On the multi-dimensional portfolio optimization with stochastic volatility

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dc.contributor.author Kufakunesu, Rodwell
dc.date.accessioned 2018-10-30T05:39:44Z
dc.date.available 2018-10-30T05:39:44Z
dc.date.issued 2018
dc.description.abstract 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. en_ZA
dc.description.department Mathematics and Applied Mathematics en_ZA
dc.description.librarian hj2018 en_ZA
dc.description.sponsorship The NRF (CSUR) Grant No: 90313. en_ZA
dc.description.uri http://www.tandfonline.com/loi/tqma20 en_ZA
dc.identifier.citation Rodwell Kufakunesu (2018) On the multi-dimensional portfolio optimization with stochastic volatility, Quaestiones Mathematicae, 41:1, 27-40, DOI: 10.2989/16073606.2017.1369468. en_ZA
dc.identifier.issn 1607-3606 (print)
dc.identifier.issn 1727-933X (online)
dc.identifier.other 10.2989/16073606.2017.1369468
dc.identifier.uri http://hdl.handle.net/2263/67105
dc.language.iso en en_ZA
dc.publisher Taylor and Francis en_ZA
dc.rights © 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. en_ZA
dc.subject Partial differential equation (PDE) en_ZA
dc.subject Stochastic volatility en_ZA
dc.subject Smooth solution en_ZA
dc.subject Hamilton-Jacobi-Bellman (HJB) en_ZA
dc.subject Hamilton-Jacobi-Bellman equation en_ZA
dc.subject Time-dependent en_ZA
dc.subject Utility optimization en_ZA
dc.title On the multi-dimensional portfolio optimization with stochastic volatility en_ZA
dc.type Postprint Article en_ZA


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