On the multi-dimensional portfolio optimization with stochastic volatility

Published in: Quaestiones Mathematicae
Volume 41, issue 1, 2018, pages: 27–40
DOI: 10.2989/16073606.2017.1369468
Author(s): Rodwell KufakunesuDepartment of Mathematics and Applied Mathematics, South Africa


In a recent paper by Mnif [18], a solution to the portfolio optimization with stochastic volatility and constraints problem has been proposed, in which most of the model parameters are time-homogeneous. However, there are cases where time-dependent parameters are needed, such as in the calibration of financial models. Therefore, the purpose of this paper is to generalize the work of Mnif [18] to the time-inhomogeneous case. We consider a time-dependent exponential utility function of which the objective is to maximize the expected utility from the investor’s terminal wealth. The derived Hamilton-Jacobi-Bellman(HJB) equation, is highly nonlinear and is reduced to a semilinear partial differential equation (PDE) by a suitable transformation. The existence of a smooth solution is proved and a verification theorem presented. A multi-asset stochastic volatility model with jumps and endowed with time-dependent parameters is illustrated.

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