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Guasoni, Paolo; Nika, Zsolt; Rásonyi, MiklóS

Trading fractional Brownian motion. (English) Zbl 1429.91290

SIAM J. Financ. Math. 10, No. 3, 769-789 (2019).
The authors consider a market with an asset price described by fractional Brownian motion, which can be traded with temporary nonlinear price impact. The asymptotically optimal strategies for the maximization of expected terminal wealth are obtained. These strategies generate an average terminal wealth that grows with a power of the horizon, the exponent depending on both the Hurst and the price-impact parameters. Obtained results are extended to long memory Gaussian processes and to a class of H-self-similar processes.
Reviewer: Aleksandr D. Borisenko (Kyïv)

Cited in 4 Documents

MSC:

91G10 Portfolio theory
91G80 Financial applications of other theories
60G22 Fractional processes, including fractional Brownian motion

Keywords:

fractional Brownian motion; transaction costs; price impact; trading; asymptotically optimal strategies; expected terminal wealth; Gaussian processes with long memory; self-similar processes
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\textit{P. Guasoni} et al., SIAM J. Financ. Math. 10, No. 3, 769--789 (2019; Zbl 1429.91290)
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References:

[1] R. T. Baillie, Long memory processes and fractional integration in econometrics, J. Econometrics, 73 (1996), pp. 5–59, https://doi.org/10.1016/0304-4076(95)01732-1.
[2] J.-P. Bouchaud, J. D. Farmer, and F. Lillo, How markets slowly digest changes in supply and demand, in Handbook of Financial Markets: Dynamics and Evolution, T. Hens and K. Schenk-Hoppe, eds., North-Holland, Amsterdam, 2008.
[3] P. Carmona and L. Coutin, Fractional Brownian motion and the Markov property, Electron. Commun. Probab., 3 (1998), pp. 95–107, https://doi.org/10.1214/ECP.v3-998. · Zbl 0921.60067
[4] P. Cheridito, Arbitrage in fractional Brownian motion models, Finance Stoch., 7 (2003), pp. 533–553, https://doi.org/10.1007/s007800300101. · Zbl 1035.60036
[5] C. Czichowsky, R. Peyre, W. Schachermayer, and J. Yang, Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs, Finance Stoch., 22 (2018), pp. 161–180, https://doi.org/10.1007/s00780-017-0351-5. · Zbl 1396.91683
[6] C. Czichowsky and W. Schachermayer, Portfolio optimisation beyond semimartingales: Shadow prices and fractional Brownian motion, Ann. Appl. Probab., 27 (2017), pp. 1414–1451, https://doi.org/10.1214/16-AAP1234. · Zbl 1414.91336
[7] A. Dasgupta and G. Kallianpur, Arbitrage opportunities for a class of Gladyshev processes, Appl. Math. Optim., 41 (2000), pp. 377–385, https://doi.org/10.1007/s002459911019. · Zbl 0960.91053
[8] E. F. Fama and K. R. French, Permanent and temporary components of stock prices, J. Political Econ., 96 (1988), pp. 246–273.
[9] L. Giraitis, H. L. Koul, and D. Surgailis, Large Sample Inference for Long Memory Processes, Imperial College Press, London, 2012, https://doi.org/10.1142/p591.
[10] M. T. Greene and B. D. Fielitz, Long-term dependence in common stock returns, J. Financ. Econ., 4 (1977), pp. 339–349.
[11] P. Guasoni, No arbitrage under transaction costs, with fractional Brownian motion and beyond, Math. Finance, 16 (2006), pp. 569–582, https://doi.org/10.1111/j.1467-9965.2006.00283.x. · Zbl 1133.91421
[12] P. Guasoni and M. Rásonyi, Hedging, arbitrage and optimality with superlinear frictions, Ann. Appl. Probab., 25 (2015), pp. 2066–2095, https://doi.org/10.1214/14-AAP1043.
[13] P. Guasoni, M. Rásonyi, and W. Schachermayer, Consistent price systems and face-lifting pricing under transaction costs, Ann. Appl. Probab., 18 (2008), pp. 491–520, https://doi.org/10.1214/07-AAP461. · Zbl 1133.91422
[14] B. Jacobsen, Long term dependence in stock returns, J. Empirical Finance, 3 (1996), pp. 393–417.
[15] A. W. Lo, Long-term memory in stock market prices, Econometrica, 59 (1991), pp. 1279–1313. · Zbl 0781.90023
[16] B. B. Mandelbrot, When can price be arbitraged efficiently? A limit to the validity of the random walk and martingale models, Rev. Econ. Statist., 53 (1971), pp. 225–236.
[17] J. M. Poterba and L. H. Summers, Mean reversion in stock prices: Evidence and implications, J. Financ. Econ., 22 (1988), pp. 27–59.
[18] L. C. G. Rogers, Arbitrage with fractional Brownian motion, Math. Finance, 7 (1997), pp. 95–105, https://doi.org/10.1111/1467-9965.00025. · Zbl 0884.90045
[19] D. M. Salopek, Tolerance to arbitrage, Stochastic Process. Appl., 76 (1998), pp. 217–230, https://doi.org/10.1016/S0304-4149(98)00025-8.
[20] V. Teverovsky, M. S. Taqqu, and W. Willinger, A critical look at Lo’s modified R/S statistic, J. Statist. Plann. Inference, 80 (1999), pp. 211–227, https://doi.org/10.1016/S0378-3758(98)00250-X. · Zbl 1044.60508
[21] W. Willinger, M. S. Taqqu, and V. Teverovsky, Stock market prices and long-range dependence, Finance Stoch., 3 (1999), pp. 1–13. · Zbl 0924.90029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.