1. P. Acworth and M. Broadie and P. Glasserman. A Comparison of some Monte Carlo and quasi Monte Carlo techniques for option pricing. preprint, 1997.

   Google Scholar 

2. L. Andersen and M. Broadie. A primal-dual simulation algorithm for pricing multi-dimensional American options. Working Paper, Columbia U., 2001.

   Google Scholar 

3. F. Black and M. Scholes. The pricing of options and corporate liabilities. J. Political Economy, 81: 637 - 654, 1973.

   Article  Google Scholar 

4. P. Bratley, B. L. Fox and H. Niederreiter. Algorithm 738 - Programs to generate Niederreiters discrepancy sequences. ACM Transactions on Math. Software, 20: 494 - 495, 1994.

   Article MATH  Google Scholar 

5. M. Broadie and P. Glasserman. Pricing American-style securities using simulation. Journal of Economic Dynamics & Control, (21):1323– 1352, 1997.

   Google Scholar 

6. R.E. Caflisch. Monte Carlo and Quasi-Monte Carlo Methods. Acta Numerica, pages 1 - 49, 1998.

   Google Scholar 

7. R.E. Caflisch and N. Goldenfeld. private communication. 2003.

   Google Scholar 

8. S.K. Chaudhary. American options and the LSM algorithm: Quasi-random sequences and Brownian bridges. 2003.

   Google Scholar 

9. S.K. Chaudhary. Numerical upper bounds on Bermudan puts using martingales, the lattice and the LSM. 2003.

   Google Scholar 

10. J.D. Evans and R. Kuske and J.B. Keller. American options on assets with dividends near expiry. Math. Finance, 12: 219 - 237, 2002.

    Article MathSciNet MATH  Google Scholar 

11. Henri Faure. Discrépance de Suites Associées à un système de Numération (en Dimension s). Acta Arithmetica, 41: 337 - 351, 1982.

    MathSciNet MATH  Google Scholar 

12. J. H. Halton. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik, 2: 84 - 90, 1960.

    Article MathSciNet  Google Scholar 

13. C.B. Haselgrove. A method for numerical integration. Mathematical Computing, 15: 323 - 337, 1961.

    Article MathSciNet MATH  Google Scholar 

14. L. K. Hua and Y. Wang. Applications of Number Theory to Numerical Analysis. Springer-Verlag, Berlin; New York, 1981.

    Google Scholar 

15. I. Karatzas and S. E. Shreve Brownian Motion and Stochastic Calculus. Springer, New York, 1991.

    Google Scholar 

16. W. J. Kennedy and J. E. Gentle. Statistical Computing. Dekker, New York, 1980.

    MATH  Google Scholar 

17. L. Kogan and M. Haugh. Pricing American options: A duality approach. MIT Sloan School of Management, Working Paper 4340 - 01, 2001.

    Google Scholar 

18. D. Lamper and S. Howison. private communication. 2002.

    Google Scholar 

19. F.A. Longstaff and E.S. Schwartz. Valuing American options by simulation: a simple least-squares approach. The Review of Financial Studies, 14 (1): 113 - 147, Spr 2001.

    Google Scholar 

20. G. Marsaglia. Normal (Gaussian) random variables for supercomputers. The Journal of Supercomputing, 5: 49 - 55, 1991.

    Article MATH  Google Scholar 

21. R.C. Merton. The theory of rational option pricing. Bell J. Econ. Manag. Science, 4: 141 - 183, 1973.

    MathSciNet  Google Scholar 

22. W. Morokoff and R.E. Caflisch. A quasi-Monte Carlo approach to particle simulation of the heat equation. SIAM Journal of Numerical Analysis, 30: 1558 - 1573, 1993.

    Article MathSciNet MATH  Google Scholar 

23. W. Morokoff and R.E. Caflisch. Quasi-random sequences and their discrepancies. SIAM Journal of Scientific and Statistical Computing, 15: 1251 - 79, 1994.

    Article MathSciNet MATH  Google Scholar 

24. W. Morokoff and R.E. Caflisch. Quasi-Monte Carlo integration. Journal of Computational Physics, 112: 218 - 30, 1995.

    Article MathSciNet  Google Scholar 

25. B. Moskowitz and R.E.Caflisch. Smoothness and dimension reduction in quasi-Monte Carlo methods. Journal of Mathematical Computer Modelling, 23: 37 - 54, 1996.

    Article MathSciNet MATH  Google Scholar 

26. H. Niederreiter. Random number generation and quasi-Monte Carlo method. SIAM, Philadelphia, 1992.

    Google Scholar 

27. A. B. Owen. Monte Carlo Variance of scrambled net quadrature. SIAM Journal of Numerical Analysis, 34: 1884 - 1910, 1997.

    Article MathSciNet MATH  Google Scholar 

28. W. H. Press and S. A. Teukolsky and W. T. Vettering and B. P. Flannery. Numerical Recipes in C. The Art of Scientific Computing, Second Edition. Cambridge U. Press, 1992.

    Google Scholar 

29. L. C. G. Rogers. Monte Carlo Valuation of American Options. Mathematical Finance, (12): 271 - 286, 2002.

    Google Scholar 

30. I.M. Sobol’. Uniformly distributed sequences with additional uniformity property. U.S.S.R. Computational Math. and Math. Phys., 16: 1332 - 1337, 1976.

    MathSciNet  Google Scholar 

31. J. Spanier and E. H. Maize. Quasi-random methods for estimating integrals using relatively small samples. SIAM Review, 36: 18 - 44, 1994.

    Article MathSciNet MATH  Google Scholar 

32. L. Stentoft. Convergence of the Least-Squares Monte Carlo Approach to American Option Valuation. Center for Analytical Finance Working Paper Series 113, University of Aarhus School of Business, 2002.

    Google Scholar 

33. J. A. Tsitsiklis and B. Van Roy. Optimal stopping of Markov processes: Hilbert space theory, approximation algorithms, and an application to pricing high-dimensional financial derivatives. IEEE Transactions on Automatic Control, 44: 1840 - 1851, 1999.

    Article MathSciNet MATH  Google Scholar 

34. C. P. Xing and H. Niederreiter. A construction of low-discrepancy sequences using global function fields. Acta Arithmetica, 73: 87 - 102, 1995.

    MathSciNet MATH  Google Scholar 

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