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L. F. Richardson in THE STATISTICS OF DEADLY QUAR- RELS formulated mathematical models dealing with the occurrence & prosecution of wars, showing that wars arise from measurable relations between nations & groups. It is concluded that, except for chance fluctuations, wars have been occurring at a constant rate throughout the 120 yr period 1820-1939. The role of chance processes in history is discussed. The application of a probabilistic model of group formation to the size distribution of war alliances extends this concept & explains the observed size distribution in the nations which fought in these tions joining & leaving war alliances with certain specified probabilities, obtained as follows: There is a fixed probability over time that any nation entering a war will fight by itself. The probability of it joining an alliance containing a particular N of nations is proportional to the N of nations already in alliances of that size. The probability of a nation leaving an alliance is independent of the alliance's size & occurs only when the entire alliance breaks up. Such a stochastic process eventually reaches an equilibrium distribution of sizes of alliances. Resulting from these assumptions is the Yule distribution, & the observed distribution of the N of war alliances with 1, 2, 3, etc, nations on a side fits the Yule distribution very closely. The rules for formation & dissolution are in accord with our intuitive assumptions concerning the dynamics operating in aggressive & peaceful groups. Such random processes play an important role in soc dynamics & in the occurrence of large scale historical events. Historians, recognizing this fact, could develop more quantitative historical laws. Modified AA.

2.5. Risk-neutral probabilities: alternative derivation of the Black-Scholes formula2.6. American options in the Black-Scholes model; 2.7. Exotic options; Chapter 3. Models of Interest Rates; 3.1. Modeling principles; 3.2. The Vašíček model; 3.3. The Cox-Ingersoll-Ross model; 3.4. The Heath-Jarrow-Morton model; Bibliography; Index; Back Cover