We develop a model for valuing revenue streams from innovations. The stochastic properties of revenue from innovations create a more difficult environment in which to value options than when the underlying is a security. There is no initial revenue, and cumulative revenue cannot decrease....

Path dependent securities depend on current and past values of underlying state variables. Consequently, the usual backward evaluation technique is difficult to apply since state variable values existing earlier in real time are unknown. This paper develops a series of propositions which makes...

In cross-spectral analysis, the tau statistic is used to infer lead-lag relationships between series in the time domain. Unfortunately, it is frequently inferred that tau is meaningful only when the phase diagram is linear. In this paper it is shown that tau is far more robust than is generally...