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From Discrete to Continuous Time Evolutionary Finance Models

Author

Listed:
  • Jan PALCZEWSKI

    (University of Leeds and University of Warsaw)

  • Klaus Reiner SCHENK-HOPPE

    (University of Leeds)

Abstract

This paper aims to open a new avenue for research in continuoustime financial market models with endogenous prices and heterogenous investors. The main result is the derivation of the limit of a discretetime evolutionary stock market model as the length of the time period tends to zero. The resulting explicit model in continuous time generalizes the workhorse model of mathematical finance by introducing asset prices that are driven by the market interaction of investors following self-financing trading strategies. Our approach also offers a numerical scheme for the simulation of the continuous-time model.

Suggested Citation

  • Jan PALCZEWSKI & Klaus Reiner SCHENK-HOPPE, 2008. "From Discrete to Continuous Time Evolutionary Finance Models," Swiss Finance Institute Research Paper Series 08-30, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp0830
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    References listed on IDEAS

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    1. Murata, Yasuo, 1977. "Mathematics for Stability and Optimization of Economic Systems," Elsevier Monographs, Elsevier, edition 1, number 9780125112505 edited by Shell, Karl.
    2. Peter Bank & Dietmar Baum, 2004. "Hedging and Portfolio Optimization in Financial Markets with a Large Trader," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 1-18, January.
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    5. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2006. "Asset price and wealth dynamics in a financial market with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1755-1786.
    6. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner (ed.), 2009. "Handbook of Financial Markets: Dynamics and Evolution," Elsevier Monographs, Elsevier, edition 1, number 9780123742582.
    7. Evstigneev, Igor V. & Hens, Thorsten & Schenk-Hoppé, Klaus Reiner, 2008. "Globally evolutionarily stable portfolio rules," Journal of Economic Theory, Elsevier, vol. 140(1), pages 197-228, May.
    8. Igor Evstigneev & Thorsten Hens & Klaus Schenk-Hoppé, 2006. "Evolutionary stable stock markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 449-468, January.
    9. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary stability of portfolio rules in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 43-66, February.
    10. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2008. "Evolutionary Finance," Swiss Finance Institute Research Paper Series 08-14, Swiss Finance Institute.
    11. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
    12. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner, 2010. "Market selection of constant proportions investment strategies in continuous time," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 248-266, March.
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    Cited by:

    1. Mikhail Zhitlukhin, 2020. "A continuous-time asset market game with short-lived assets," Papers 2008.13230, arXiv.org.
    2. Mikhail Zhitlukhin, 2018. "Survival investment strategies in a continuous-time market model with competition," Papers 1811.12491, arXiv.org, revised Sep 2019.

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    More about this item

    Keywords

    evolutionary finance; market interaction; wealth dynamics; self-financing strategies; endogenous prices.;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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