Optimal Portfolio with Nonparametric Learning
نویسندگان
چکیده
We consider the optimal investment-consumption problem with an unknown distribution for the investment returns. After taking the Bayesian approach, the problem is formulated as a Markov decision process in a nonparametric context. We discuss the existence of the optimal strategy and derive the closed form solution of the optimal portfolio. When the prior distribution is a Dirichlet process, the optimal portfolio is based on both the prior guess of the unknown distribution and the empirical distribution. This provides the rationale for the use of empirical distribution when making investment-consumption decisions.
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