The stochastic maximum principle for a singular control problem

Cadenillas, Abel; Haussmann, U. G.

doi:10.1080/17442509408833921

Cited by 77 publications

(60 citation statements)

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“…Stochastic maximum principle for optimal control problems of forward backward systems involving impulse controls has been studied in Wu and Zhang [3,12]. The stochastic maximum principle for singular control was considered by many authors, see for instance [1,2,[4][5][6][7][8][9][10]. The first version of maximum principle for singular stochastic control problems was obtained by Cadenillas and Haussmann [9].…”

Section: L(t)dξ(t)mentioning

confidence: 99%

“…The stochastic maximum principle for singular control was considered by many authors, see for instance [1,2,[4][5][6][7][8][9][10]. The first version of maximum principle for singular stochastic control problems was obtained by Cadenillas and Haussmann [9]. In Dufour and Miller [10], the authors derived stochastic maximum principle where the singular part has a linear form.…”

Section: L(t)dξ(t)mentioning

confidence: 99%

“…The stochastic singular control problems have received considerable research attention in recent years due to wide applicability in a number of different areas, see for instance [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] . In most classical cases, the optimal singular control problem was investigated through dynamic programming principle.…”

Section: L(t)dξ(t)mentioning

confidence: 99%

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Singular mean-field optimal control for forward-backward stochastic systems and applications to finance

Hafayed

2014

Int. J. Dynam. Control

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In this paper, we study a class of singular stochastic optimal control problems for systems described by mean-field forward-backward stochastic differential equations, in which the coefficient depend not only on the state process but also its marginal law of the state process through its expected value. Moreover, the cost functional is also of mean-field type. The control variable has two components, the first being absolutely continuous and the second singular control. Necessary conditions for optimal control for this systems in the form of a Pontrygin maximum principle are established by means convex perturbation techniques for both continuous and singular parts. Our stochastic maximum principle differs from the classical one in the sense that here the adjoint equation has a mean-field type. The control domain is assumed to be convex. As an illustration of our results, we consider a mean-variance portfolio selection mixed with a recursive utility functional optimization problem involving singular control. The explicit expression of the optimal portfolio selection strategy is obtained in the state feedback form involving both state process and its marginal distribution, via the solutions of Riccati ordinary differential equations with time-inconsistent solution.Keywords Singular stochastic control · Mean-field forward-backward stochastic differential equation · Mean-field type maximum principle · Time-inconsistent control problem · McKean-Vlasov systems M. Hafayed

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Section: L(t)dξ(t)mentioning

confidence: 99%

Section: L(t)dξ(t)mentioning

confidence: 99%

Section: L(t)dξ(t)mentioning

confidence: 99%

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Singular mean-field optimal control for forward-backward stochastic systems and applications to finance

Hafayed

2014

Int. J. Dynam. Control

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“…The above conditions are reminiscent of the maximum principle derived in [CH94] for problems where the objective is linear in the singular part of the control. While the maximum principle of [CH94] characterizes optimal control processes as minimizers of a certain integral functional, the above conditions give explicit pointwise characterizations for both the absolutely continuous and singular parts.…”

Section: Maximum Principle In Singular Stochastic Controlmentioning

confidence: 99%

“…While the maximum principle of [CH94] characterizes optimal control processes as minimizers of a certain integral functional, the above conditions give explicit pointwise characterizations for both the absolutely continuous and singular parts.…”

Section: Maximum Principle In Singular Stochastic Controlmentioning

confidence: 99%

Convex integral functionals of regular processes

Pennanen

Perkkiö

2018

Stochastic Processes and their Applications

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This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be identified with the space of optional Radon measures with essentially bounded variation. Combined with classical Banach space techniques, our results allow for a systematic treatment of stochastic optimization problems over BV processes and, in particular, yields a maximum principle for a general class of singular stochastic control problems.

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