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A Microeconomic Approach to Diffusion Models For Stock Prices

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  • Hans Föllmer
  • Martin Schweizer

Abstract

This paper studies a class of diffusion models for stock prices derived by a microeconomic approach. We consider discrete-time processes resulting from a market equilibrium and then apply an invariance principle to obtain a continuous-time model. the resulting process is an Ornstein-Uhlenbeck process in a random environment, and we analyze its qualitative behavior. In particular, we provide simple criteria for the stability or instability of the corresponding stock price model, and we give explicit formulae for the invariant distributions in the recurrent case. Copyright 1993 Blackwell Publishers.

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  • Hans Föllmer & Martin Schweizer, 1993. "A Microeconomic Approach to Diffusion Models For Stock Prices," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 1-23.
  • Handle: RePEc:bla:mathfi:v:3:y:1993:i:1:p:1-23
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    References listed on IDEAS

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    1. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, pages 179-189.
    2. Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
    3. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    4. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, pages 60-66.
    5. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, pages 351-373.
    6. A. Jobert & L. C. G. Rogers, 2008. "Valuations And Dynamic Convex Risk Measures," Mathematical Finance, Wiley Blackwell, pages 1-22.
    7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, pages 203-228.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Föllmer, H. & Schweizer, M., 1989. "Hedging by Sequential Regression: an Introduction to the Mathematics of Option Trading," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 19(S1), pages 29-42, November.
    10. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
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