SIAM Journal on Control and Optimization· 2026Q1
Maximum Principle for Optimal Control of Infinite Horizon Stochastic Difference Equations Driven by Fractional Noises
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- Q1SCImago
- 2026year
Short summary
A stochastic maximum principle is proven for discrete-time optimal control problems driven by fractional noise over an infinite horizon, overcoming challenges posed by the noise's self-dependence.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces infinite horizon stochastic and backward difference equations with fractional noise.
- Proves a stochastic maximum principle for discrete-time control problems with fractional noise over an infinite horizon.
- Addresses the challenge of fractional noise's self-dependence on an infinite horizon.
- Applies the principle to solve an optimal consumption and investment problem.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract. In this paper, infinite horizon stochastic difference equations and backward stochastic difference equations with fractional noise are studied. The main difficulty comes from the self-dependence of fractional noise on an infinite horizon. By introducing the infinite horizon stochastic difference equations and backward stochastic difference equations with fractional noise, the stochastic maximum principle for the discrete-time control problem driven by fractional noise on an infinite horizon is proved. As an application, an optimal consumption and investment problem is solved.
The authors' abstract, as published at the source. SIAM Journal on Control and Optimization, 2026 · DOI ↗
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Field: Finance
FinanceEconomics, Econometrics and Finance