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Limited Attention Allocation in a Stochastic Linear Quadratic System with Multiplicative Noise

Xiangyu Cui, Jianjun Gao, Lingjie Kong

TL;DR

An analytical optimal control is provided and a numerical method is proposed for optimal attention allocation in a stochastic linear quadratic system with multiplicative noise to enhance noise estimation and improve control decisions.

Abstract

This study addresses limited attention allocation in a stochastic linear quadratic system with multiplicative noise. Our approach enables strategic resource allocation to enhance noise estimation and improve control decisions. We provide analytical optimal control and propose a numerical method for optimal attention allocation. Additionally, we apply our ffndings to dynamic mean-variance portfolio selection, showing effective resource allocation across time periods and factors, providing valuable insights for investors.

Limited Attention Allocation in a Stochastic Linear Quadratic System with Multiplicative Noise

TL;DR

An analytical optimal control is provided and a numerical method is proposed for optimal attention allocation in a stochastic linear quadratic system with multiplicative noise to enhance noise estimation and improve control decisions.

Abstract

This study addresses limited attention allocation in a stochastic linear quadratic system with multiplicative noise. Our approach enables strategic resource allocation to enhance noise estimation and improve control decisions. We provide analytical optimal control and propose a numerical method for optimal attention allocation. Additionally, we apply our ffndings to dynamic mean-variance portfolio selection, showing effective resource allocation across time periods and factors, providing valuable insights for investors.
Paper Structure (5 sections, 2 theorems, 29 equations, 3 figures)

This paper contains 5 sections, 2 theorems, 29 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Basic Setting
  3. Optimal Attention Allocation Policy and Optimal Control Policy
  4. Application in Dynamic Mean-Variance Portfolio Selection
  5. Conclusion

Key Result

Theorem 3.1

Under Assumption asmp:1, the optimal control policy and optimal attention allocation policy for problem $(P_{AC})$ at period $t$ are given by, where $h_t(\Lambda_t, \bm f_t)$ represents the optimal objective value of the optimization problem (eq:lambda) and $h_T(\Lambda_T, \bm f_T)=q_T$, $E_{t+}[\cdot] = E[\cdot|\mathcal{F}_{t+}]$ and $E_{t}[\cdot]=E[\cdot|\mathcal{F}_t]$. And the optimal objecti

Figures (3)

  • Figure 1: The attention allocation procedure and system control procedure at period $t$
  • Figure 2: The total optimal attention allocation in different cases of factors and different periods
  • Figure 3: The optimal attention allocation among different factors

Theorems & Definitions (2)

  • Theorem 3.1
  • Theorem 4.1