  We simulate a simplified version of the price process including bubbles and
crashes proposed in Kreuser and Sornette (2018). The price process is defined
as a geometric random walk combined with jumps modelled by separate, discrete
distributions associated with positive (and negative) bubbles. The key
ingredient of the model is to assume that the sizes of the jumps are
proportional to the bubble size. Thus, the jumps tend to efficiently bring back
excess bubble prices close to a normal or fundamental value (efficient
crashes). This is different from existing processes studied that assume jumps
that are independent of the mispricing. The present model is simplified
compared to Kreuser and Sornette (2018) in that we ignore the possibility of a
change of the probability of a crash as the price accelerates above the normal
price. We study the behaviour of investment strategies that maximize the
expected log of wealth (Kelly criterion) for the risky asset and a risk-free
asset. We show that the method behaves similarly to Kelly on Geometric Brownian
Motion in that it outperforms other methods in the long-term and it beats
classical Kelly. As a primary source of outperformance, we determine knowledge
about the presence of crashes, but interestingly find that knowledge of only
the size, and not the time of occurrence, already provides a significant and
robust edge. We then perform an error analysis to show that the method is
robust with respect to variations in the parameters. The method is most
sensitive to errors in the expected return.
