Overshoot in the Case of Normal Variables: Chernoff's Integral, Latta's Observation, and Wijsman's Sum

REFERENCES

• Broadie , M. , Glasserman , P. , and Kou , S. ( 1997 ). A Continuity Correction for Discrete Barrier Options, Mathematical Finance 7 : 325 – 349 .
   Web of Science ®Google Scholar
• Chang , J. T. and Peres , Y. ( 1997 ). Ladder Heights, Gaussian Random Walks and the Riemann Zeta Function, Annals of Probability 25 : 787 – 802 .
   Web of Science ®Google Scholar
• Chernoff , H. ( 1965 ). Sequential Tests for the Mean of a Normal Distribution IV (Discrete Case), Annals of Mathematical Statistics 36 : 55 – 68 .
   Google Scholar
• Graham , R. L. , Knuth , D. E. , and Patashnik , O. ( 1989 ). Concrete Mathematics: A Foundation for Computer Science , Reading: Addison-Wesley.
   Google Scholar
• Hull , J. C. ( 2003 ). Options, Futures, and Other Derivatives, , fifth edition , New Jersey: Prentice Hall.
   Google Scholar
• Knopp , K. ( 1928 ). Theory and Application of Infinite Series, , first English edition , London : Blackie & Son .
   Google Scholar
• Kou , S. G. ( 2003 ). On Pricing of Discrete Barrier Options, Statistica Sinica 13 : 955 – 964 .
   Web of Science ®Google Scholar
• Martinsek , A. T. ( 2006 ). The Contributions of Robert A. Wijsman to Sequential Analysis, Sequential Analysis 25 : 3 – 18 .
   Google Scholar
• Ramanujan , S. ( 1915 ). On the Sum of the Square Roots of the First n Natural Numbers, Journal of Indian Mathematical Society 7 : 173 – 175 .
   Google Scholar
• Saalschütz , L. ( 1893 ). Vorlesungen über die Bernoullischen Zahlen, ihren Zusammenhang mit den Secanten-Coefficienten und ihre wichtigeren Anwendungen , Berlin: Springer.
   Google Scholar
• Siegmund , D. ( 1985 ). Sequential Analysis: Tests and Confidence Intervals , New York: Springer.
   Google Scholar
• Spitzer , F. ( 1957 ). The Wiener-Hopf Equation whose Kernel Is a Probability Density, Duke Mathematical Journal 24 : 327 – 343 .
   Web of Science ®Google Scholar
• Spitzer , F. ( 1960 ). The Wiener-Hopf Equation whose Kernel Is a Probability Density. II, Duke Mathematical Journal 27 : 363 – 372 .
   Google Scholar
• Takahashi , H. ( 1987 ). Asymptotic Expansion in Anscombe's Theorem for Repeated Significance Tests and Estimation after Sequential Testing, Annals of Statistics 15 : 278 – 295 .
   Google Scholar
• Wald , A. ( 1947 ). Sequential Analysis , New York: Wiley.
   Google Scholar
• Whitehead , J. ( 1997 ). The Design and Analysis of Sequential Clinical Trials, , revised second edition , Chichester: Wiley.
   Google Scholar
• Whitehead , J. and Stratton , I. ( 1983 ). Group Sequential Clinical Trials with Triangular Continuation Regions, Biometrics 39 : 227 – 236 . Correction, Biometrics 39(1983): 1137 .
   PubMed Web of Science ®Google Scholar
• Wijsman , R. A. ( 2004 ). Overshoot in the Case of Normal Variables, Sequential Analysis 23 : 275 – 284 .
   Google Scholar
• Woodroofe , M. ( 1982 ). Nonlinear Renewal Theory in Sequential Analysis , Philadelphia: SIAM .
   Google Scholar
• Recommended by N. Mukhopadhyay
   Google Scholar