Decision, Operations & Information Technologies Research Works

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

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Online Appendix for “Gradient-Based Myopic Allocation Policy: An Efficient Sampling Procedure in a Low-Confidence Scenario”
(2017) Peng, Yijie; Chen, Chun-Hung; Fu, Michael; Hu, Jian-Qiang
This is the online appendix, which includes theoretical and numerical supplements containing some technical details and three additional numerical examples, which could not fit in the main body due to page limits by the journal for a technical note. The abstract for the main body is as follows: In this note, we study a simulation optimization problem of selecting the alternative with the best performance from a finite set, or a so-called ranking and selection problem, in a special low-confidence scenario. The most popular sampling allocation procedures in ranking and selection do not perform well in this scenario, because they all ignore certain induced correlations that significantly affect the probability of correct selection in this scenario. We propose a gradient-based myopic allocation policy (G-MAP) that takes the induced correlations into account, reflecting a trade-off between the induced correlation and the two factors (mean-variance) found in the optimal computing budget allocation formula. Numerical experiments substantiate the efficiency of the new procedure in the low-confidence scenario.
Online Supplement to `Efficient Simulation Resource Sharing and Allocation for Selecting the Best'
(2012) Peng, Yijie; Chen, Chun-Hung; Fu, Michael; Hu, Jian-Qiang
This is the online supplement to the article by the same authors, "Efficient Simulation Resource Sharing and Allocation for Selecting the Best," published in the IEEE Transactions on Automatic Control.
Sensitivity Analysis for Monte Carlo Simulation of Option Pricing
(1995) Fu, Michael C.; Hu, Jian-Qiang
Monte Carlo simulation is one alternative for analyzing options markets when the assumptions of simpler analytical models are violated. We introduce techniques for the sensitivity analysis of option pricing which can be efficiently carried out in the simulation. In particular, using these techniques, a single run of the simulation would often provide not only an estimate of the option value but also estimates of the sensitivities of the option value to various parameters of the model. Both European and American options are considered, starting with simple analytically tractable models to present the idea and proceeding to more complicated examples. We then propose an approach for the pricing of options with early exercise features by incorporating the gradient estimates in an iterative stochastic approximation algorithm. The procedure is illustrated in a simple example estimating the option value of an American call. Numerical results indicate that the additional computational effort required over that required to estimate a European option is relatively small.