This is Manan Shah's PhD dissertation on Amazon. (external link)
Read thoughts from our book (in draft) on benign neglect and micromanagement. What causes benign neglect? What does micromanagement lead to? How do we keep these mismanagement traits away? (.pdf downloads)
The papers given below all have Manan Shah as an author. These papers are published in peer-reviewed journals.
Finding a good set of random numbers is hard. This paper shows that random permutations of the Halton sequence gives faster convergence than standard Monte Carlo simulation. It also demonstrates that random permutations combined with the random-start method effectively eliminate high-dimensional correlation — an important requirement when evalauting high-dimensional functions. (external link)
Valuing mortgages under a variety of stochastic factors such as prepayment, default, interest rate risk, etc. requires the use of good random numbers in a high-dimensional space. This paper shows that randomized quasi-Monte Carlo methods are a viable solution. Additionally, the rate of convergence is considerably faster than standard Monte Carlo. (external link)
The star-discrepancy is a measure of uniformity for points on an n-dimensional hypercube. This measure can be used to rate the quality of uniformity of quasi-random points. This paper gives a novel algorithm for estimating the star-discrepancy. (external link)
An introductory article about why programming and simulation are essential requirements for today's student (external link)
A non-technical introduction to Monte Carlo methods (.pdf download)