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2064. Bilevel models in portfolio selection problems

Invited abstract in session TC-34: Portfolio optimization , stream Stochastic, Robust and Distributionally Robust Optimization.

Tuesday, 12:30-14:00
Room: 43 (building: 303A)

Authors (first author is the speaker)

1. Monika Kaľatová
Department of Probability and Mathematical Statistics, Charles University
2. Milos Kopa
Department of Probability and Mathematical Statistics, Charles University in Prague, Faculty of Mathematics and Physics

Abstract

It is a common practice that an investor makes a decision based on not only in-sample efficiency, but also takes into account out-of-sample performance of the portfolios. To combine in-sample efficiency with out-of-sample optimality, one can employ a bilevel stochastic optimization problem. In our paper, the lower level of the problem consists of the mean-risk optimization model, where Conditional Value-at-Risk as a frequently used risk measure is applied. The upper level searches for in-sample efficient (lower level) portfolios with maximal out-of-sample performance (out-of-sample return).

The reformulation of the problem assuming a discrete probability distribution yields to a linear bilevel optimization problem. Additional assumption can be made about variables in the upper level. In a moving window analysis, these variables can vary or remain the same for all windows. Therefore, two linear bilevel optimization problems with multiple followers are considered. One of them can be split in time, the other one not. The results for these two cases will be presented.

Keywords

Status: accepted

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