On the multi-dimensional portfolio optimization with stochastic volatility
dc.contributor.author | Kufakunesu, Rodwell | |
dc.contributor.email | rodwell.kufakunesu@up.ac.za | en_ZA |
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 |