Conditional Monte Carlo Estimation of Quantile Sensitivities

Estimating quantile sensitivities is important in many optimization applications, from hedging in financial engineering to service-level constraints in inventory control to more general chance constraints in stochastic programming. Recently, Hong (Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res. 57 118–130) derived a batched infinitesimal perturbation analysis estimator for quantile sensitivities, and Liu and Hong (Liu, G., L. J. Hong. 2009. Kernel estimation of quantile sensitivities. Naval Res. Logist. 56 511–525) derived a kernel estimator. Both of these estimators are consistent with convergence rates bounded by n −1/3 and n −2/5 , respectively. In this paper, we use conditional Monte Carlo to derive a consistent quantile sensitivity estimator that improves upon these convergence rates and requires no batching or binning. We illustrate the new estimator using a simple but realistic portfolio credit risk example, for which the previous work is inapplicable.

• 저널Management Science · 55(12) · 2019–2027
• 토픽Risk and Portfolio Optimization · Management Science and Operations Research
• DOI10.1287/mnsc.1090.1090
• 저자Michael C. Fu, L. Jeff Hong, Jian-Qiang Hu