1. This article proposes a simple bubble and crash model which can be used to develop crash- and rally-aware optimal portfolios.
2. The model stresses the importance of positive feedback, with financial markets self-correcting only at long time scales while exhibiting significant departure from “normality” at short times.
3. The model combines a geometric random walk with a discrete Poisson distributions of crashes/rallies, and is arbitrage free.
The article provides an interesting insight into the development of a bubble and crash model which can be used to develop crash- and rally-aware optimal portfolios. The article is well written and provides clear explanations of the concepts discussed, as well as examples on real financial time series that exhibited bubbles and crashes.
However, there are some potential biases in the article which should be noted. Firstly, the article does not provide any evidence for its claims or explore any counterarguments to its proposed model. Secondly, it does not present both sides equally; instead it focuses solely on the benefits of its proposed model without exploring any potential risks or drawbacks associated with it. Thirdly, there is some promotional content in the article which could be seen as biased towards its proposed model.
In conclusion, while this article provides an interesting insight into bubble and crash models, it should be read critically due to potential biases in its presentation of information.