Journal ArticleDOI
A Linear Quadratic Control for Discrete Systems with Random Parameters and Multiplicative Noise and Its Application to Investment Portfolio Optimization
TLDR
A quadratic control for discrete stochastic systems with random parameters and additive and multiplicative noises dependent on state and controls is studied and equations for the optimal linear static and dynamic output controllers are derived.Abstract:
A quadratic control for discrete stochastic systems with random parameters and additive and multiplicative noises dependent on state and controls is studied. Equations for the optimal linear static and dynamic output controllers are derived. The controllers are robust to the type of the distribution of the vector of random parameters. The results are applied to dynamic investment portfolio optimization.read more
Citations
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Journal ArticleDOI
Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems
TL;DR: The stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems is considered and a state feedback solution can be derived from a set of coupled generalized Riccati difference equations interconnected with aSet of coupled linear recursive equations.
Journal ArticleDOI
Finite Horizon $H_{2}/H_{\infty}$ Control for Discrete-Time Stochastic Systems With Markovian Jumps and Multiplicative Noise
Ting Hou,Weihai Zhang,Hongji Ma +2 more
TL;DR: A stochastic bounded real lemma (SBRL) is derived, which is used to establish a necessary and sufficient condition for the existence of the mixed finite horizon mixed H/sub 2/H/sub∞ control problem for discrete-time Stochastic linear systems subject to Markov jump parameters and multiplicative noise.
Journal ArticleDOI
Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises
TL;DR: This paper considers the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria: an unconstrained mean-variance trade-off performance criterion along the time and a minimum variance criterionAlong the time with constraints on the expected output.
Journal ArticleDOI
Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems
TL;DR: A solution is presented for the discounted and long run average cost problems when the performance criterion is assumed to be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables.
References
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Book
Continuous-Time Finance
TL;DR: In this article, the authors introduce the concept of Continuous-Time Models and propose a model for portfolio selection and portfolio selection in a continuous-time model, based on the theory of rational option pricing and the Modigliani-Miller Theorem.
Journal ArticleDOI
The matrix minimum principle
TL;DR: The purpose of this paper is to provide an alternate statement of the Pontryagin maximum principle as applied to systems which are most conveniently and naturally described by matrix, rather than vector, differential or difference equations.
Journal ArticleDOI
Feedback control of a class of linear systems with jump parameters
TL;DR: In this paper, a class of linear systems are studied which are subject to sudden changes in parameter values and an algorithm similar in form to Kushner's stochastic maximum principle is derived.
Journal ArticleDOI
Optimal limited state variable feedback controllers for linear systems
TL;DR: In this article, the problem of designing compensators, the dimensions of which are fixed a priori, for linear systems is considered, and two types of compensators are considered: static (gain only) compensators which operate directly upon the output signals to generate the controls, and dynamic compensators of fixed dimension.
Journal ArticleDOI
Infinite horizon optimal control of linear discrete time systems with stochastic parameters
TL;DR: The infinite horizon optimal control problem is considered in the general case of linear discrete time systems and quadratic criteria, both with stochastic parameters which are independent with respect to time.
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