This paper investigates a class of stochastic linear-quadratic (SLQ) control problems over an infinite horizon for Markov regime-switching jump-diffusion systems. Unlike classical diffusion models modulated by a Markov chain, we assume that the state process undergoes abrupt jumps that are synchronous with the regime switches of the Markov chain. In contrast to conventional Poisson jump-diffusion models, the jumps in the state process are entirely induced by the state transitions of the Markov chain, which can be interpreted as losses or gains of state process incurred during regime changes. Under this formulation, we thoroughly discuss the closed-loop solvability of the SLQ control problem and provide a feedback representation of the optimal control via the stabilizing solution of a system of coupled algebraic Riccati equations (CAREs). Finally, we further apply our results to a lifetime wealth tracking problem and derive the corresponding optimal investment strategy.
This paper investigates a stochastic linear-quadratic (SLQ) control problem for a regime-switching jump-diffusion system. Unlike traditional regime-switching diffusion systems that couple a diffusion process with a Markov chain, we incorporate the jumps of the Markov chain into the state equation. This modeling methodo...
This paper investigates an indefinite stochastic linear-quadratic (SLQ) control problem with parameters subject to Markov regime-switching. Based on the well-posedness of the SLQ problem, we introduce a relaxed compensator that extends SLQ control problems from the positive definite case to the indefinite case. We anal...
Many stochastic systems in operations and economics exhibit feedback between their long-run state distribution and the transition law governing their dynamics. In this paper, we develop a computational framework for stationary equilibria in such measure-dependent Markov systems when this feedback operates through a fin...
We address the optimal control problem for a novel class of fractional-order uncertain--stochastic dynamical systems perturbed simultaneously by stochastic and epistemic jump disturbances. The system dynamics are governed by Caputo fractional derivatives and driven by a multi-noise framework comprising Brownian motion,...
Philip Ajibola Bankole, Sunday Emmanuel Fadugba, M. E. Adeosun et al.· Journal of the Nigerian Soci...· 0 citations
We study nonlinear stochastic dynamical systems that evolve in a Markov environment with separated fast and slow transition scales. These systems are also subject to impulsive perturbations under a Poisson approximation scheme. The environment is represented on a product state space, and phase aggregation is used to av...
S. Bekešienė, A. Nikitin, A. Prus· Mathematics· 0 citations
A Taylor series expansion is derived for the invariant probability measure of the singularly perturbed Markov chain and this expansion is applied to analyze the expected long-run average cost (EAC) for singularly perturbed Markov decision processes (MDPs).
Qing-Wei Jiang, Yuan-Yuan Liu, Zhexin Wen· SIAM Journal of Control and...· 0 citations
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