On Stock Trading Via Feedback Control When Underlying Stock Returns Are Discontinuous

Trading rules based on feedback laws have recently attracted significant attention in the control community. One of the main results in this area states that the gain obtained by so-called simultaneously long short strategies has positive expectation for price processes governed by geometric Brownian motion. This technical note shows that this result extends to Merton's jump diffusion model. Particularly, we show that the expected total profit is invariant to the jumps and so still positive.

[1]  B. Ross Barmish,et al.  A drawdown formula for stock trading via linear feedback in a market governed by Brownian Motion , 2013, 2013 European Control Conference (ECC).

[2]  B. Ross Barmish,et al.  On the use of model-free linear feedback to trade stock: Two open research problems , 2014, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[3]  The Conservative Expected Value: A New Measure with Motivation from Stock Trading via Feedback , 2014 .

[4]  F. Black,et al.  The Valuation of Option Contracts and a Test of Market Efficiency , 1972 .

[5]  R. C. Merton,et al.  Optimum consumption and portfolio rules in a continuous - time model Journal of Economic Theory 3 , 1971 .

[6]  B. Ross Barmish,et al.  On arbitrage possibilities via linear feedback in an idealized Brownian Motion stock market , 2011, IEEE Conference on Decision and Control and European Control Conference.

[7]  R. C. Merton,et al.  Optimum Consumption and Portfolio Rules in a Continuous-Time Model* , 1975 .

[8]  B. Barmish,et al.  On Stock Trading Over a Lattice via Linear Feedback , 2014 .

[9]  S Iwarere,et al.  A confidence interval triggering method for stock trading via feedback control , 2010, Proceedings of the 2010 American Control Conference.

[10]  Michael Heinrich Baumann,et al.  Effects of linear feedback trading in an interactive market model , 2015, 2015 American Control Conference (ACC).

[11]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[12]  B. Ross Barmish,et al.  On market-neutral stock trading arbitrage via linear feedback , 2012, 2012 American Control Conference (ACC).

[13]  B. Ross Barmish,et al.  On a New Paradigm for Stock Trading Via a Model-Free Feedback Controller , 2016, IEEE Transactions on Automatic Control.

[14]  B. Ross Barmish,et al.  On the basics for simulation of feedback-based stock trading strategies: An invited tutorial session , 2013, 52nd IEEE Conference on Decision and Control.

[15]  G. Calafiore,et al.  Experiments on stock trading via feedback control , 2010, 2010 2nd IEEE International Conference on Information and Financial Engineering.

[16]  B. Ross Barmish,et al.  ACC 2012 tutorial session: An introduction to hedged-like stock trading from a control theoretic point of view , 2012, 2012 American Control Conference (ACC).

[17]  B. Ross Barmish,et al.  How useful are mean-variance considerations in stock trading via feedback control? , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[18]  B. Ross Barmish,et al.  On stock trading using a PI controller in an idealized market: The robust positive expectation property , 2013, 52nd IEEE Conference on Decision and Control.

[19]  B. Ross Barmish,et al.  Stock Trading via Feedback Control , 2015, Encyclopedia of Systems and Control.

[20]  B. Ross Barmish,et al.  On Trading of Equities: A Robust Control Paradigm , 2008 .

[21]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[22]  H. J. Kushner,et al.  Stochastic Stability , 2005 .

[23]  B. Ross Barmish,et al.  On performance limits of feedback control-based stock trading strategies , 2011, Proceedings of the 2011 American Control Conference.

[24]  S. James Press,et al.  A Compound Events Model for Security Prices , 1967 .

[25]  B. Ross Barmish,et al.  ACC 2011 tutorial session: An introduction to option trading from a control perspective , 2011, Proceedings of the 2011 American Control Conference.