Simultaneously long short trading in discrete and continuous time

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Baumann, Michael Heinrich ; Grüne, Lars:
Simultaneously long short trading in discrete and continuous time.
In: Systems & Control Letters. Vol. 99 (2017) . - pp. 85-89.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2016.11.011

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Simultaneously long short (SLS) feedback trading strategies are known to yield positive expected gain by zero initial investment for price processes governed by, e.g., geometric Brownian motion or Merton’s jump diffusion model. In this paper, we generalize these results to positive prices with stochastically independent multiplicative growth and constant trend in discrete and continuous time as well as for sampled-data systems and show that in all cases the SLS strategies’ expected gain does not depend on the price model but only on the trend.