Keywords: evolutionary game theory, stochastic differential equation, evolutionary dynamics.
@article{TVP_2023_68_4_a4,
author = {M. V. Zhitlukhin},
title = {On a diffusion approximation of some prediction game},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {751--768},
year = {2023},
volume = {68},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2023_68_4_a4/}
}
M. V. Zhitlukhin. On a diffusion approximation of some prediction game. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 4, pp. 751-768. http://geodesic.mathdoc.fr/item/TVP_2023_68_4_a4/
[1] R. Amir, I. V. Evstigneev, T. Hens, K. R. Schenk-Hoppé, “Market selection and survival of investment strategies”, J. Math. Econom., 41:1-2 (2005), 105–122 | DOI | MR | Zbl
[2] R. Amir, I. V. Evstigneev, K. R. Schenk-Hoppé, “Asset market games of survival: a synthesis of evolutionary and dynamic games”, Ann. Finance, 9:2 (2013), 121–144 | DOI | MR | Zbl
[3] A. Beygelzimer, J. Langford, D. M. Pennock, “Learning performance of prediction markets with Kelly bettors”, AAMAS{'}12: Proceedings of the 11th international conference on autonomous agents and multiagent systems, v. 3, IFAAMAS, Richland, SC, 2012, 1317–1318 https://dl.acm.org/doi/abs/10.5555/2343896.2343982
[4] L. Blume, D. Easley, “Evolution and market behavior”, J. Econom. Theory, 58:1 (1992), 9–40 | DOI | MR | Zbl
[5] G. Bottazzi, P. Dindo, “Evolution and market behavior with endogenous investment rules”, J. Econom. Dynam. Control, 48 (2014), 121–146 | DOI | MR | Zbl
[6] G. Bottazzi, D. Giachini, “Wealth and price distribution by diffusive approximation in a repeated prediction market”, Phys. A, 471 (2017), 473–479 | DOI | MR | Zbl
[7] G. Bottazzi, D. Giachini, “Far from the madding crowd: collective wisdom in prediction markets”, Quant. Finance, 19:9 (2019), 1461–1471 | DOI | MR | Zbl
[8] S. Boyd, L. Vandenberghe, Convex optimization, Cambridge Univ. Press, Cambridge, 2004, xiv+716 pp. | DOI | MR | Zbl
[9] I. V. Evstigneev, T. Hens, K. R. Schenk-Hoppé, “Market selection of financial trading strategies: Global stability”, Math. Finance, 12:4 (2002), 329–339 | DOI | MR | Zbl
[10] I. Evstigneev, T. Hens, K. R. Schenk-Hoppé, “Evolutionary behavioral finance”, The handbook of post crisis financial modeling, Palgrave Macmillan, London, 2016, 214–234 | DOI
[11] D. Fudenberg, C. Harris, “Evolutionary dynamics with aggregate shocks”, J. Econom. Theory, 57:2 (1992), 420–441 | DOI | MR | Zbl
[12] T. Holtfort, “From standard to evolutionary finance: a literature survey”, Manag. Rev. Q., 69:2 (2019), 207–232 | DOI
[13] W. Kets, D. Pennock, R. Sethi, N. Shah, “Betting strategies, market selection, and the wisdom of crowds”, The 28th AAAI conference on artificial intelligence, Proceedings of the AAAI conference on artificial intelligence, 28, no. 1, AAAI Press, Palo Alto, CA, 2014, 735–741 | DOI
[14] A. Kolmogoroff, “Sulla teoria di Volterra della lotta per l'esistenza”, Giorn. Ist. Ital. Attuari, 7 (1936), 74–80 | Zbl
[15] P. D. Taylor, L. B. Jonker, “Evolutionary stable strategies and game dynamics”, Math. Biosci., 40:1-2 (1978), 145–156 | DOI | MR | Zbl
[16] J. Wolfers, E. Zitzewitz, “Prediction markets”, J. Econ. Perspect., 18:2 (2004), 107–126 | DOI
[17] I. I. Gihman, A. V. Skorohod, Stochastic differential equations, Ergeb. Math. Grenzgeb., 72, Springer-Verlag, New York–Heidelberg, 1972, viii+354 pp. | MR | MR | Zbl | Zbl
[18] J. Jacod, A. N. Shiryaev, Limit theorems for stochastic processes, Grundlehren Math. Wiss., 288, Springer-Verlag, Berlin, 1987, xviii+601 pp. | DOI | MR | MR | MR | Zbl | Zbl
[19] A. N. Kolmogorov, “Kachestvennoe izuchenie matematicheskikh modelei dinamiki populyatsii”, Problemy kibernetiki, 25, Nauka, M., 1972, 101–106 | MR | Zbl
[20] R. Sh. Liptser, A. N. Shiryayev, Theory of martingales, Math. Appl. (Soviet Ser.), 49, Kluwer Acad. Publ., Dordrecht, 1989, xiv+792 pp. | DOI | MR | MR | Zbl | Zbl