Volume 27, 2021
|Number of page(s)||47|
|Published online||26 October 2021|
Infinite horizon backward stochastic Volterra integral equations and discounted control problems★
Graduate School of Engineering Science, Department of Systems Innovation, Osaka University.
** Corresponding author: firstname.lastname@example.org
Accepted: 7 October 2021
Infinite horizon backward stochastic Volterra integral equations (BSVIEs for short) are investigated. We prove the existence and uniqueness of the adapted M-solution in a weighted L2-space. Furthermore, we extend some important known results for finite horizon BSVIEs to the infinite horizon setting. We provide a variation of constant formula for a class of infinite horizon linear BSVIEs and prove a duality principle between a linear (forward) stochastic Volterra integral equation (SVIE for short) and an infinite horizon linear BSVIE in a weighted L2-space. As an application, we investigate infinite horizon stochastic control problems for SVIEs with discounted cost functional. We establish both necessary and sufficient conditions for optimality by means of Pontryagin’s maximum principle, where the adjoint equation is described as an infinite horizon BSVIE. These results are applied to discounted control problems for fractional stochastic differential equations and stochastic integro-differential equations.
Mathematics Subject Classification: 60H20 / 45G05 / 49K45 / 49N15
Key words: Infinite horizon backward stochastic Volterra integral equation / stochastic Volterra integral equation / duality principle / discounted stochastic control
© The authors. Published by EDP Sciences, SMAI 2021
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