From the problem of the points to value an option, then no one knows: a Journey whitout ending
From the problem of the points to value an option, then no one knows: a Journey whitout ending
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Avellaneda Hortúa, M. 2016. From the problem of the points to value an option, then no one knows: a Journey whitout ending. ODEON. 10 (oct. 2016), 29–64. DOI:https://doi.org/10.18601/17941113.n10.03.
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This article seeks to commemorate the 100th anniversary of Japanese Kiyosi Itô’s (1915-2008) birth, whose research in the field of mathematics has had an unexpected impact on different areas of human life, for example, biology, economics, engineering, finance and physics. This essay, rather than carry out a detail review of the different jobs that Itô has made throughout his lifetime, intends to make a tribute to some researchers and their developments from the past. Researchers, whose work sometimes remained forgotten for a while and thanks to a new stream of researchers interested in history and the stories of the development of finance knowledge, rediscovered and brought it again to light. As a consequence of this archeological work, it would be possible for a new wave of researchers to analyze their progress and may be find unanticipated applications to such efforts.
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Baskin, J. B., & Miranti, P. J. (2003). A History of Corporate Finance. Cambridge UK: Cambridge University Press.
Bernstein, P. L. (1998). Against the Gods. the remarkable story of risk. USA: John Wiley & Sons.
Black, F. (1989). How we came up with the option formula. Journal of Portfolio Management, 15(2), 4-8.
Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. The Journalist Political Economy, 81(3), 637-654.
Brown, R. (September de 1828). A brief account of microscopical observations made in the months of June, July and August, 1827 on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. In Taylor, R., & Phillips, R. (eds.). The Philosophical Magazine, or annals of chemistry, mathematics, Astronomy, Natural History, and general science, 4(21),
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Brown, R. (September de 1829). Additional Remarks on Active Molecules. The Philosophical Magazine, as annals of Chemistry, Mathematics, astronomy, natural history, and general science, 6(33), 161-6.
Bru, B., & Yor, M. (2002). Comments on the life and mathematical legacy of Wolfgang Doeblin. Finance and Stochastics, 6(1), 3-47.
Devlin, K. (2008). The unfinished game. Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. New York: B. B. Group.
Evening Mail (1858, June 18). The Late Mr. Robert Brwon (13,807), p. 8.
Fama, E. (1970). Efficient Capital Markets: A review of Theory and Empirical Work. The Journal of Finance, 25(2), 383-417.
Gaarder Haug, E. (2007). The Complete Guide to Option Pricing Formulas (2 ed.). New York: McGraw Hill.
García Cruz, J. A. (Febrero de 2000). Historia de un problema: el reparto de la apuesta. Suma. Revista para la enseñanza y el aprendizaje de las matemáticas(33), 25-36.
Hull, J. C. (2005). Fundamentals of Futures and Options Markets (5 ed.). New Jersey: P. P. Hall.
Ikeda, N., Watanabe, S., Fukushima, M., & Kunita, H. (eds.) (1996). Itô’s Stochastic Calculus and Probability Theory. Tokyo: Springer.
Itô, K. (1941). On stochastic processes. Infinitely divisible laws of probability. Japenese Journal of Mathematics, 18, 261-301.
Itô, K. (1944). Stochastic Integral. Proceedings of the Imperial Academy, 20(8), 519-524.
Itô, K. (1998). My Sixty Years along the Path of Probability Theory.
Jarrow, R., & Protter, P. (2004). A short history of stochastic integration and mathematical finance the early years, 1880-1970. Lecture Notes Monograph Series, Cornell University. doi:10.1214/lnms/1196285381
Jovanovic, F. (2004). Éléments biographiques inédits sur Jules Regnault (1834-1894), inventeur du modèle de marché aléatoire pour représenter les variations boursières. Revue d’Histoire des Sciences Humaines, 11(2), 215-230. doi:10.3917/rhsh.011.0215
Jovanovic, F. (2006). Economic Instruments and Theory in the Construction of Henri Lefèvre’s “Science of the Stock Market”. En G. Poitras (ed.). Pioneers of Financial Economics, 1, 169-190.
Jovanovic, F., & Le Gall, P. (2001). Does God practice a random walk? The ‘financial physics’ of a nineteenth-century forerunner, Jules Regnault. The European Journal of the History of Economic Though, 8(3), 332-62. doi:10.1080/09672560110062960
King, B. (1965). Book Review. the Random Character of Stock Market Prices. Journal of Finance, 20(3), 547-548.
Lefèvre, H. (1873). Physiologie et mécanique sociales. En Journal des Actuaries Francais, 2, 211-250, 351-388).
Levèvre, H. (1874). Physologie et mecánique sociales. En Journal del Actuaries Francais, 93-118.
Lucretius (2001). On the Nature of Things. Indianapolis: Hackett Publishing.
