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Wealth and Price Distribution by Diffusive Approximation in a Repeated Prediction Market

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  • Giulio Bottazzi
  • Daniele Giachini

Abstract

The approximate agents' wealth and price invariant densities of a repeated prediction market model is derived using the Fokker-Planck equation of the associated continuous-time jump process. We show that the approximation obtained from the evolution of log-wealth difference can be reliably exploited to compute all the quantities of interest in all the acceptable parameter space. When the risk aversion of the trader is high enough, we are able to derive an explicit closed-form solution for the price distribution which is asymptotically correct.

Suggested Citation

  • Giulio Bottazzi & Daniele Giachini, 2016. "Wealth and Price Distribution by Diffusive Approximation in a Repeated Prediction Market," LEM Papers Series 2016/13, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    • Handle: RePEc:ssa:lemwps:2016/13
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    References listed on IDEAS

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    1. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
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    3. Bottazzi, Giulio & Dindo, Pietro, 2014. "Evolution and market behavior with endogenous investment rules," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 121-146.
    4. Giulio Bottazzi & Pietro Dindo, 2015. "Drift criteria for persistence of discrete stochastic processes on the line with examples of application," LEM Papers Series 2015/26, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    5. Leonard Maclean & William Ziemba & Yuming Li, 2005. "Time to wealth goals in capital accumulation," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 343-355.
    6. Garibaldi,Ubaldo & Scalas,Enrico, 2010. "Finitary Probabilistic Methods in Econophysics," Cambridge Books, Cambridge University Press, number 9780521515597, October.
    7. Alina Beygelzimer & John Langford & David Pennock, 2012. "Learning Performance of Prediction Markets with Kelly Bettors," Papers 1201.6655, arXiv.org.
    8. Anna, Petrenko, 2016. "Мaркування готової продукції як складова частина інформаційного забезпечення маркетингової діяльності підприємств овочепродуктового підкомплексу," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 2(1), March.
    9. repec:reg:rpubli:460 is not listed on IDEAS
    10. G. Bottazzi & D. Giachini, 2019. "Far from the madding crowd: collective wisdom in prediction markets," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1461-1471, September.
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    Cited by:

    1. Bottazzi, Giulio & Giachini, Daniele & Ottaviani, Matteo, 2023. "Market selection and learning under model misspecification," Journal of Economic Dynamics and Control, Elsevier, vol. 156(C).
    2. Vandin, Andrea & Giachini, Daniele & Lamperti, Francesco & Chiaromonte, Francesca, 2022. "Automated and distributed statistical analysis of economic agent-based models," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    3. Mikhail Zhitlukhin, 2021. "Asymptotically optimal strategies in a diffusion approximation of a repeated betting game," Papers 2108.11998, arXiv.org.
    4. Andrea Vandin & Daniele Giachini & Francesco Lamperti & Francesca Chiaromonte, 2021. "Automated and Distributed Statistical Analysis of Economic Agent-Based Models," Papers 2102.05405, arXiv.org, revised Nov 2023.
    5. Andrea Vandin & Daniele Giachini & Francesco Lamperti & Francesca Chiaromonte, 2020. "Automated and Distributed Statistical Analysis of Economic Agent-Based Models," LEM Papers Series 2020/31, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    6. G. Bottazzi & D. Giachini, 2019. "Far from the madding crowd: collective wisdom in prediction markets," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1461-1471, September.
    7. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2019. "Momentum and reversal in financial markets with persistent heterogeneity," Annals of Finance, Springer, vol. 15(4), pages 455-487, December.
    8. Mikhail Zhitlukhin, 2022. "A continuous-time asset market game with short-lived assets," Finance and Stochastics, Springer, vol. 26(3), pages 587-630, July.
    9. Bottazzi, Giulio & Dindo, Pietro, 2022. "Drift criteria for persistence of discrete stochastic processes on the line," Journal of Mathematical Economics, Elsevier, vol. 101(C).

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