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Publication details

Empirical Estimates in Economic and Financial Optimization Problems

Journal Article

Houda Michal, Kaňková Vlasta

serial: Bulletin of the Czech Econometric Society vol.19, 29 (2012), p. 50-69

research: CEZ:AV0Z10750506

project(s): GAP402/10/1610, GA ČR, GAP402/11/0150, GA ČR, GAP402/10/0956, GA ČR

keywords: stochastic programming, empirical estimates, moment generating functions, stability, Wasserstein metric, L1-norm, Lipschitz property, consistence, convergence rate, normal distribution, Pareto distribution, Weibull distribution, distribution tails, simulation

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abstract (eng):

Many applications from economic and nancial practice lead to optimization problems depending on a probability measure. A complete knowledge of the underlying measure is a necessary assumption to determine an exact optimal solution and an exact optimal value. Since this condition is not usually fullled, the solution is often determined using empirical data. Estimates of the optimal value and the optimal solution sets can be obtained by this approach only. Many eorts has been paid to the investigation of the above mentioned estimates. Especially the consistency and the convergence rate have been investigated. However, it was mostly done for classical problems and underlying distributions with thin tails. The aim of this paper is to analyze these estimates from the point of the distribution tails. To this end, first, we recall some known results. We recall stability results based on the Wasserstein metric corresponding to L1 norm and employ them to the case of heavy tails.


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Last modification: 21.12.2012
Institute of Information Theory and Automation