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An `ℏ-Brownian motion' and the existence of stochastic option prices

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  • Haven, Emmanuel

Abstract

We introduce a particular type of Brownian motion, i.e., a Brownian motion with a diffusion coefficient containing ℏ. We show that under classical Black–Scholes methodology we can obtain a PDE with a stochastic rate of return. In this environment of `non-classical' uncertainty valued preferences for risk may exist.

Suggested Citation

  • Haven, Emmanuel, 2004. "An `ℏ-Brownian motion' and the existence of stochastic option prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 152-155.
    • Handle: RePEc:eee:phsmap:v:344:y:2004:i:1:p:152-155
    DOI: 10.1016/j.physa.2004.06.107
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    References listed on IDEAS

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    1. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    2. Haven, Emmanuel, 2002. "Fuzzy interval and semi-orders," European Journal of Operational Research, Elsevier, vol. 139(2), pages 302-316, June.
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    Cited by:

    1. Chargoy-Corona, Jesús & Ibarra-Valdez, Carlos, 2006. "A note on Black–Scholes implied volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 681-688.
    2. Nasiri, S. & Bektas, E. & Jafari, G.R., 2018. "The impact of trading volume on the stock market credibility: Bohmian quantum potential approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1104-1112.

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