Conditional Monte Carlo Estimation of Quantile Sensitivities

Management Science (Impact Factor: 2.48). 12/2009; 55(12):2019-2027. DOI: 10.1287/mnsc.1090.1090
Source: DBLP


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.

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Available from: L. Jeff Hong, Oct 01, 2015
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    • "θ, which is not the case in (3) since indicator functions induce discontinuities on the boundary of the corresponding sets. It is worth noting that under appropriate additional conditions IPA can be applied to this type of problems, see [12] [11] [9]. In general, however, to be able to deal with discontinuities of sample path functions, an extension of IPA, called smoothed perturbation analysis (SPA), has been applied that integrates out discontinuities. "

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