Sequential $\delta$-optimal consumption and investment for stochastic volatility markets with unknown parameters

Belkacem Berdjane () and Sergey Pergamenshchikov ()
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Belkacem Berdjane: LMRS - Laboratoire de Mathématiques Raphaël Salem - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université - CNRS - Centre National de la Recherche Scientifique

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Abstract: We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic volatility and unknown stock appreciation rate. The volatility parameter is driven by an external economic factor modeled as a diffusion process of Ornstein-Uhlenbeck type with unknown drift. We use the dynamical programming approach and find an optimal financial strategy which depends on the drift parameter. To estimate the drift coefficient we observe the economic factor $Y$ in an interval $[0,T_0]$ for fixed $T_0>0$, and use sequential estimation. We show, that the consumption and investment strategy calculated through this sequential procedure is $\delta$-optimal.

Keywords: Sequential analysis; Truncate sequential estimate; Black-Scholes market model; Stochastic volatility; Optimal Consumption and Investment; Hamilton-Jacobi-Bellman equation (search for similar items in EconPapers)
Date: 2012-12-14
New Economics Papers: this item is included in nep-ore
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Working Paper: Sequential $\delta$-optimal consumption and investment for stochastic volatility markets with unknown parameters (2015)
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