In the present work, we consider an optimal control for a three-factor stochastic factor model. We assume that one of the factors is not observed and use classical filtering technique to transform the partial observation control problem for stochastic differential equation (SDE) to a full observation control problem for stochastic partial differential equation (SPDE). We then give a sufficient maximum principle for a system of controlled SDEs and degenerate SPDE. We also derive an equivalent stochastic maximum principle. We apply the obtained results to study a pricing and hedging problem of a commodity derivative at a given location, when the convenience yield is not observable.
Accepté le :
DOI : 10.1051/cocv/2017053
Mots-clés : Stochastic partial differential equations, stochastic factor model, stochastic maximum principle, Zakai equation
@article{COCV_2018__24_2_495_0,
author = {Socgnia, Virginie Konlack and Pamen, Olivier Menoukeu},
title = {A maximum principle for controlled stochastic factor model},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {495--517},
publisher = {EDP-Sciences},
volume = {24},
number = {2},
year = {2018},
doi = {10.1051/cocv/2017053},
mrnumber = {3816409},
zbl = {1401.93231},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2017053/}
}
TY - JOUR AU - Socgnia, Virginie Konlack AU - Pamen, Olivier Menoukeu TI - A maximum principle for controlled stochastic factor model JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 495 EP - 517 VL - 24 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2017053/ DO - 10.1051/cocv/2017053 LA - en ID - COCV_2018__24_2_495_0 ER -
%0 Journal Article %A Socgnia, Virginie Konlack %A Pamen, Olivier Menoukeu %T A maximum principle for controlled stochastic factor model %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 495-517 %V 24 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2017053/ %R 10.1051/cocv/2017053 %G en %F COCV_2018__24_2_495_0
Socgnia, Virginie Konlack; Pamen, Olivier Menoukeu. A maximum principle for controlled stochastic factor model. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 495-517. doi : 10.1051/cocv/2017053. http://www.numdam.org/articles/10.1051/cocv/2017053/
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