Research project P 14194 Statistical data sensitivity in financial optimization Georg PFLUG 06.03.2000
We consider typical stochastic optimization problems appearing in finance, such as portfolio optimization
problems. Such problems contain unknown probability distributions, like the distribution of asset returns, interest
rates, exchange rates etc.
The optimal decisions depend on the probability distributions. However, these distributions are not completely
known and must be guessed by statistical models.
This leads in a natural way to the problem of the sensitivity of the optimal decision and of the optimal value with
respect to misspecifications or missestimations of the probability model.
We intend to derive results about the approximation error which results from replacing a theoretical distribution by
an empirical one, i.e. a distribution which stems from historical or simulated data. We assume that the data are
independent, Markov dependent or come from a stationary time series.
Results of uniform approximation errors exist for independent data and the expectation functional. We want to
extend these results not only in the direction of dependence but also to include much more general objective
functions than than just the expectation. Minimzing popular risk measures such as semivariances and values-at-risk
will be included in our considerations. Besides, new risk measures such as Yaari`s measures or those based on the
Minkowski gauge will also be studied.