A maximum principle for controlled stochastic factor model

Socgnia, Virginie Konlack; Pamen, Olivier Menoukeu

ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 495-517.

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.

Classification : 93E20, 60H15
Mots clés : Stochastic partial differential equations, stochastic factor model, stochastic maximum principle, Zakai equation

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