<<

. 2
( 2 .)




[67] Karatzas, I. , Shreve, S.E. (1999) Brownian Motion and Stochastic Calculus
Springer-Verlag, New York. Second Edition

[68] Kloeden, P.E. and Platen, E. (1992) Numerical Solution of Stochastic Dif-
ferential Equations. Springer-Verlag, New York.

[69] Knuth, D.E. (2002, 1968,1969,1973) The Art of Com-
puter Programming, Vol I-III Addison-Wesley, Reading. See
http://Sunburn.Stanford.EDU/˜knuth/news02.html.

[70] Kou, S.G., Broadie, Mark, Glasserman, Paul (1999) Connecting discrete
and continuous path-dependent options Finance and Stochastics 3. (1) 55-
82.

[71] L™Ecuyer, P. and Blouin, F. (1988) Linear congruential generators of order
k > 1, Proceedings of the 1988 winter simulation conference, IEEE Press,
New York, 432-439.

[72] Lehmann, E. (1983) The Theory of Point Estimation Wiley, New York

[73] Lewis, P.A., Goodman, A.S. and Miller, J.M. (1969) A pseudo-random
number generator for the System/360, IBM Systems Journal 8, 136-146.

[74] Liu, Jun S. (2001) Monte Carlo Strategies in Scienti¬c Computing,
Springer, New York

[75] Marsaglia, G. (1968) Random numbers fall mainly in the Planes. Proc. Nat.
Acad. Sci. 60 25-28.

[76] Matsumoto, M. and Nishimura, T. (1998) Mersenne Twister: A 623-
dimensionally equidistributed uniform pseudo-random number generator,
ACM Transactions on Modeling and Computer Simulation, 8, 3”30.

[77] Merton, R.C. (1973): Theory of Rational Option Pricing. Bell Journal of
Economics and Management Science, no 4, Spring 1973, pp.141-183
442 BIBLIOGRAPHY

[78] McLeish, D.L. and S. Rollans, (1992). Conditioning for variance reduction
in estimating the sensitivity of simulations. Annals of Operations Research,
Vol. 39, 157-172.

[79] McLeish, D. L. and Kolkiewicz, A. (1997) Fitting Di¬usion Models in Fi-
nance. Selected Proceedings of the Conference on Estimating Functions,.
Inst. Math. Statist. Lecture Notes. Ed. I.V. Basawa, V.P. Godambe, R.L.
Taylor, p. 309-332.

[80] McLeish, D. L., (2002) Highs and Lows: Some Properties of the Extremes
of a Di¬usion and Applications in Finance Canadian Journal of Statist.
30,243-267

[81] McLeish, D.L. (2004) Estimating the Correlation of Processes using Ex-
treme Values (2004) Fields Institute Communications 44, 447-467

[82] Michael, J.R., Schucany, W.R. and Haas, R.W. (1976). Generating random
Variates using Transformations with Multiple Roots. American Statistician,
30, 88-89.

[83] Metropolis, N. Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and
Teller E. (1953). Equations of state calculations by fast computing machines.
J. Chem Phys. 21 1087-1092.

[84] Niederreiter, H. (1978) Quasi-Monte Carlo methods and pseudo-random
numbers. Bull Amer. Math. Soc. 84, 957-1041.

[85] Niederreiter, H. (1992), Random Number Generation and Quasi-Monte
Carlo Methods, Society for Industrial and Applied Mathematics, Philadel-
phia.

[86] Papageorgiou, A. and Traub, J. (1996) Beating Monte Carlo, Risk 9, 63-65.

[87] Parkinson, 1980, The Extreme Value Method for Estimating the Variance
of the Rate of Return, Journal of Business.

[88] Paskov, S.H. and J.F. Traub,(1995) ”Faster Valuation of Financial Deriv-
atives”, Journal of Portfolio Management, pp 113-120.

[89] Peters, E.E. (1996) Chaos and Order in the Capital Markets : A New View
of Cycles, Prices, and Market Volatility (Second Edition)Wiley, New York.

[90] Prause, Karsten. (1999) The Generalized Hyperbolic Model: Estimation,
Financial Derivatives and Risk Measures. Dissertation, Albert-Ludwigs-U.,
Freiburg.

