Robust Portfolio Optimization with Multi-Factor Stochastic Volatility
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Robust Portfolio Optimization with Multi-Factor Stochastic Volatility Ben-Zhang Yang1 · Xiaoping Lu2
· Guiyuan Ma3 · Song-Ping Zhu2
Received: 13 November 2019 / Accepted: 13 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper studies a robust portfolio optimization problem under a multi-factor volatility model. We derive optimal strategies analytically under the worst-case scenario with or without derivative trading in complete and incomplete markets and for assets with jump risk. We extend our study to the case with correlated volatility factors and propose an analytical approximation for the robust optimal strategy. To illustrate the effects of ambiguity, we compare our optimal robust strategy with the strategies that ignore the information of uncertainty, and provide the welfare analysis. We also discuss how derivative trading affects the optimal strategies. Finally, numerical experiments are provided to demonstrate the behavior of the optimal strategy and the utility loss. Keywords Robust portfolio selection · Multi-factor volatility · Jump risks · Non-affine stochastic volatility · Ambiguity effect Mathematics Subject Classification 91B28 · 60H30 · 91C47 · 91B70
Communicated by Kok Lay Teo.
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Xiaoping Lu [email protected] Ben-Zhang Yang [email protected] Guiyuan Ma [email protected] Song-Ping Zhu [email protected]
1
Department of Mathematics, Sichuan University, Chengdu, China
2
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, Australia
3
Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China
123
Journal of Optimization Theory and Applications
1 Introduction During the past decades, various stochastic volatility models have been proposed to explain volatility smile, to address term structure effects, and to describe more complex financial markets (for example, [1–10]). Stochastic volatility models also address term structure effects by modeling the mean reversion in variance dynamics. The existing literature includes not only one-factor stochastic volatility model, such as [11–13], but also multi-factor stochastic volatility model, such as [14–16]. Optimal portfolio selection problems with multi-factor volatility have attracted a lot of attention in the recent literature, with the view of multi-factor models potentially capturing market volatility better than classical single-factor models. Escobar et al. [17] considered an optimal investment problem under a multi-factor stochastic volatility. Assuming that the eigenvalues of the covariance matrix of asset returns follow independent square-root stochastic processes, they derived the optimal investment strategies in closed form. In practice, investors quite often face model uncertainty about the probability distribution of the dynamic process [18–20]. As a result, an investor may consider a robust alternative model for the stock and its volatilities to avoid missspecification, when making investment decisions [21,22]. The investor should a
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