The hyperbolic banker and price

The hyperbolic currency banker alwyays has an liabilities and assets as cosh and sinh, respectively. The former is deposits, the later loans. His clearing function are accumulatn rates projected two period ahead, cosh^2 - sinh^2 = 1.

He is adjusting the cummulant rates to define a unit variance such that prices stabilize over the shortest term. Buried in those function is principal, and the outcome is never exact.

So, for the firm, what is sinh/cosh? That is the firms liabilities over assets, almost always less than one, the firm is profitable. That is the firms purchase price for inventory, price.

So we have (1/2)*p'' +p * p' = 0, the standard hyperbolic equation.  The ' market means finite derivative over the firms inventory cycle. I think this is right, but the pros need to check me on this.