Abstract
In a financial market, the appreciation rates of stocks are statistically difficult to estimate, and typically only some confidence intervals in which the rates reside can be estimated. In this paper we study continuous-time portfolio selection under ambiguity, in the sense that the appreciation rates are only known to be in a certain convex closed set and the portfolios are allowed to be based on only the historical stocks prices. We formulate the problem in both the expected utility and the mean--variance frameworks, and derive robust portfolios explicitly for both models.
Highlights
Portfolio selection has been studied in great width and depth since Markowitz [16] proposed the seminal mean–variance model
Formulated and studied in the last half century, including the expected utility maximization model and some generalization of the mean–variance model. In all those models built for portfolio selection, several parameters of the market, such as the stocks appreciation rates and volatility rates, must be specified in order to implement the optimal portfolios derived from the models
We study continuous-time portfolio selection under ambiguity, in the sense that the appreciation rates are only known to be in a certain convex closed set; namely, the model ambiguity lies in the values of the parameters rather than in the subjective priors
Summary
Portfolio selection has been studied in great width and depth since Markowitz [16] proposed the seminal mean–variance model. Formulated and studied in the last half century, including the expected utility maximization model and some generalization of the mean–variance model In all those models built for portfolio selection, several parameters of the market, such as the stocks appreciation rates and volatility rates, must be specified in order to implement the optimal portfolios derived from the models. We study continuous-time portfolio selection under ambiguity, in the sense that the appreciation rates are only known to be in a certain convex closed set; namely, the model ambiguity lies in the values of the parameters rather than in the subjective priors. With this setup we aim to derive explicit, rather than abstract, results.
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