bv_cvxbook_extra_exercises

Examples of such distributions include the standard

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: + R2 , and the probability of a loss (including breaking even, i.e., R1 + R2 = 0) is ploss = prob(R1 + R2 ≤ 0). The goal is to find the worst-case (i.e., maximum possible) value of ploss , consistent with the following information. Both R1 and R2 have Gaussian marginal distributions, with known means µ1 and µ2 and known standard deviations σ1 and σ2 . In addition, it is known that R1 and R2 are correlated with correlation coefficient ρ, i.e., E(R1 − µ1 )(R2 − µ2 ) = ρσ1 σ2 . Your job is to find the worst-case ploss over any joint distribution of R1 and R2 consistent with the given marginals and correlation coefficient. We will consider the specific case with data µ1 = 8, µ2 = 20, σ1 = 6, 56 σ2 = 17.5, ρ = −0.25. We can compare the results to the case when R1 and R2 are jointly Gaussian. In this case we have 2 2 R1 + R2 ∼ N (µ1 + µ2 , σ1 + σ2 + 2ρσ1 σ2 ), which for the data given above gives ploss = 0.050. Your job is to see how much larger ploss can possibly be. This is an infinite-dimensional optimization pr...
View Full Document

Ask a homework question - tutors are online