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Evolutionary finance and dynamic games

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Abstract

The paper examines a game-theoretic evolutionary model of an asset market with endogenous equilibrium asset prices. Assets pay dividends that are partially consumed and partially reinvested. The investors use general, adaptive strategies (portfolio rules), distributing their wealth between assets, depending on the exogenous states of the world and the observed history of the game. The main objective of the work is to identify strategies, allowing an investor to “survive”, i.e. to possess a positive, bounded away from zero, share of market wealth over the whole infinite time horizon. This work brings together recent studies on evolutionary finance with the classical topic of non-cooperative market games.

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References

  1. Algoet P.H., Cover T.M.: Asymptotic optimality and asymptotic equipartition properties of log-optimum investment. Ann. Probab. 16, 876–898 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Amir R., Sahi S., Shubik M., Yao S.: A strategic market game with complete markets. J. Econ. Theory 51, 126–143 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  3. Amir, R., Evstigneev, I.V., Hens, T., Schenk-Hoppé, K.R.: Market selection and survival of investment strategies. J. Math. Econ. 41, 105–122 (2005) (special issue on Evolutionary Finance)

    Google Scholar 

  4. Amir, R., Evstigneev, I.V., Schenk-Hoppé, K.R.: Asset market games of survival: a synthesis of evolutionary and dynamic games. Swiss Finance Institute research paper no. 08-31 (2010)

  5. Arkin V.I., Evstigneev I.V.: Stochastic Models of Control and Economic Dynamics. Academic Press, London (1987)

    Google Scholar 

  6. Arthur W.B., Holland J.H., LeBaron B., Palmer R.G., Taylor P.: Asset pricing under endogenous expectations in an artificial stock market. In: Arthur, W.B., Durlauf, S., Lane, D. (eds.) The Economy as an Evolving Complex System, vol. II, pp. 15–44. Addison Wesley, Reading (1997)

    Google Scholar 

  7. Blume L., Easley D.: Evolution and market behavior. J. Econ. Theory 58, 9–40 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Breiman, L.: Optimal gambling systems for favorable games. In: Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 65–78. University of California Press, Berkeley (1961)

  9. Brock, A.W., Hommes, C.H., Wagener, F.O.O.: Evolutionary dynamics in markets with many trader types. J. Math. Econ. 41, 7–42 (2005) (special issue on Evolutionary Finance)

    Google Scholar 

  10. Dempster M.A.H., Evstigneev I.V., Schenk-Hoppé K.R.: Volatility-induced financial growth. Quant. Finance 7, 151–160 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Dempster M.A.H., Evstigneev I.V., Schenk-Hoppé K.R.: Financial markets. The joy of volatility. Quant. Finance 8, 1–3 (2008)

    Article  MATH  Google Scholar 

  12. Dempster M.A.H., Mitra G., Pflug G.: Quantitative Fund Management. Chapman and Hall/CRC Financial Mathematics Series. Taylor and Francis Group, Boca Raton (2009)

    Google Scholar 

  13. Dempster, M.A.H., Evstigneev, I.V., Schenk-Hoppé, K.R.: Growing wealth with fixed-mix strategies. In: MacLean, L.C., Thorp, E.O., Ziemba, W.T. (eds.) The Kelly Capital Growth Investment Criterion: Theory and Practice, pp. 427–455. World Scientific, Singapore (2011)

  14. Dubey P., Geanakoplos J., Shubik M.: The revelation of information in strategic market games. A critique of rational expectations equilibrium. J. Math. Econ. 16, 105–137 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  15. Evstigneev I.V., Hens T., Schenk-Hoppé K.R.: Evolutionary stable stock markets. Econ. Theory 27, 449–468 (2006)

    Article  MATH  Google Scholar 

  16. Evstigneev I.V., Hens T., Schenk-Hoppé K.R.: Globally evolutionarily stable portfolio rules. J. Econ. Theory 140, 197–228 (2008)

    Article  MATH  Google Scholar 

  17. Evstigneev I.V., Hens T., Schenk-Hoppé K.R.: Evolutionary finance. In: Hens, T., Schenk-Hoppé, K.R. (eds.) Handbook of Financial Markets: Dynamics and Evolution, Chapter 9, pp. 507–566. Elsevier, Amsterdam (2009)

    Chapter  Google Scholar 

  18. Evstigneev, I.V., Hens, T., Schenk-Hoppé, K.R.: Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset. Swiss Finance Institute research paper no. 10–36 (2011)

  19. Farmer J.D., Lo A.W.: Frontiers of finance: evolution and efficient markets. Proc. Natl. Acad. Sci. USA 96, 9991–9992 (1999)

