An optimal consumption model with stochastic volatility

Wendell H. Fleming () and Daniel Hernández-Hernández ()
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Wendell H. Fleming: Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Daniel Hernández-Hernández: Centro de Investigación en Matemáticas, Apartado Postal 402, Guanajuato, Gto. 36000, México Manuscript

Finance and Stochastics, 2003, vol. 7, issue 2, 245-262

Abstract: We consider an optimal consumption and investment model in continuous time, which is an extension of the original Merton's problem. In the proposed model, the asset prices are affected by correlated economic factors, modelled as diffusion processes. Writing the value function in a special form, it can be seen that another optimal control problem is involved and studying its associated HJB equation smoothness properties of the original value function can be derived as well as optimal policies.

Keywords: Stochastic volatility; portfolio optimization; factor modelling; mean reverting (search for similar items in EconPapers)
JEL-codes: C6 E2 G1 (search for similar items in EconPapers)
Date: 2002-12-10
Note: received: November 2001; final version received: May 2002
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