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From discrete to continuous time evolutionary finance models

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  • Palczewski, Jan
  • Schenk-Hoppé, Klaus Reiner

Abstract

This paper aims to open a new avenue for research in continuous-time financial market models with endogenous prices and heterogenous investors. To this end we introduce a discrete-time evolutionary stock market model that accommodates time periods of arbitrary length. The dynamics is time-consistent and allows the comparison of paths with different frequency of trade. The main result in this paper is the derivation of the limit model as the length of the time period tends to zero. The resulting 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 that satisfies constraints such as market clearing at every time step. An illustration is provided.

Suggested Citation

  • Palczewski, Jan & Schenk-Hoppé, Klaus Reiner, 2010. "From discrete to continuous time evolutionary finance models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 913-931, May.
    • Handle: RePEc:eee:dyncon:v:34:y:2010:i:5:p:913-931
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    1. Mikhail Zhitlukhin, 2018. "Survival investment strategies in a continuous-time market model with competition," Papers 1811.12491, arXiv.org, revised Sep 2019.
    2. Mikhail Zhitlukhin, 2020. "A continuous-time asset market game with short-lived assets," Papers 2008.13230, arXiv.org.

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    More about this item

    Keywords

    Evolutionary finance Market interaction Wealth dynamics Self-financing strategies Endogenous prices Continuous-time limit;

    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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