    Article  Google Scholar 

  20. Gale D.: On optimal development in a multi-sector economy. Rev. Econ. Stud. 34, 1–18 (1967)

    Article  MathSciNet  Google Scholar 

  21. Grandmont, J.-M. (ed.): Temporary Equilibrium. Academic Press, San Diego (1988)

    MATH  Google Scholar 

  22. Hakansson N.H., Ziemba W.T.: Capital growth theory. In: Jarrow, R.A., Maksimovic, V., Ziemba, W.T. (eds.) Handbooks in Operations Research and Management Science, vol. 9: Finance, pp. 65–86. Elsevier, Amsterdam (1995)

    Google Scholar 

  23. Kelly J.L.: A new interpretation of information rate. Bell Syst. Techn. J. 35, 917–926 (1956)

    Google Scholar 

  24. Kuhn D., Luenberger D.G.: Analysis of the rebalancing frequency in log-optimal portfolio selection. Quant. Finance 10, 221–234 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  25. LeBaron B., Arthur W.B., Palmer R.: Time series properties of an artificial stock market. J. Econ. Dyn. Control 23, 1487–1516 (1999)

    Article  MATH  Google Scholar 

  26. Luce R., Raiffa H.: Games and Decisions, 2nd edn. Dover, New York (1989)

    Google Scholar 

  27. Lux T.: Stochastic behavioral asset pricing models and the stylized facts. In: Hens, T., Schenk-Hoppé, K.R. (eds.) Handbook of Financial Markets: Dynamics and Evolution, Chapter 3, pp. 161–211. Elsevier, Amsterdam (2009)

    Chapter  Google Scholar 

  28. Magill M., Quinzii M.: Theory of Incomplete Markets. MIT Press, Cambridge (1996)

    Google Scholar 

  29. Maitra A., Sudderth W.D.: Discrete Gambling and Stochastic Games. Springer, New York (1996)

    MATH  Google Scholar 

  30. Marshall A.: Principles of Economics, 8th edn. Macmillan, London (1949)

    Google Scholar 

  31. Maynard Smith J.: Evolution and the Theory of Games. Cambridge University Press, Cambridge (1982)

    MATH  Google Scholar 

  32. McKenzie, L.W.: Optimal economic growth, turnpike theorems and comparative dynamics. In: Arrow, K.J., Intrilligator, M.D. (eds.) Handbook of Mathematical Economics, vol. III, pp. 1281–1355. Amsterdam, North Holland (1986)

  33. Nikaido H.: Convex Structures and Economic Theory. Academic Press, New York (1968)

    MATH  Google Scholar 

  34. Radner R.: Existence of equilibrium of plans, prices, and price expectations in a sequence of markets. Econometrica 40, 289–303 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  35. Sahi S., Yao S.: The noncooperative equilibria of a trading economy with complete markets and consistent prices. J. Math. Econ. 18, 325–346 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  36. Samuelson L.: Evolutionary Games and Equilibrium Selection. MIT Press, Cambridge (1997)

    MATH  Google Scholar 

  37. Samuelson P.A.: Foundations of Economic Analysis. Harvard University Press, Cambridge (1947)

    MATH  Google Scholar 

  38. Schlicht E.: Isolation and Aggregation in Economics. Springer, Berlin (1985)

    Book  MATH  Google Scholar 

  39. Secchi P., Sudderth W.D.: Stay-in-a-set games. Int. J. Game Theory 30, 479–490 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  40. Shapley L.S.: Stochastic games. Proc. Natl. Acad. Sci. USA 39, 1095–1100 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  41. Shapley, L.S.: Noncooperative general exchange. In: Lin, S.A.Y. (ed.) Theory and Measurement of Economic Externalities, pp. 155–175. Academic Press, New York (1976)

  42. Shapley L.S., Shubik M.: Trade using one commodity as a means of payment. J. Political Econ. 85, 937–968 (1977)

    Article  Google Scholar 

  43. Shubik M.: A theory of money and financial institutions. Fiat money and noncooperative equilibrium in a closed economy. Int. J. Game Theory 1, 243–268 (1972)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Economics, University of Arizona, Tucson, AZ, 85721-0108, USA

    Rabah Amir

  2. Department of Economics, School of Social Sciences, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

    Igor V. Evstigneev

  3. Department of Banking and Finance, University of Zurich, Plattenstrasse 32, 8032, Zurich, Switzerland

    Thorsten Hens

  4. Department of Finance and Management, Norwegian School of Economics and Business Administration, Helleveien 30, 5045, Bergen, Norway

    Thorsten Hens

  5. Department of Strategy and Policy, Business School, National University of Singapore, 15 Kent Ridge Drive, Singapore, 119245, Singapore

    Le Xu

Authors
  1. Rabah Amir
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  2. Igor V. Evstigneev
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  3. Thorsten Hens
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  4. Le Xu
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Correspondence to Igor V. Evstigneev.

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Amir, R., Evstigneev, I.V., Hens, T. et al. Evolutionary finance and dynamic games. Math Finan Econ 5, 161–184 (2011). https://doi.org/10.1007/s11579-011-0053-2

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  • DOI: https://doi.org/10.1007/s11579-011-0053-2

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