2025.06.11 meeting notes

MFBM

• pypi: https://pypi.org/project/mfbm/
• github: github.com/leonardo-toffalini/mfbm

Rewrote entire infra

• instead of multiple envs, now there is only one general env
• the general env supports any number of stocks
• the general env can be customized with the following:
  • time horizon generator, this enables the time horizon to vary each time the env is reset, example usage is function that returns based on the number of calls
  • num stocks, this enables for any number of stocks to be traded simultaniously
  • process generator, this alow any kind of $\mathbb{R}\to {\mathbb{R}}^n$ process where n is num stocks, for example mfBm
  • optional utility, to be a true generalization of the other envs a utility is needed, default is the identity $u(x)=x$

for example, the previous AREnv is equivalent to this general environment instantiated with the following:

• constant time horizon generator
• num stocks = 1
• AR(1) process generator with the added arguments
• $u(x)=1-e^{-x}$ utility function
• self._lambda = 0 for no friction

another example is the previously non existent mfBm environment:

• constant time horizon generator

• num stocks = p

• mfBm process generator with the added arguments like hursts, rho, etc.

• identity utility

• many common sense strategies come with the general env:

  • contrarian strategy
  • momentum strategy
  • buy and hold strategy
  • piecewise fBm optimal strategy

• many time horizon generators are implemented:

  • constant
  • linear
  • exp
  • log
  • noisy log
  • random uniform

• some other utility functions are also provided, for plotting rollouts and prices etc.

TODO:

• maybe num_stocks is not necessary for instantiating MultiInvestEnv, because we only need to check the process generator output shape
• implement OU process generator
• implement optimal OU strat as defined in Rasonyi Guasoni Nika Example 5.3.