[91] Press, 1967, A Compound Events Model for Security Prices, Journal of
Business, 40, pp317-335.
BIBLIOGRAPHY 443

[92] Propp, J.G. and Wilson, D. B. (1996) Exact sampling with coupled Markov
chains and applications to statistical mechanics, Random Structures and
Algorithms 9, 223-252

[93] Redekop, J. (1995) Extreme-Value Distributions for generalizations of
Brownian motion. Ph.D. dissertation, University of Waterloo.

[94] Reesor, M. (2002)

[95] Ripley, B. (1983) Computer generation of random variables: a tutorial. Int.
Statist. Rev. 51. 301-319.

[96] Ripley, B. (1987) Stochastic Simulation Wiley, New York.

[97] Ripley (1988) Uses and abuses of statistical simulation. Mathematical pro-
gramming 42. 53-68.

[98] Robert, C. P. (1996). Mixtures of distributions: Inference and estimation.
In Markov Chain Monte Carlo in Practice (W. R. Gilks, S. Richardson and
D. J. Spiegelhalter, eds.) Chapman & Hall, London.

[99] Robert, C.P and Casella, G. (1999) Monte Carlo Statistical Methods.
Springer, New York.

[100] Robbins, H. and Monro, S. (1951) A Stochastic Approximation Method,
Ann. Math. Statist. 22, 400-407.

[101] Rogers, L.C.G. and Satchell, S.E. (1991) Estimating variance from high,
low and closing prices. Ann. Applied Probability. 1, 504-512.

[102] Rollans, R.S. (1993) Sensitivity Analysis of Simulations and the Monte
Carlo Optimization of Stochastic Systems University of Waterloo Ph.D. The-
sis.

[103] Rubinstein, R.Y., (1981). Simulation and the Monte Carlo Method, John
Wiley and Sons, New York.

[104] Samperi, D. (1998) Inverse Problems, Model Selection and Entropy in
Derivatives Security Pricing, PhD Thesis, New York University

[105] Shepp, L. A. (1979). The joint density of the maximum and its location
for a Wiener process with drift. J. Appl. Prob. 16, 423-427.

[106] Sprott, D.A. (2000) Statistical Inference in Science. Springer, New York

[107] Stadlober, E. (1989) Ratio of uniforms as a convenient method for sam-
pling from classical discrete distributions. Proceedings of the 1989 Winter
Sim. Conf.

[108] Stuart, A. (1962) Gamma distributed products of independent random
variables. Biometrika 49. 564-565.
444 BIBLIOGRAPHY

[109] Tadikamalla (1978) Computer generation of gamma variables I and II
Communications of the ACM 21. 419-422, 925-929
[110] Tan, K.S. and P.P. Boyle (2001). Applications of Scrambled Low Discrep-
ancy Sequences to the Valuation of Complex Securities, Journal of Economic
Dynamics and Control.
[111] J.F. Traub and H. Wozniakowski, (1994) “Breaking Intractability”, Sci-
enti¬c American, pp 102-107.
[112] Trippi, R. and Turban, E. (1996) Neural Networks in Finance and In-
vesting, Second Edition. McGraw-Hill
[113] Vasicek, O. (1977): An Equilibrium Characterization of Term Structure
J. Financial Economics, 5, pp.177-188
[114] Walker, A.J. (1974), New fast method for generating discrete random
numbers with arbitrary frequency distributions. Electronics Letters 10, 127-
128.
[115] Walker, A.J. (1977), An e¬cient method for generating discrete random
variables with general distributions. ACM Transactions on Mathematical
Software. 3 253-256.
[116] Wichmann, B.A. and Hill, I.D. (1982) An e¬cient and portable pseudo-
randnom number generator, Applied Statistics 31, 188-190; correction (1984)
ibid 33, 123.
[117] Wiggins, J.B. (1991) Empirical tests of the bias and e¬ciency of the
extreme-value estimator for common stocks. Journal of Business. 64, pp.
417-432.
[118] Wilmott, P., Howison, S., Dewynne, J. (1995) The Mathematics of Finan-
cial Derivatives: A Student Introduction Cambridge U. Press, Cambridge
[119] Small, C.G. and Wang, J. (2003). Numerical Methods for Nonlinear Esti-
mating Equations. Oxford University Press, Oxford

<<

. 2
( 2 .)