Markov chains and the determination of fair premiums

The relationships between actuarial and pure mathematics are curious. Actuaries have contributed to the development of mathematical theory: it is sufficient to mention, as examples, Fredholm of an earlier, and Cramér of a more recent generation. Scandinavian mathematicians, in particular, have been concerned with a very special type of stochastic process, reflected in the collective theory of risk, and the work of Philipson, Ammeter and others in this field is well known to readers of this Bulletin. However, the main stream of the theory of stochastic processes has little contact with actuarial applications.On the other hand, many actuaries have studied and assimilated pure mathematics and have thrown light on actuarial matters by describing their own preoccupations in the terminology of modern, often abstract, mathematics. E. Franckx is one of their number.The Instituto di Matematica Finanziaria of the University of Trieste (Faculty of Economics and Commerce) has published a booklet entitledEssai d'une théorie opérationnelle des risques Markoviens which contains three lectures delivered by Professor Franckx in Trieste and a contribution which he presented to the 17th Congress of Actuaries, held in London in 1964.