Kufakunesu, Rodwell2018-10-302018-10-302018Rodwell Kufakunesu (2018) On the multi-dimensional portfolio optimization with stochastic volatility, Quaestiones Mathematicae, 41:1, 27-40, DOI: 10.2989/16073606.2017.1369468.1607-3606 (print)1727-933X (online)10.2989/16073606.2017.1369468http://hdl.handle.net/2263/67105In 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.en© 2017 NISC (Pty) Ltd. This is an electronic version of an article published in Quaestiones Mathematicae, vol. 41, no. 1, pp. 27-40, 2018. doi : 10.2989/16073606.2017.1369468. Quaestiones Mathematicae is available online at : http://www.tandfonline.comloi/tqma20.Partial differential equation (PDE)Stochastic volatilitySmooth solutionHamilton-Jacobi-Bellman (HJB)Hamilton-Jacobi-Bellman equationTime-dependentUtility optimizationPostprint Article