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EMA-type trading strategies maximize utility under partial information

  • *Corresponding author

    *Corresponding author

The second author was supported by a Simons Collaboration Grant

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  • 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.

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


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  • [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. FouqueA. 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. KoijenJ. 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. LorigZ. 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. ReidRiccati Differential Equations, Academic Press, 1972. 
    [19] Jie XiongAn Introduction to Stochastic Filtering Theory, Oxford University Press, 2008. 
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