights for Jump-Diffusion Systems with Random Coefficients}},
author = {Xinyu Ma and Yang Liu and Qingxin Meng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02530},
eprint = {2610.02530},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02530},
}
RIS
TY - UNPB
TI - Recursive Stochastic Linear-Quadratic Control with Indefinite Weights for Jump-Diffusion Systems with Random Coefficients
AU - Xinyu Ma
AU - Yang Liu
AU - Qingxin Meng
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02530
UR - https://arxiv.org/abs/2610.02530
AB - We study finite-horizon stochastic linear-quadratic (LQ) control for finite-activity jump diffusions with bounded random coefficients, indefinite weights and a linear recursive cost. The cost is defined by a backward stochastic differential equation (BSDE) whose generator has bounded deterministic coefficients multiplying the Brownian and jump integrands. A Brownian-Poisson change of measure and an integrating factor reduce the criterion to a nonrecursive LQ functional. On the intersection of the physical and transformed square-integrable control spaces, we establish recursive evaluation for L^1 quadratic data under the transformed measure and equality with the full transformed value. Under transformed uniform convexity and invertibility of the uncontrolled jump map, we identify the stochastic Riccati equation from the nonrecursive value kernel. Conditional energy estimates justify transferring its martingale coefficients to the physical measure. Completion of squares gives feedback representation, comparison and uniqueness in the feedback-admissible class. For each initial pair, the recursive value is attained exactly when the transformed optimizer has finite physical control energy. Analytical examples illustrate nonzero feedback and uniform convexity with a negative control weight.
ER -