Optimizing Optimization: The Next Generation of Optimization Applications and Theory (Quantitative Finance)
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© Elsevier Limited. All rights reserved. Doi:10.1016/B978-0-12-374952-9.00010-5. 2010 Some properties of averaging simulated opt ...
226 Optimizing Optimization terms of absolute, i.e., unbenchmarked, portfolios. These portfolios are typically unconstrained; th ...
Some properties of averaging simulated optimization methods 227 Compute efficient frontier portfolios ... Repeat steps 1 – 3 50 ...
228 Optimizing Optimization straightforward to see that as λ ranges from 0 to ∞ , we move down the fron- tier from the maximum e ...
Some properties of averaging simulated optimization methods 229 It is straightforward to compute the information ratio defined a ...
230 Optimizing Optimization 10.4 Section 3: Finite sample properties of estimators of alpha and tracking error To compute the bi ...
Some properties of averaging simulated optimization methods 231 where the two χ 2 variables in Equation (10.7) are independent. ...
232 Optimizing Optimization and E k (( ) )k k k () χ() , ν ν ν ν 2 2 22 2 Γ Γ () / Eg ekk F N k N k T ThN [] N () ,; ...
Some properties of averaging simulated optimization methods 233 For other quantiles, we have: ETE F N Th N () N () ,; ...
234 Optimizing Optimization The corresponding results for^ IR^ and^ TE are given by: EIR n nh n () () → ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ 1 ⎟⎟ 1 1 ...
Some properties of averaging simulated optimization methods 235 and thus αμω μμ βλ γ λ μ ˆ ˆ ˆˆˆ ˆ ˆ (^1) ΩΩ^11 ˆˆ ⎛ ...
236 Optimizing Optimization 10.6 Remark 3 A similar analysis to that outlined above could be undertaken for other port- folios. ...
Some properties of averaging simulated optimization methods 237 (i) Q a β βγ ⎛ ⎝ ⎜⎜ ⎜⎜ ⎞ ⎠ ⎟⎟ ⎟⎟ ⎛ ⎝ ⎜⎜ ⎜⎜ ⎞ ⎠ ⎟⎟ ⎟⎟ 0 125 6 ...
238 Optimizing Optimization θ : h 16, λ 2 h 4, λ 12.5 α 0.03125 TE 0.125 IR 0.25 α 0.02 TE 0.04 IR 0.5 NE4( ...
Some properties of averaging simulated optimization methods 239 where QR RˆK(ˆ,μμ)Ωˆ^1 (ˆ, ) with QWTNKˆ (,) T KK^1 1 ...
240 Optimizing Optimization That is, for K 1, hh ak 11 (/)βγ^211 ^1 and when Khha (^2) K 21211 12 12 22 1 1 2 ,( ββ) γ ...
Some properties of averaging simulated optimization methods 241 u , y , and v such that all four vectors together satisfy the ab ...
242 Optimizing Optimization with ∂ ∂ ∂ ∂ ∂ ∂ L i L L i ω ωθμθ θ μω π θ ω Ω 12 1 2 0 0 10 Consequently, ωμ θ θ ...
Some properties of averaging simulated optimization methods 243 Next , letting Q ab bc ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ we have: Ψ^121 ...
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