EMA-type trading strategies maximize utility under partial information

Xiaodong Chen; Roger Lee

doi:10.3934/fmf.2023005

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2023, Volume 2, Issue 1: 124-140. Doi: 10.3934/fmf.2023005 open access

This issue Previous Article Data-driven nonparametric robust control under dependence uncertainty Next Article

EMA-type trading strategies maximize utility under partial information

Xiaodong Chen^1, and
Roger Lee^1, ,

1.
Department of Mathematics, University of Chicago, USA

^*Corresponding author
^*Corresponding author

Received: September 2022

Revised: December 2022

Early access: March 2023

Published: March 2023

The second author was supported by a Simons Collaboration Grant

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Abstract

Consider a partially-informed trader who does not observe the true drift of a financial asset. Under Gaussian price dynamics with stochastic unobserved drift, including cases of mean-reversion and momentum dynamics, we take a filtering approach to solve explicitly for trading strategies which maximize expected logarithmic, exponential, and power utility. We prove that the optimal strategies depend on current price and an exponentially-weighted moving average (EMA) price, and in some cases current wealth – not on any other stochastic variables. We establish optimality over all price-history-dependent strategies satisfying integrability criteria, not just EMA-type strategies. Thus the condition that the optimal trading strategy reduces to a function of EMA and current price is not an assumption but rather a consequence of our analysis. We solve explicitly for the optimal parameters of the EMA-type strategies, and verify optimality rigorously.

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Mathematics Subject Classification: Primary: 91G10; Secondary: 93E11.

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References

[1]	M. Boguslavsky and E. Boguslavskaya, Arbitrage under power, RISK Magazine, (2004), 69-73.
[2]	S. Brendle, Portfolio selection under incomplete information, Stochastic Processes and their Applications, 116 (2006), 701-723. doi: 10.1016/j.spa.2005.11.010.
[3]	M. H. A. Davis and S. Lleo, Risk-Sensitive Investment Management, World Scientific, 2014. doi: 10.1142/9026.
[4]	J. Detemple, Asset pricing in a production economy with incomplete information, Journal of Finance, 41 (1986), 383-391. doi: 10.1111/j.1540-6261.1986.tb05043.x.
[5]	J.-P. Fouque, A. Papanicolaou and R. Sircar, Filtering and portfolio optimization with stochastic unobserved drift in asset returns, Communications in Mathematical Sciences, 13 (2015), 935-953.
[6]	R. Frey, A. Gabih and R. Wunderlich, Portfolio optimization under partial information with expert opinions, International Journal of Theoretical and Applied Finance, 15 (2012), 1250009, 18 pp. doi: 10.1142/9789814407892_0011.
[7]	P. Guasoni, Asymmetric information in fads models, Finance and Stochastics, 10 (2006), 159-177. doi: 10.1007/s00780-006-0006-4.
[8]	G. Kallianpur, Stochastic Filtering Theory, Springer, 1980. doi: 10.1007/978-1-4757-6592-2.
[9]	I. Karatzas and X. Zhao, Bayesian adaptive portfolio optimization, in Handbooks in Mathematical Finance: Option Pricing, Interest Rates and Risk Management, chapter 17, 632-669. Cambridge University Press, 2001.
[10]	T. S. Kim and E. Omberg, Dynamic nonmyopic portfolio behavior, Review of Financial Studies, 9 (1996), 141-161. doi: 10.1093/rfs/9.1.141.
[11]	F. Klebaner and R. Liptser, When a stochastic exponential is a true martingale. Extension of the Beneš method, Theory of Probability and its Applications, 58 (2014), 38-62.
[12]	R. S. J. Koijen, J. C. Rodríguez and A. Sbuelz, Momentum and mean reversion in strategic asset allocation, Management Science, 55 (2009), 1199-1213.
[13]	P. Lakner, Optimal trading strategy for an investor: The case of partial information, Stochastic Processes and their Applications, 76 (1998), 77-97. doi: 10.1016/S0304-4149(98)00032-5.
[14]	S. Lee and A. Papanicolaou, Pairs trading of two assets with uncertainty in co-integration's level of mean reversion, International Journal of Theoretical and Applied Finance, 19 (2016), 1650054, 36 pp.
[15]	R. Liptser and A. Shiryaev, Statistics of Random Processess Ⅱ, Springer, 2nd edition, 2001.
[16]	M. Lorig, Z. Zhou and B. Zou, A mathematical analysis of technical analysis, Applied Mathematical Finance, 26 (2019), 38-68. doi: 10.1080/1350486X.2019.1588136.
[17]	R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, Review of Economics and Statistics, 51 (1969), 247-257. doi: 10.2307/1926560.
[18]	W. Reid, Riccati Differential Equations, Academic Press, 1972.
[19]	Jie Xiong, An Introduction to Stochastic Filtering Theory, Oxford University Press, 2008.