Local stability and differentiability of the Mean–Conditional Value at Risk model defined on the mixed–integer loss functions

Branda, Martin. "Local stability and differentiability of the Mean–Conditional Value at Risk model defined on the mixed–integer loss functions." Kybernetika 46.3 (2010): 362-373. <http://eudml.org/doc/196376>.

@article{Branda2010,
abstract = {In this paper, we study local stability of the mean-risk model with Conditional Value at Risk measure where the mixed-integer value function appears as a loss variable. This model has been recently introduced and studied in~Schulz and Tiedemann [16]. First, we generalize the qualitative results for the case with random technology matrix. We employ the contamination techniques to quantify a possible effect of changes in the underlying probability distribution on the optimal value. We use the generalized qualitative results to express the explicit formula for the directional derivative of the local optimal value function with respect to the underlying probability measure. The derivative is used to construct the bounds. Similarly, we can approximate the behavior of the local optimal value function with respect to the changes of the risk-aversion parameter which determines our aversion to risk.},
author = {Branda, Martin},
journal = {Kybernetika},
keywords = {mean-CVaR model; mixed-integer value function; stability analysis; contamination techniques; derivatives of optimal value function; contamination techniques; derivatives of optimal value function},
language = {eng},
number = {3},
pages = {362-373},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Local stability and differentiability of the Mean–Conditional Value at Risk model defined on the mixed–integer loss functions},
url = {http://eudml.org/doc/196376},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Branda, Martin
TI - Local stability and differentiability of the Mean–Conditional Value at Risk model defined on the mixed–integer loss functions
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 3
SP - 362
EP - 373
AB - In this paper, we study local stability of the mean-risk model with Conditional Value at Risk measure where the mixed-integer value function appears as a loss variable. This model has been recently introduced and studied in~Schulz and Tiedemann [16]. First, we generalize the qualitative results for the case with random technology matrix. We employ the contamination techniques to quantify a possible effect of changes in the underlying probability distribution on the optimal value. We use the generalized qualitative results to express the explicit formula for the directional derivative of the local optimal value function with respect to the underlying probability measure. The derivative is used to construct the bounds. Similarly, we can approximate the behavior of the local optimal value function with respect to the changes of the risk-aversion parameter which determines our aversion to risk.
LA - eng
KW - mean-CVaR model; mixed-integer value function; stability analysis; contamination techniques; derivatives of optimal value function; contamination techniques; derivatives of optimal value function
UR - http://eudml.org/doc/196376
ER -