On the Relation Between Option and Stock Prices: A Convex Optimization Approach
Operations Research
Probabilistic Combinatorial Optimization: Moments, Semidefinite Programming, and Asymptotic Bounds
SIAM Journal on Optimization
Introduction to Probability Models, Ninth Edition
Introduction to Probability Models, Ninth Edition
Analysis of particle interaction in particle swarm optimization
Theoretical Computer Science
TI: an efficient indexing mechanism for real-time search on tweets
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Hi-index | 0.00 |
In this article, we study the problem of finding tight bounds on the expected value of the kth-order statistic E [Xk:n] under first and second moment information on n real-valued random variables. Given means E [Xi] = &mgr;i and variances Var[Xi] = σi2, we show that the tight upper bound on the expected value of the highest-order statistic E [Xn:n] can be computed with a bisection search algorithm. An extremal discrete distribution is identified that attains the bound, and two closed-form bounds are proposed. Under additional covariance information Cov[Xi,Xj] = Qij, we show that the tight upper bound on the expected value of the highest-order statistic can be computed with semidefinite optimization. We generalize these results to find bounds on the expected value of the kth-order statistic under mean and variance information. For k n, this bound is shown to be tight under identical means and variances. All of our results are distribution-free with no explicit assumption of independence made. Particularly, using optimization methods, we develop tractable approaches to compute bounds on the expected value of order statistics.