Obviously, if the 'blow-ups' are removed from the hedge-fund community, they will not be in contact with the susceptibles group. Therefore, the number of susceptible hedge funds is only proportional to both the number of infected hedge-funds and the number of susceptibles, and so we have:
However, the removals (i.e the blow-ups) should be considered in the differential equation for the number of infected hedge funds i.e equation (A1.2), which should be modified to:
The equation for the number of hedge funds removed from the infectives with removal rate γ then becomes:
At the start of the crisis, when t = 0 , we assume that there are no removals, a very small number of infectives, Io , and the remaining population is susceptible, S, which is approximately equal to n. Thus, at t = 0, (S,I,R) take the values (So,Io,0). For convenience, we make use of
μ = γ/β, as the relative removal rate.
From equation (A1.5), it follows that unless μ is less than So there will not be a crisis the in hedge-fund sub-group as [dl/dt]t=0 is required to be greater than zero. On the other hand, for the case μ > So, the number of affected hedge-funds will be increasing. Therefore, the relative removal rate, μ = So , gives a threshold density of susceptibles.
Stay tuned for Part 3
Please Note: This model is inspired by a paper co-authored by Jim Caldwell and Kei Shing Ng, titled: Deterministic Model in Contagious Disease, and is going through a continual overhaul to make it more robust. So far I've had this model critiqued by Rick Bookstaber, author of A Demon Of Our Own Design: Markets, Hedge Funds And The Perils of Financial Innovation, and he highlighted a lot of flaws, in the model and its presentation, that I'm currently addressing. Dr. Ernest Chan, the author of a quantitative text titled Quantitative Trading: How to Build Your Own Algorithmic Trading Business is also in the process of critiquing the model, and I'll also take his opinions on board. Furthermore, Dr. Jim Caldwell, the originator of the model I drew analogies from, also gave me a few pointers on how to make the model more realistic, and I'll also be taking his pointers on board. I also benefited from Eric Falkenstein's critique of the model, and I will be taking his suggestions on board as well. Please stay tuned!
However, the removals (i.e the blow-ups) should be considered in the differential equation for the number of infected hedge funds i.e equation (A1.2), which should be modified to:
The equation for the number of hedge funds removed from the infectives with removal rate γ then becomes:
At the start of the crisis, when t = 0 , we assume that there are no removals, a very small number of infectives, Io , and the remaining population is susceptible, S, which is approximately equal to n. Thus, at t = 0, (S,I,R) take the values (So,Io,0). For convenience, we make use ofμ = γ/β, as the relative removal rate.
From equation (A1.5), it follows that unless μ is less than So there will not be a crisis the in hedge-fund sub-group as [dl/dt]t=0 is required to be greater than zero. On the other hand, for the case μ > So, the number of affected hedge-funds will be increasing. Therefore, the relative removal rate, μ = So , gives a threshold density of susceptibles.
Please Note: This model is inspired by a paper co-authored by Jim Caldwell and Kei Shing Ng, titled: Deterministic Model in Contagious Disease, and is going through a continual overhaul to make it more robust. So far I've had this model critiqued by Rick Bookstaber, author of A Demon Of Our Own Design: Markets, Hedge Funds And The Perils of Financial Innovation, and he highlighted a lot of flaws, in the model and its presentation, that I'm currently addressing. Dr. Ernest Chan, the author of a quantitative text titled Quantitative Trading: How to Build Your Own Algorithmic Trading Business is also in the process of critiquing the model, and I'll also take his opinions on board. Furthermore, Dr. Jim Caldwell, the originator of the model I drew analogies from, also gave me a few pointers on how to make the model more realistic, and I'll also be taking his pointers on board. I also benefited from Eric Falkenstein's critique of the model, and I will be taking his suggestions on board as well. Please stay tuned!
