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On martingale measures for stochastic processes with discrete time

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Języki publikacji
EN
Abstrakty
EN
Let (X(t); t ϵ N+) be a random sequence adopted to a filtration (ℱt) in (Ω, ℱ, P ) satisfying some natural assumption. If none of the events (X (t + 1) > X (t)), (X (t + 1) < X (t)) can be predicted, i.e, none contains some A € ℱt, P (A) > 0, then (X (t), ℱt) is a martingale for some probability P* on ℱ. It is a version of the "fundamental theorem of option pricing".
Rocznik
Strony
203--209
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
  • Łódź Technical University, Institute of Mathematics, Żwirki 36, 90-924 Łódź, Poland
  • Department of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland
Bibliografia
  • [1] F. Black and M. Scholes, The pricing of options and corporate liabilities; J. Political Economy 3 (1973), pp. 637-659.
  • [2] R. C. Dalang, A. Morton and W. Willinger, Equivalent martingale measures and no-arbitrage in stochastic securities market models, Stochastics and Stochastic Reports 29 (1990), pp. 185-201.
  • [3] F. Delbean and W. Schachermayer, A general version of the fundamental theorem of asset pricing, Math. Ann. 300 (1994), pp. 463-520.
  • [4] I. I. Gihman and A. V. Skorohod, Stochastic Differential Equations, Springer, Berlin 1972.
  • [5] - Theory of Stochastic Processes, Vol. 1, Springer, New York-Berlin 1974-1979.
  • [6] J. M. Harrison and D. M. Kreps, Martingales and arbitrage in multiperiod security markets, J. Econom. Theory 20 (1979), pp. 381-408.
  • [7] J. M. Harrison and S. R. Pliska, A stochastic calculus modes of continuous trading: complete markets, Stochastic Process. Appl. 15 (1983), pp. 313-316.
  • [8] - Martingales and stochastic arbitrage in multiperiod security markets, J. Econom. Theory 20 (1979), pp. 381-408.
  • [9] E. Jouini, Market imperfections, equilibrium and arbitrage, in: B. Biais et al., Financial Mathematics, Lecture Notes in Math. 1656 (1997), pp. 247-307.
  • [10] I. Karatzas, Lectures on the Mathematics and Finance, Centre de Recherches Mathématiques Université de Montréal, Amer. Math. Soc., CRM Monograph Series 8 (1997).
  • [11] - and S. E. Shreve, Brownian Motion and Stochastic Calculus, 2nd edition, Springer, New York 1991.
  • [12] M. Musiela and M. Rutkowski, Martingale Methods in Financial Modelling, Springer, 1997.
  • [13] M. M. Rao, Stochastic Processes: General Theory, Kluwer Acad. Publ., Math. Appl. 342 (1995).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f623dae6-acbf-4245-a39e-3c1d82b3f47c
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