December 2013 Optimal portfolios for financial markets with Wishart volatility
Nicole Bäuerle, Zejing Li
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J. Appl. Probab. 50(4): 1025-1043 (December 2013). DOI: 10.1239/jap/1389370097


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, we do this 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 to identify when the solution of the Hamilton-Jacobi-Bellman equation is finite. This involves a couple of matrix analytic arguments. In a numerical study we discuss the influence of the investors' risk aversion on the hedging demand.


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Nicole Bäuerle. Zejing Li. "Optimal portfolios for financial markets with Wishart volatility." J. Appl. Probab. 50 (4) 1025 - 1043, December 2013.


Published: December 2013
First available in Project Euclid: 10 January 2014

zbMATH: 1283.93306
MathSciNet: MR3161371
Digital Object Identifier: 10.1239/jap/1389370097

Primary: 91G10 , 91G80 , 93E20

Keywords: CRRA utility , Hamilton-Jacobi-Bellman equation , matrix exponential , portfolio problem , Stochastic control , Wishart process

Rights: Copyright © 2013 Applied Probability Trust


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Vol.50 • No. 4 • December 2013
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