Optimal portfolio allocation with volatility and co-jump risk that Markowitz would like

We study a continuous time optimal portfolio allocation problem with volatility and co-jump risk, allowing prices, variances and covariances to jump simultaneously. Differently from the traditional approach, we deviate from affine models by specifying a flexible Wishart jump-diffusion for the co-pre...

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Bibliographic Details
Published in:Journal of economic dynamics & control 2018-09, Vol.94, p.242-256
Main Authors: Oliva, I., Renò, R.
Format: Article
Language:English
Subjects:
Asset allocation
Co-jumps
Dynamic programming
Hedge funds
Stochastic volatility
Wishart process
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Summary:We study a continuous time optimal portfolio allocation problem with volatility and co-jump risk, allowing prices, variances and covariances to jump simultaneously. Differently from the traditional approach, we deviate from affine models by specifying a flexible Wishart jump-diffusion for the co-precision (the inverse of the covariance matrix). The optimal portfolio weights that solve the dynamic programming problem are genuinely dynamic and proportional to the instantaneous co-precision, reconciling optimal dynamic allocation with the static Markowitz-type economic intuition. An application to the optimal allocation problem across hedge fund investment styles illustrates the importance of having jumps in volatility associated with jumps in price.
ISSN:0165-1889
1879-1743
DOI:10.1016/j.jedc.2018.05.004