Maistrov, L. (1974). Probability Theory. A Historical Sketch. New York: Academic Press.
Mathematical Society of Japan (1987). Encyclopedic Dictionary of Mathematics: (2 ed.). T. M. Press.
Mathematical Society of Japan (1993). Encyclopedic Dictionary of Mathematics (Vol. 1, K. Itô, ed.). Cambridge MA.
McKean, H. P. (1969). Stochastic Integrals. New York: A. Press.
Nelson, E. (2001). Dynamical Theories of Brownian Motion (2 ed.). Princeton: Princeton University Press.
Pacioli, L. (1494). Summa de Arithmetica Geometria Proportioni et Proportionalita. Venice: P. Paganini.
Pacioli, L. (2010). The Rules of Double-Entry Bookkeeping. USA: M. Schemmann.
Pochet, L. (1873). Géométrie des jeux de bourse. En Journal des Actuaries Francais, 153-160.
Powles, J. G. (1978). Brownian motion - june 1827 (for teachers). Physics Education, 13(5), 310-312.
Pulskamp, R. J. (2009). Summa de Arithmetica Geometria Proportioni et Proportionalita. Cincinnati: Xavier University, Department of Mathematics and Computer Science.
Regnault, J. (1863). Calcus des Chances et Philosphie de la Bourse. Paris.
Rubinstein, M. (2006). A History of the Theory of Investments. My annotated bibliography. New Jersey: John Wiley & Sons.
Shreve, S. E. (2004). Stochastic Calculus for Finance II. Continuous Time Models. Springer.
Stanford University (1978). Memoria Resolution. Paul H Cootner (1930-1978). Stanford.
Stringham, E. (2003). The extralegal development of securities trading in seventeenthcentury Amsterdam. The Quarterly Review of Economics and Finance, 43(2), 321- 344.
Szpiro, G. G. (2011). Pricing the Future. Finance, Physics, and the 300-year journey to the Black-Scholes Equation. New York: B. B. Group.
Taqqu, M. S. (2001). Bachelier and his Times: A Conversation with Bernard Bru. Boston: Boston University, Department of Mathematics.
The Prize in Economics Science 1997 Press Release (17 de October de 1997).
Thiele, T. N. (1880). Sur la Compensation de Quelques Erreurs quasi-Systématiques par La Méthode des Moindres Carrés. Copenhague C. A. Reitzel, Libraire-Editeur.
Turvey, C. G. (2010). Biography: Kiyosi Itô and his influence on the study of agricultural finance and economics. Agricultural Finance Review, 70(1), 5-20. doi:10.1108/00021461011042602
University of York (s. f.). Fermat and Pascal on Probability. University of York.
van der Pas, P. E. (1971). The discovery of the brownian motion. Scientiarum historia, 13, 27-35.
Weatherall, J. O. (2013). The Physics of Wall Street. A Brief History of Predicting the Unpredictable. New York: H. H. Company.
Bachelier, L. (2006). Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance. New Jersey: Princeton University Press.
Baskin, J. B., & Miranti, P. J. (2003). A History of Corporate Finance. Cambridge UK: Cambridge University Press.
Bernstein, P. L. (1998). Against the Gods. the remarkable story of risk. USA: John Wiley & Sons.
Black, F. (1989). How we came up with the option formula. Journal of Portfolio Management, 15(2), 4-8.
Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. The Journalist Political Economy, 81(3), 637-654.
Brown, R. (September de 1828). A brief account of microscopical observations made in the months of June, July and August, 1827 on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. In Taylor, R., & Phillips, R. (eds.). The Philosophical Magazine, or annals of chemistry, mathematics, Astronomy, Natural History, and general science, 4(21),
161-173.
Brown, R. (September de 1829). Additional Remarks on Active Molecules. The Philosophical Magazine, as annals of Chemistry, Mathematics, astronomy, natural history, and general science, 6(33), 161-6.
Bru, B., & Yor, M. (2002). Comments on the life and mathematical legacy of Wolfgang Doeblin. Finance and Stochastics, 6(1), 3-47.
Devlin, K. (2008). The unfinished game. Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. New York: B. B. Group.
Evening Mail (1858, June 18). The Late Mr. Robert Brwon (13,807), p. 8.
Fama, E. (1970). Efficient Capital Markets: A review of Theory and Empirical Work. The Journal of Finance, 25(2), 383-417.
Gaarder Haug, E. (2007). The Complete Guide to Option Pricing Formulas (2 ed.). New York: McGraw Hill.
García Cruz, J. A. (Febrero de 2000). Historia de un problema: el reparto de la apuesta. Suma. Revista para la enseñanza y el aprendizaje de las matemáticas(33), 25-36.
Hull, J. C. (2005). Fundamentals of Futures and Options Markets (5 ed.). New Jersey: P. P. Hall.
