On the multi-dimensional portfolio optimization with stochastic volatility

dc.contributor.authorKufakunesu, Rodwell
dc.contributor.emailrodwell.kufakunesu@up.ac.zaen_ZA
dc.date.accessioned2018-10-30T05:39:44Z
dc.date.available2018-10-30T05:39:44Z
dc.date.issued2018
dc.description.abstractIn 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.departmentMathematics and Applied Mathematicsen_ZA
dc.description.librarianhj2018en_ZA
dc.description.sponsorshipThe NRF (CSUR) Grant No: 90313.en_ZA
dc.description.urihttp://www.tandfonline.com/loi/tqma20en_ZA
dc.identifier.citationRodwell 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.issn1607-3606 (print)
dc.identifier.issn1727-933X (online)
dc.identifier.other10.2989/16073606.2017.1369468
dc.identifier.urihttp://hdl.handle.net/2263/67105
dc.language.isoenen_ZA
dc.publisherTaylor and Francisen_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.subjectPartial differential equation (PDE)en_ZA
dc.subjectStochastic volatilityen_ZA
dc.subjectSmooth solutionen_ZA
dc.subjectHamilton-Jacobi-Bellman (HJB)en_ZA
dc.subjectHamilton-Jacobi-Bellman equationen_ZA
dc.subjectTime-dependenten_ZA
dc.subjectUtility optimizationen_ZA
dc.titleOn the multi-dimensional portfolio optimization with stochastic volatilityen_ZA
dc.typePostprint Articleen_ZA

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