On the small risk approximation
Faculty of Applied Economics
Insurance: mathematics and economics. - Amsterdam
, p. 151-157
University of Antwerp
A small risk is a random variable whose deviation from its mean is small in some sense, so that we may replace, for example, X by μ+z(X − μ) and expand related functions and random variables in terms of powers of z. Several models are revisited (the problem of Pareto optimal risk exchanges, equilibrium, the reinsurer's monopoly and the Bowley solution) and approximate solutions are found. The last model (chains of reinsurance) is new.