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Figure 1.1. Simulated mean reward—usual practice for calibration.the investor’s utility function values is taken over 50 bootstrap samples, attainingthe maximum atselection (ii) consists ofdata set at [34], and the average of the log-likelihood (y-axis) is
Figure 1.2. Bootstrap robust mean-variance frontiers of the two examples.The above plots show the relation between the mean and the variance of the sim-ulated reward through bootstrap
Figure 8.1. Out-of-sample robust mean variance frontiers fordata points, and the true frontier generated by solutions of DRO under the datagenerating model for different values of the robustness parameter n = 10, 30 and 50 δ.
Figure 8.3. Bootstrap frontier vs out-of-sample frontier (with normalization).Both frontiers are scaled and normalized so that both the mean and variance equal1 when δ = 0 (i.e., empirical optimization) and 0 in the most robust case (δ = 100).We see that as n increases, the points on the frontier corresponding to the samevalues of δ converge.
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