How to work out the optimum burn rate for a startup

Interesting. If you replaced R(t) with a stochastic process, perhaps with a time-dependent drift, you could incorporate a degree of uncertainty into your revenue predictions. You would then be able to solve for the optimal burn rate B(t) using stochastic optimal control. Maybe that's getting a bit too extreme though.

I wonder if anybody has applied stochastic modelling to the early stages of a start-up; treating the choice of VC funding, exit timing, etc as real-options.