In this work we study the stochastic recursive control problem, in which the aggregator (or generator) of the backward stochastic differential equation describing the running cost is continuous but not necessarily Lipschitz with respect to the first unknown variable and the control, and monotonic with respect to the first unknown variable. The dynamic programming principle and the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation are established in this setting by the generalized comparison theorem for backward stochastic differential equations and the stability of viscosity solutions. Finally we take the control problem of continuous-time Epstein−Zin utility with non-Lipschitz aggregator as an example to demonstrate the application of our study.
Accepted:
DOI: 10.1051/cocv/2017016
Keywords: Stochastic recursive control problem, non-Lipschitz aggregator, dynamic programming principle, Hamilton-Jacobi-Bellman equation, continuous-time Epstein−Zin utility, viscosity solution
@article{COCV_2018__24_1_355_0, author = {Pu, Jiangyan and Zhang, Qi}, title = {Dynamic programming principle and associated {Hamilton-Jacobi-Bellman} equation for stochastic recursive control problem with {non-Lipschitz} aggregator}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {355--376}, publisher = {EDP-Sciences}, volume = {24}, number = {1}, year = {2018}, doi = {10.1051/cocv/2017016}, mrnumber = {3843188}, zbl = {1396.93135}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017016/} }
TY - JOUR AU - Pu, Jiangyan AU - Zhang, Qi TI - Dynamic programming principle and associated Hamilton-Jacobi-Bellman equation for stochastic recursive control problem with non-Lipschitz aggregator JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 355 EP - 376 VL - 24 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017016/ DO - 10.1051/cocv/2017016 LA - en ID - COCV_2018__24_1_355_0 ER -
%0 Journal Article %A Pu, Jiangyan %A Zhang, Qi %T Dynamic programming principle and associated Hamilton-Jacobi-Bellman equation for stochastic recursive control problem with non-Lipschitz aggregator %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 355-376 %V 24 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017016/ %R 10.1051/cocv/2017016 %G en %F COCV_2018__24_1_355_0
Pu, Jiangyan; Zhang, Qi. Dynamic programming principle and associated Hamilton-Jacobi-Bellman equation for stochastic recursive control problem with non-Lipschitz aggregator. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 1, pp. 355-376. doi : 10.1051/cocv/2017016. http://archive.numdam.org/articles/10.1051/cocv/2017016/
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