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Explore or exploit? A generic model and an exactly solvable case

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  • Thomas Gueudr'e
  • Alexander Dobrinevski
  • Jean-Philippe Bouchaud

Abstract

Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimisation, evolutionary dynamics, or the problem of optimal pinning of vortices or dislocations in disordered materials. We find the exact growth rate of this model for tree-like geometries and prove the existence of an optimal migration rate in this case. Numerical simulations in the one-dimensional case confirm the generic existence of an optimum.

Suggested Citation

  • Thomas Gueudr'e & Alexander Dobrinevski & Jean-Philippe Bouchaud, 2013. "Explore or exploit? A generic model and an exactly solvable case," Papers 1310.5114, arXiv.org, revised Dec 2013.
  • Handle: RePEc:arx:papers:1310.5114
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    File URL: http://arxiv.org/pdf/1310.5114
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    References listed on IDEAS

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    1. Luciano Campi & Umut Çetin & Albina Danilova, 2013. "Equilibrium model with default and dynamic insider information," Finance and Stochastics, Springer, vol. 17(3), pages 565-585, July.
    2. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September.
    3. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    4. Luciano Campi & Umut Çetin, 2007. "Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling," Finance and Stochastics, Springer, vol. 11(4), pages 591-602, October.
    5. Kerry Back & Shmuel Baruch, 2004. "Information in Securities Markets: Kyle Meets Glosten and Milgrom," Econometrica, Econometric Society, vol. 72(2), pages 433-465, March.
    6. Back, Kerry, 1992. "Insider Trading in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    7. Umut c{C}etin & Hao Xing, 2012. "Point process bridges and weak convergence of insider trading models," Papers 1205.4358, arXiv.org, revised Jan 2013.
    8. repec:dau:papers:123456789/4436 is not listed on IDEAS
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