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2426. Measures of Stochastic Non-Dominance
Invited abstract in session TC-34: Portfolio optimization , stream Stochastic, Robust and Distributionally Robust Optimization.
Tuesday, 12:30-14:00Room: 43 (building: 303A)
Authors (first author is the speaker)
| 1. | Jana Junova
|
| Department of Probability and Mathematical Statistics, Charles University MFF | |
| 2. | Milos Kopa
|
| Department of Probability and Mathematical Statistics, Charles University in Prague, Faculty of Mathematics and Physics |
Abstract
We introduce measures of stochastic non-dominance to provide insights in situations when stochastic dominance between two random variables does not hold. They quantify how far a given random variable is from dominating a benchmark random variable by a specified order stochastic dominance. They are found by solving an optimization problem that searches for an optimal random variable, which is as close as possible to the given one but dominates the benchmark. The measure of stochastic non-dominance is then the Wasserstein distance between the optimal and the given random variable. Depending on the assumptions imposed on the optimal variable, we distinguish the general and the specific measures of stochastic non-dominance.
We derive closed-form expressions of the measures of stochastic non-dominance under various parametric assumptions. Moreover, we present relations to selected types of almost stochastic dominance. Finally, a formula is derived for the computation of the measures of stochastic non-dominance for discrete distributions with equiprobable atoms. It is applied to portfolio optimization problems in the empirical part.
Keywords
- Stochastic Optimization
- Robust Optimization
Status: accepted
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