Decision, Operations & Information Technologies Research Works

Permanent URI for this collectionhttp://hdl.handle.net/1903/1588

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A Large Deviations Analysis of Quantile Estimation with Application to Value at Risk
(2005-07-01T12:31:49Z) Jin, Xing; Fu, Michael C.
Quantile estimation has become increasingly important, particularly in the financial industry, where Value-at-Risk has emerged as a standard measurement tool for controlling portfolio risk. In this paper we apply the theory of large deviations to analyze various simulation-based quantile estimators. First, we show that the coverage probability of the standard quantile estimator converges to one exponentially fast with sample size. Then we introduce a new quantile estimator that has a provably faster convergence rate. Furthermore, we show that the coverage probability for this new estimator can be guaranteed to be 100% with sufficiently large, but finite, sample size. Numerical experiments on a VaR example illustrate the potential for dramatic variance reduction.
Stochastic Gradient Estimation
(2005-07-01T12:31:02Z) Fu, Michael C.
We consider the problem of efficiently estimating gradients from stochastic simulation. Although the primary motivation is their use in simulation optimization, the resulting estimators can also be useful in other ways, e.g., sensitivity analysis. The main approaches described are finite differences (including simultaneous perturbations), perturbation analysis, the likelihood ratio/score function method, and the use of weak derivatives.