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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 95, 2023 - Issue 1
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Research Article

Asymptotic minimization of expected time to reach a large wealth level in an asset market game

Pages 67-78 | Received 09 Jul 2020, Accepted 07 Feb 2022, Published online: 28 Feb 2022

References

  • P.H. Algoet and T.M. Cover, Asymptotic optimality and asymptotic equipartition properties of log-optimum investment, Ann. Probab. 16 (1988), pp. 876–898.
  • R. Amir, I.V. Evstigneev and K.R. Schenk-Hoppé, Asset market games of survival: a synthesis of evolutionary and dynamic games, Ann. Finance 9 (2013), pp. 121–144.
  • D.C. Aucamp, An investment strategy with overshoot rebates which minimizes the time to attain a specified goal, Manage. Sci. 23 (1977), pp. 1234–1241.
  • L. Blume and D. Easley, Evolution and market behavior, J. Econ. Theory 58 (1992), pp. 9–40.
  • L. Breiman, Optimal gambling systems for favorable games, in Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 1961, pp. 63–68.
  • S. Browne, Beating a moving target: optimal portfolio strategies for outperforming a stochastic benchmark, Financ. Stoch. 3 (1999), pp. 275–294.
  • M.A.H. Dempster, I.V. Evstigneev and K.R. Schenk-Hoppé, Volatility-induced financial growth, Quant. Finance 7 (2007), pp. 151–160.
  • Y. Drokin and M. Zhitlukhin, Relative growth optimal strategies in an asset market game, Ann. Finance. 16 (2020), pp. 529–546.
  • I. Evstigneev, T. Hens and K.R. Schenk-Hoppé, Evolutionary behavioral finance, in The Handbook of Post Crisis Financial Modelling, E. Haven, P. Molyneux and J. Wilson, eds., Palgrave Macmillan, London, 2016, pp. 214–234.
  • I.V. Evstigneev, T. Hens and K.R. Schenk-Hoppé, Market selection of financial trading strategies: global stability, Math. Finance. 12 (2002), pp. 329–339.
  • R. Fernholz and B. Shay, Stochastic portfolio theory and stock market equilibrium, J. Finance. 37 (1982), pp. 615–624.
  • M. Finkelstein and R. Whitley, Optimal strategies for repeated games, Adv. Appl. Probab. 13 (1981), pp. 415–428.
  • L. Györfi, G. Ottucsák and H. Walk, The growth optimal investment strategy is secure, too, in Optimal Financial Decision Making Under Uncertainty, G. Consigli, D. Kuhn, P. Brandimarte, eds., Springer, Cham, 2017, pp. 201–223.
  • T. Hens and K.R. Schenk-Hoppé, Evolutionary stability of portfolio rules in incomplete markets, J. Math. Econ. 41 (2005), pp. 43–66.
  • T. Holtfort, From standard to evolutionary finance: a literature survey, Manag. Rev. Q. 69 (2019), pp. 207–232.
  • I. Karatzas and C. Kardaras, The numéraire portfolio in semimartingale financial models, Financ. Stoch. 11 (2007), pp. 447–493.
  • C. Kardaras and E. Platen, Minimizing the expected market time to reach a certain wealth level, SIAM J. Financ. Math. 1 (2010), pp. 16–29.
  • J.L. Kelly Jr, A new interpretation of information rate, Bell Syst. Tech. J. 35 (1956), pp. 917–926.
  • H.A. Latane, Criteria for choice among risky ventures, J. Polit. Econ. 67 (1959), pp. 144–155.
  • J.B. Long, The numeraire portfolio, J. Financ. Econ. 26 (1990), pp. 29–69.
  • D. Luenberger, Investment Science, Oxford University Press, New York, 1998.
  • L.C. MacLean, E.O. Thorp and W.T. Ziemba, The Kelly Capital Growth Investment Criterion: Theory and Practice, Handbook in Financial Economic, Vol. 3, World Scientific, Singapore, 2011.
  • E. Platen and D. Heath, A Benchmark Approach to Quantitative Finance, Springer-Verlag, Berlin, 2006.
  • A.N. Shiryaev, Probability-2, 3rd ed., Springer, New York, 2019.
  • M. Zhitlukhin, Capital growth and survival strategies in a market with endogenous prices (2021). Available at arXiv:2101.09777.

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