Infinite horizon backward stochastic Volterra integral equations and discounted control problems
Infinite horizon backward stochastic Volterra integral equations and discounted control problems
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DOI：
10.1051/cocv/2021098
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
Yushi Hamaguchi
中科院分区：
文献类型：
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作者：
Yushi Hamaguchi
研究了无限视界倒向随机Volterra积分方程。证明了加权L2space中自适应m解的存在唯一性。此外，我们将有限视界BSVIEs的一些重要已知结果推广到无限视界。本文给出了一类无限视界线性BSVIE的常数公式的一个变式，并证明了加权l2空间中线性（正）随机Volterra积分方程（简称SVIE）与无限视界线性BSVIE的对偶原理。作为应用，我们研究了具有折现代价泛函的svie的无限视界随机控制问题。利用庞特里亚金极大值原理，给出了最优性的充分必要条件，其中伴随方程被描述为无限视界BSVIE。这些结果应用于分数阶随机微分方程和随机积分微分方程的折现控制问题。
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 L2space. 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.