Volume 24, Number 2, April–June 2018
|Page(s)||639 - 676|
|Published online||26 January 2018|
A maximum principle for controlled stochastic factor model
Department of Mathematics, University of Yaounde I, PO Box 812 Yaounde, Cameroon
2 African Institute for Mathematical Sciences, Biriwa, Ghana
3 University of Ghana, Accra, Ghana
4 Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, L69 7ZL, UK
a Corresponding author: firstname.lastname@example.org
Revised: 15 January 2017
Accepted: 11 August 2017
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.
Mathematics Subject Classification: 93E20 / 60H15
Key words: Stochastic partial differential equations / stochastic factor model / stochastic maximum principle / Zakai equation
© EDP Sciences, SMAI 2018
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