Mark E. Burke | Searcharxiv

arXiv2020

A Generalized Framework for Simultaneous Long-Short Feedback Trading

We present a generalization of the Simultaneous Long-Short (SLS) trading strategy described in recent control literature wherein we allow for different parameters across the short and long sides of the controller; we refer to this new strategy as Generalized SLS (GSLS). Furthermore, we investigate the conditions under which positive gain can be assured within the GSLS setup for both deterministic stock price evolution and geometric Brownian motion. In contrast to existing literature in this area (which places little emphasis on the practical application of SLS strategies), we suggest optimization procedures for selecting the control parameters based on historical data, and we extensively test these procedures across a large number of real stock price trajectories (495 in total). We find that the implementation of such optimization procedures greatly improves the performance compared with fixing control parameters, and, indeed, the GSLS strategy outperforms the simpler SLS strategy in general.

q-fin.TR↗

arXiv2020

A Generalization of the Classical Kelly Betting Formula to the Case of Temporal Correlation

For sequential betting games, Kelly's theory, aimed at maximization of the logarithmic growth of one's account value, involves optimization of the so-called betting fraction $K$. In this Letter, we extend the classical formulation to allow for temporal correlation among bets. To demonstrate the potential of this new paradigm, for simplicity of exposition, we mainly address the case of a coin-flipping game with even-money payoff. To this end, we solve a problem with memory depth $m$. By this, we mean that the outcomes of coin flips are no longer assumed to be i.i.d.random variables. Instead, the probability of heads on flip $k$ depends on previous flips $k-1,k-2,...,k-m$. For the simplest case of $n$ flips, with $m = 1$, we obtain a closed form solution $K_n$ for the optimal betting fraction. This generalizes the classical result for the memoryless case. That is, instead of fraction $K^* = 2p-1$ which pervades the literature for a coin with probability of heads $p\geq 1/2$, our new fraction $K_n$ depends on both $n$ and the parameters associated with the temporal correlation. Generalizations of these results for $m > 1$ and numerical simulations are also included. Finally, we indicate how the theory extends to time-varying feedback and alternative payoff distributions.

math.OC↗