# Measures of risk in stochastic optimization

Thursday, October 21, 2010 - 9:30am - 10:30am

Keller 3-180

R. Tyrrell Rockafellar (University of Washington)

A fundamental difficulty in stochastic optimization is the fact that

decisions may not be able pin down the values of future costs, but

rather can only, within limits, shape their distributions as random variables.

An upper bound on a ramdom cost is often impossible, or too expensive, to

enforce with certainty, and so some compromise attitude must be taken to

the violations that might occur. Similarly, there is no instant

interpretation of what it might mean to minimize a random cost, apart

from trying to determine a lowest threshold which would be exceeded only

to an acceptable degree.

Clearly, it is essential in this picture to have a

theoretical framework which provides guidelines about preferences and

elucidates their mathematical pros and cons. Measures of risk, coming from financial mathematics but finding uses

also in engineering, are the key. Interestingly, they relate also to

concepts in statistics and estimation. For example, standard deviation

can be replaced by a generalized measure of deviation which is not

symmetric between ups and downs, as makes sense in applications in which

overestimation may be riskier than underestimation.

decisions may not be able pin down the values of future costs, but

rather can only, within limits, shape their distributions as random variables.

An upper bound on a ramdom cost is often impossible, or too expensive, to

enforce with certainty, and so some compromise attitude must be taken to

the violations that might occur. Similarly, there is no instant

interpretation of what it might mean to minimize a random cost, apart

from trying to determine a lowest threshold which would be exceeded only

to an acceptable degree.

Clearly, it is essential in this picture to have a

theoretical framework which provides guidelines about preferences and

elucidates their mathematical pros and cons. Measures of risk, coming from financial mathematics but finding uses

also in engineering, are the key. Interestingly, they relate also to

concepts in statistics and estimation. For example, standard deviation

can be replaced by a generalized measure of deviation which is not

symmetric between ups and downs, as makes sense in applications in which

overestimation may be riskier than underestimation.

MSC Code:

93E 20

Keywords: