The purpose of this editorial is to consider whether or not the classical “Lanchester equations” of military combat are useful for modeling the financial risks associated with contemporary terrorist attacks.
The paper begins by describing Lanchester's original model and its realm of applicability; then identifies shortcomings of the original equations, which, having been aggravated by differences between classical military combat and modern terrorist engagements, impede the application of the Lanchester paradigm in today's world. Finally, the paper explores whether or not these obstacles can be overcome by appropriate extensions of Lanchester's mathematical theory.
The principal result is that the Lanchester equations may be extended in a very natural way to include stochastic elements, difficult‐to‐quantify components, and various force asymmetries, thereby enabling the modeling of engagements between conventional and terrorist forces. Specifically, a family of diffusion processes is proposed to capture the terrorists' progress toward destroying a target, and provide a method for explicitly calculating the probability of target destruction.
The editorial seeks to model a category of catastrophe risk – terrorist attacks – for which the current mathematical literature (both military and financial) is somewhat limited.
