We study a class of infinite-dimensional singular stochastic control problems that might find applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially ordered infinite-dimensional space X, it takes values in the positive cone of X, and it has right-continuous and nondecreasing paths. Our main contribution is to provide a rigorous formulation of the problem by properly defining the controlled dynamics and integrals with respect to the control process, and then to derive necessary and sufficient first-order conditions for optimality. The latter are finally exploited in a specification of the model where we determine an optimal control. The techniques used are those of semigroup theory, vector-valued integration, convex analysis, and general theory of stochastic processes.

On a class of infinite-dimensional singular stochastic control problems / Federico S.; Ferrari G.; Riedel F.; Rockner M.. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 59:2(2021), pp. 1680-1704. [10.1137/20M136757X]

On a class of infinite-dimensional singular stochastic control problems

Federico S.;
2021

Abstract

We study a class of infinite-dimensional singular stochastic control problems that might find applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially ordered infinite-dimensional space X, it takes values in the positive cone of X, and it has right-continuous and nondecreasing paths. Our main contribution is to provide a rigorous formulation of the problem by properly defining the controlled dynamics and integrals with respect to the control process, and then to derive necessary and sufficient first-order conditions for optimality. The latter are finally exploited in a specification of the model where we determine an optimal control. The techniques used are those of semigroup theory, vector-valued integration, convex analysis, and general theory of stochastic processes.
2021
On a class of infinite-dimensional singular stochastic control problems / Federico S.; Ferrari G.; Riedel F.; Rockner M.. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 59:2(2021), pp. 1680-1704. [10.1137/20M136757X]
Federico S.; Ferrari G.; Riedel F.; Rockner M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/944380
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