Corporate crack filling

In my recent post, I described a simple model of firms.  I'm now reflecting on what I left out and how to situate the main areas of study of the company.  First of all, there's no concept of spatial location between companies.  Second, there's no concept of what the companies do.  Third, their value is a single number which compresses down to a single point the whole balance sheet and income statement, and, more generally still, the set of internal actions which constitute the life of a company, including representation of its debt and outstanding securities (the behaviour of the company's finance department).  Fourth, there's only one kind of ownership style, whereas in reality there are many.

In general the system doesn't move.  Modelling 120,000,000 companies, I'm going to have to make some simplifications. But that's OK and is done often in analysing the company from an economic point of view.  I briefly explained how it could be initially calibrated so that value is distributed and ownership is distributed according to the Zipf/Pareto power laws we see in our own economies.

Also, just as it can be said that all humans are the final owners of all company value, so too in general with economic value. It would be good to know how much extra-corporate wealth there is and to similarly arrange it.  This at the very least would put a constraint on the scope of purchases.

There also needs to be a random element (a stochastic process) to the growth and contraction of wealth within any one particular company.  Clearly, the singular 'value' of a company is not entirely randomly driven, but is expressed as an algorithm, whose parameters determine the current 'health' of that company.

Adding a spatial constraint will guide which companies to 'interact' with which others.

Everything is expressed in one currency.  Having a spatial element will allow there to be a number of regions with their own currency domains, and with the possibility of calculating macro-economic measures, like balance of trade, foreign investment, currency controls.

The shape and behaviour of a modern company is also hugely a function of the policy and legal framework within which it works, and that itself is enormous and complex.  The availability of credit also drives some of the key parameters around risk taking within companies.

Insofar as the market capitalisation (value) of a company is a function of the equity, then all those options models (Heston etc) might be useful for building an equity-as-call Merton model of the company.

I also have a long-standing idea to model news arrival as an inhomogeneous Poisson process, but that's  all going to have to wait until much later.