Quantum Finance: The Finite Dimensional Case

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Chen, Zeqian (2001)
  • Subject: Mathematics - Probability | Mathematics - Functional Analysis | Quantum Physics

In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As examples, the quantum model of binomial markets is studied. We show that this quantum model ceases to pose the paradox which appears in the classical model of the binomial market. Furthermore, we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering multi-period quantum binomial markets.
  • References (17)
    17 references, page 1 of 2

    L.Bachelier, Th´eorie de la sp´eculation, Ann. Sci. E´cole Norm. Sup., 17, 21-86 (1900). English translation in: The Random Character of Stock Market Prices, P.Cootner ed., Cambridge, Mass.: MIT Press, 1964, pp 17-78

    F.Black, M.Scholes, The pricing of options and corporate liabilities, J. Political Econ., 81, 637-659 (1973) DS94 F.Delbaen, W.Schachermayer, A general version of the fundamental theorem of asset

    pricing, Math. Ann., 300, 463-520 (1994)

    F.Delbaen, W.Schachermayer, The fundamental theorem of asset pricing for unbounded stochastic processes, Math. Ann., 312, 215-250 (1998)

    F.Delbaen, W.Schachermayer, Applications to mathematical finance, In: Handbook of the Geometry of Banach Spaces, W.B.Johnson and J.Lindenstrauss, eds., Amsterdam: Elsevier Science B.V., 2001, pp 367-391

    D.Duffie, C.F.Huang, Multiperiod security markets with differential information: martingales and resolution times, J. Math. Econom., 15, 283-303 (1986) J.Eisert, M.Wilkens, Quantum games, J. Mod. Opt., 47, 2543-2555 (2000) EWL99 J.Eisert, M.Wilkens, M.Lewenstein, Quantum games and quantum strategies,

    Phys. Rev. Lett., 83, 3077-3800 (1999)

    K.R.Parthasarathy, An Introduction to Quantum Stochastic Calculus, Basel: Birkh¨auser Verlag 1992

    G.Pisier, Q.Xu, Non-commutative martingale inequalities, Comm. Math. Physics, 189, 667-698 (1997)

    P.A.Samuelson, Proof that properly anticipated prices fluctuate randomly, Industrial Manage. Review, 6, 42-49 (1965)

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