Patent Valuation under Spatial Point Processes with Delayed and Decreasing Jump Intensity

This article is set within the real options approach applied to patent valuation. Such evaluation is based on the knowledge of the impact of some events on the underlying state, which is modeled in discrete time as a spatial point process, i.e. both size and time of the jumps can be treated as random variables. This assumption allows us to improve upon the current theory of patent valuation in some respects. In particular, the propagation of the jumps from the economic environment to the patent value is not restricted to be immediate, but can occur with a random delay and with varying intensity, depending on the time to maturity. These actual features lead to a more general formula for patent value that may give rise to a non-trivial difference not accounted for in the existing literature.