Martingales and stochastic integrals in the theory of continuous trading. (English) Zbl 0482.60097


60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
60H05 Stochastic integrals
60G44 Martingales with continuous parameter
91B99 Mathematical economics
91G20 Derivative securities (option pricing, hedging, etc.)
Full Text: DOI


[1] Bachelier, L., Theory of speculation, (Cootner, P. H., The Random Character of Stock Market Prices (1964), M.I.T. Press: M.I.T. Press Cambridge, MA) · JFM 31.0241.02
[2] Black, F.; Scholes, M., The pricing of options and corporate liabilities, J. Polit. Econom., 81, 637-659 (1973) · Zbl 1092.91524
[3] Bremaud, P.; Jacod, J., Processus ponctuels et martingales: Resultats recents sur la modelisation et la filtrage, Advances in Appl. Probability, 9, 362-416 (1977) · Zbl 0369.60059
[4] Clarke, J. M.C., The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Statist.. Ann. Math. Statist., Ann. Math. Statist., 42, 1282-1295 (1971), Correction · Zbl 0213.19402
[5] Cox, J.; Ross, S., The valuation of options for alternative stochastic processes, J. Fin. Econom., 3, 145-166 (1976)
[6] Cox, J. C.; Ross, S. A.; Rubenstein, M., Option pricing: A simplified approach, J. Fin. Econom., 7, 229-263 (1979) · Zbl 1131.91333
[7] Davis, M. H.A.; Varaiya, P. P., The multiplicity of an increasing family of σ-fields, Ann. Probab., 2, 958-963 (1974) · Zbl 0292.60071
[8] Dellacherie, C., Integrales stochastique par rapport aux processus de Wiener et de Poisson, (Seminaire de Probabilité VIII and IX. Seminaire de Probabilité VIII and IX, Lecture Notes in Mathematics, 465 (1975), Springer: Springer New York), 495
[9] Dellacherie, C., Un survol de la theorie de l’integrale stochastique, Stochastic Process. Appl., 10, 115-144 (1980) · Zbl 0436.60043
[10] Dellacherie, C.; Meyer, P.-A., Probabilities and Potentials (1978), North-Holland: North-Holland New York
[11] Dudley, R. M., Wiener functionals as Ito integrals, Ann. Probab., 5, 140-141 (1977) · Zbl 0359.60071
[12] Girsanov, I. I., On transforming a certain class of stochastic processes by absolutely continuous substitution of measures, Theory Probab. Appl., 5, 285-301 (1960) · Zbl 0100.34004
[13] Harrison, J. M.; Kreps, D. M., Martingales and arbitrage in multiperiod securities markets, J. Econom. Theory, 20, 381-408 (1979) · Zbl 0431.90019
[14] Ito, K., Multiple Wiener integral, J. Math. Soc. Japan, 3, 158-169 (1951) · Zbl 0044.12202
[15] Jacod, J., Multivariate point processes: Predictable projection, Radon-Nikodym derivative, representation of martingales, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 31, 235-253 (1975) · Zbl 0302.60032
[16] Jacod, J., Un theorème de representation pour les martingales discontinues, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 35, 1-37 (1976) · Zbl 0315.60026
[17] Jacod, J., A general theorem of representation for martingales, (Proc. Symp. Pure Math., Vol. 31 (1977), American Mathematical Society: American Mathematical Society Providence), 37-53
[18] Jacod, J., Calcul Stochastique et Problèmes de Martingales, (Lecture Notes in Mathematics, 714 (1979), Springer: Springer New York) · Zbl 0414.60053
[19] Jacod, J.; Yor, M., Etudes des solutions extremales et representation integrale des solutions pour certains problèmes de martingales, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 83-125 (1977) · Zbl 0346.60032
[20] Kreps, D. M., Multiperiod securities and the efficient allocation of risk: A comment on the Black-Scholes option pricing model, U-NBER Conference on the Economics of Information and Uncertainty (1979), Boston, U.S.A.
[21] Kreps, D. M., Three essays on capital markets, (Tech. Rept. No. 298 (1979), Institute for Mathematical Studies in the Social Sciences, Stanford Univ: Institute for Mathematical Studies in the Social Sciences, Stanford Univ Stanford, CA)
[22] D.M. Kreps, Arbitrage and equilibrium in economies with infinitely many commodities, J. Math. Econom., to appear.; D.M. Kreps, Arbitrage and equilibrium in economies with infinitely many commodities, J. Math. Econom., to appear. · Zbl 0454.90010
[23] Kunita, H.; Watanabe, S., On square integrable martingales, Nagoya Math. J., 30, 209-245 (1967) · Zbl 0167.46602
[24] Liptser, R. S.; Shiryaev, A. N., Statistics of Random Processes, Vol. I (1977), Springer: Springer New York
[25] Magill, M.; Constantinides, G., Portfolio selection with transaction costs, J. Econom. Theory, 13, 245-263 (1976) · Zbl 0361.90001
[26] Merton, R. C., Lifetime portfolio selection under uncertainty, the continuous-time case, Rev. Econom. Stud. LI, 247-257 (1969)
[27] Merton, R. C., Optimum consumption and portfolio rules in a continuous-time model, J. Econom. Theory, 3, 373-413 (1971) · Zbl 1011.91502
[28] Merton, R. C., Theory of rational option pricing, Bell J. Econom. Management Sci., 4, 141-183 (1973) · Zbl 1257.91043
[29] Merton, R. C., Option pricing when underlying stock returns are discontinuous, J. Fin. Econom., 3, 125-144 (1976) · Zbl 1131.91344
[30] Merton, R. C., On the pricing of contingent claims and the Modigliani-Miller theorem, J. Fin. Econom., 5, 241-249 (1977)
[31] Metivier, M.; Pellaumail, J., Stochastic Integration (1980), Academic Press: Academic Press New York · Zbl 0463.60004
[32] Meyer, P.-A., Un cours sur les integrales stochastiques, (Seminaire de Probabilité X. Seminaire de Probabilité X, Lecture Notes in Mathematics, 511 (1976), Springer: Springer New York), 245-400 · Zbl 0374.60070
[33] Meyer, P.-A., Introduction au calcul differentiel stochastique, (Contrib. en Prob. y Est. Mat. Ens. de la Mat. y Analisis (1979), Univ. de Granada), 91-108 · Zbl 0455.60046
[34] Samuelson, P. A., Rational theory of warrant pricing, Ind. Management Rev., 6, 13-39 (1965)
[35] Samuelson, P. A., Mathematics of speculative price, SIAM Rev., xx, 1-42 (1973) · Zbl 0261.90009
[36] Sharpe, W., Investments (1978), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[37] Smith, C. W., Option pricing: A review, J. Fin. Econom., 3, 3-51 (1976)
[38] Williams, D., Diffusions, Markov Processes and Martingales, Vol. 1 (1979), Wiley: Wiley New York
[39] Yor, M., Sous-espaces denses dans \(L^1\) ou \(H^1\) et representation des martingales, (Seminaire de Probabilité XII. Seminaire de Probabilité XII, Lecture Notes in Mathematics, 649 (1978), Springer: Springer New York), 265-309
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