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Optimal portfolios for financial markets with Wishart volatility

Bäuerle, Nicole; Li, Zejing

We consider a multi asset financial market with stochastic volatility modeled by a Wishart process. This is an extension of the one-dimensional Heston model. Within this framework we study the problem of maximizing the expected utility of terminal wealth for power and logarithmic utility. We apply the usual stochastic control approach and obtain explicitly the optimal portfolio strategy and the value function in some parameter settings. In particular when the drift of the assets is a linear function of the volatility matrix. In this case the affine structure of the model can be exploited. In some cases we obtain a Feynman-Kac representation of the candidate value function. Though the approach we use is quite standard, the hard part is indeed to identify when the solution of the HJB equation is finite. This involves a couple of matrix analytic arguments. In a numerical study we discuss the in uence of the investors' risk aversion on the hedging demand.

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DOI: 10.5445/IR/1000039668
DOI: 10.1239/jap/1389370097
Zitationen: 17
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Jahr 2013
Sprache Englisch
Identifikator ISSN: 0021-9002
KITopen-ID: 1000039668
Erschienen in Journal of applied probability
Band 50
Heft 4
Seiten 1025-1043
Schlagworte Wishart Process, Portfolio Problem, CRRA Utility, Stochastic Control, HJB Equation, Matrix Exponential
Nachgewiesen in Scopus
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