Sample Average Approximation Method for Chance Constrained ...

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1.011.0051.00.99530 80 130 1800.10.0750.050.0250.0Figure 7: γN-plot <strong>for</strong> the portfolio problem with normal returns.1.006.950.956.450.905.5 6.0 6.5 7.0 7.55.955.450.02560801000.051200.075 1400.1Figure 8: Blending problem, γ = 0.025.Figure 9: γN-plot (blending problem).36
Page 1 and 2: Sample Average Approximation Method
Page 4 and 5: distribution in chance constraint b
Page 6 and 7: Carathéodory function, i.e., G(x,
Page 8 and 9: (i) for any sequence x k converging
Page 10 and 11: y a version of the uniform law of l
Page 12 and 13: f(¯x) ≥ ϑ ∗ . Also f(ˆx N )
Page 14 and 15: us choose two positive integers M a
Page 16 and 17: Note that, of course, E [ r T x ] =
Page 18 and 19: problem (5), with γ = 0, to be inf
Page 20 and 21: estimation of the parameters was ta
Page 22 and 23: original problem, we observe in Fig
Page 24 and 25: 3.3 Upper BoundsA method to compute
Page 26 and 27: priate choice of the parameters sin
Page 28 and 29: It is possible to write the SAA of
Page 30 and 31: 5 ConclusionsWe have discussed chan
Page 32 and 33: References1. Charnes, A., Cooper, W
Page 34 and 35: 15. Markowitz, H.: Portfolio select

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