We develop a stochastic maximum principle for a finite-dimensional stochastic control problem in infinite horizon under a polynomial growth and joint monotonicity assumption on the coefficients. The second assumption generalizes the usual one in the sense that it is formulated as a joint condition for the drift and the diffusion term. The main difficulties concern the construction of the first and second order adjoint processes by solving backward equations on an unbounded time interval. The first adjoint process is characterized as a solution to a backward SDE, which is well-posed thanks to a duality argument. The second one can be defined via another duality relation written in terms of the Hamiltonian of the system and linearized state equation. Some known models verifying the joint monotonicity assumption are discussed as well.

Accepted:

DOI: 10.1051/cocv/2015054

Keywords: Stochastic maximum principle, dissipative systems, backward stochastic differential equation, stochastic discounted control problem, infinite time horizon, necessary conditions for optimality

^{1}; Veverka, Petr

^{2}

@article{COCV_2017__23_1_337_0, author = {Orrieri, Carlo and Veverka, Petr}, title = {Necessary stochastic maximum principle for dissipative systems on infinite time horizon}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {337--371}, publisher = {EDP-Sciences}, volume = {23}, number = {1}, year = {2017}, doi = {10.1051/cocv/2015054}, mrnumber = {3601027}, zbl = {1354.93178}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2015054/} }

TY - JOUR AU - Orrieri, Carlo AU - Veverka, Petr TI - Necessary stochastic maximum principle for dissipative systems on infinite time horizon JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 337 EP - 371 VL - 23 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015054/ DO - 10.1051/cocv/2015054 LA - en ID - COCV_2017__23_1_337_0 ER -

%0 Journal Article %A Orrieri, Carlo %A Veverka, Petr %T Necessary stochastic maximum principle for dissipative systems on infinite time horizon %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 337-371 %V 23 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015054/ %R 10.1051/cocv/2015054 %G en %F COCV_2017__23_1_337_0

Orrieri, Carlo; Veverka, Petr. Necessary stochastic maximum principle for dissipative systems on infinite time horizon. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 1, pp. 337-371. doi : 10.1051/cocv/2015054. http://archive.numdam.org/articles/10.1051/cocv/2015054/

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