Multivariate Portfolio Choice via Quantiles
Abstract
Agents who optimize a univariate law-invariant increasing objective (e.g., an expected utility, a Cumulative Prospect Theory objective function) obtain optimal payoffs that are decreasing in the pricing kernel. Such observation plays a key role in the theory developed by He and Zhou (2011) on ``Portfolio Choice via Quantiles’’. In this paper, we first show how it is possible to extend this quantile approach to solve a multivariate optimal portfolio for some multivariate preferences (e.g., multivariate expected utility, inf-convolution of tail risk measures). Second, we develop a new approach allowing us to solve the multivariate optimal portfolio problem numerically. This is based on joint papers with Luca Aquino De Gennaro, Andrea Perchiazzo and Steven Vanduffel.
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