Ikeda, N., Watanabe, S., Fukushima, M., & Kunita, H. (eds.) (1996). Itô’s Stochastic Calculus and Probability Theory. Tokyo: Springer.
Itô, K. (1941). On stochastic processes. Infinitely divisible laws of probability. Japenese Journal of Mathematics, 18, 261-301.
Itô, K. (1944). Stochastic Integral. Proceedings of the Imperial Academy, 20(8), 519-524.
Itô, K. (1998). My Sixty Years along the Path of Probability Theory.
Jarrow, R., & Protter, P. (2004). A short history of stochastic integration and mathematical finance the early years, 1880-1970. Lecture Notes Monograph Series, Cornell University. doi:10.1214/lnms/1196285381
Jovanovic, F. (2004). Éléments biographiques inédits sur Jules Regnault (1834-1894), inventeur du modèle de marché aléatoire pour représenter les variations boursières. Revue d’Histoire des Sciences Humaines, 11(2), 215-230. doi:10.3917/rhsh.011.0215
Jovanovic, F. (2006). Economic Instruments and Theory in the Construction of Henri Lefèvre’s “Science of the Stock Market”. En G. Poitras (ed.). Pioneers of Financial Economics, 1, 169-190.
Jovanovic, F., & Le Gall, P. (2001). Does God practice a random walk? The ‘financial physics’ of a nineteenth-century forerunner, Jules Regnault. The European Journal of the History of Economic Though, 8(3), 332-62. doi:10.1080/09672560110062960
King, B. (1965). Book Review. the Random Character of Stock Market Prices. Journal of Finance, 20(3), 547-548.
Lefèvre, H. (1873). Physiologie et mécanique sociales. En Journal des Actuaries Francais, 2, 211-250, 351-388).
Levèvre, H. (1874). Physologie et mecánique sociales. En Journal del Actuaries Francais, 93-118.
Lucretius (2001). On the Nature of Things. Indianapolis: Hackett Publishing.
Maistrov, L. (1974). Probability Theory. A Historical Sketch. New York: Academic Press.
Mathematical Society of Japan (1987). Encyclopedic Dictionary of Mathematics: (2 ed.). T. M. Press.
Mathematical Society of Japan (1993). Encyclopedic Dictionary of Mathematics (Vol. 1, K. Itô, ed.). Cambridge MA.
McKean, H. P. (1969). Stochastic Integrals. New York: A. Press.
Nelson, E. (2001). Dynamical Theories of Brownian Motion (2 ed.). Princeton: Princeton University Press.
Pacioli, L. (1494). Summa de Arithmetica Geometria Proportioni et Proportionalita. Venice: P. Paganini.
Pacioli, L. (2010). The Rules of Double-Entry Bookkeeping. USA: M. Schemmann.
Pochet, L. (1873). Géométrie des jeux de bourse. En Journal des Actuaries Francais, 153-160.
Powles, J. G. (1978). Brownian motion - june 1827 (for teachers). Physics Education, 13(5), 310-312.
Pulskamp, R. J. (2009). Summa de Arithmetica Geometria Proportioni et Proportionalita. Cincinnati: Xavier University, Department of Mathematics and Computer Science.
Regnault, J. (1863). Calcus des Chances et Philosphie de la Bourse. Paris.
Rubinstein, M. (2006). A History of the Theory of Investments. My annotated bibliography. New Jersey: John Wiley & Sons.
Shreve, S. E. (2004). Stochastic Calculus for Finance II. Continuous Time Models. Springer.
Stanford University (1978). Memoria Resolution. Paul H Cootner (1930-1978). Stanford.
Stringham, E. (2003). The extralegal development of securities trading in seventeenthcentury Amsterdam. The Quarterly Review of Economics and Finance, 43(2), 321- 344.
Szpiro, G. G. (2011). Pricing the Future. Finance, Physics, and the 300-year journey to the Black-Scholes Equation. New York: B. B. Group.
Taqqu, M. S. (2001). Bachelier and his Times: A Conversation with Bernard Bru. Boston: Boston University, Department of Mathematics.
The Prize in Economics Science 1997 Press Release (17 de October de 1997).
Thiele, T. N. (1880). Sur la Compensation de Quelques Erreurs quasi-Systématiques par La Méthode des Moindres Carrés. Copenhague C. A. Reitzel, Libraire-Editeur.
Turvey, C. G. (2010). Biography: Kiyosi Itô and his influence on the study of agricultural finance and economics. Agricultural Finance Review, 70(1), 5-20. doi:10.1108/00021461011042602
University of York (s. f.). Fermat and Pascal on Probability. University of York.
van der Pas, P. E. (1971). The discovery of the brownian motion. Scientiarum historia, 13, 27-35.
Weatherall, J. O. (2013). The Physics of Wall Street. A Brief History of Predicting the Unpredictable. New York: H. H. Company.
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