A Short Note on Overall Risk Management in an Insurance Concern

1. At an earlier ASTIN Colloquium participants were invited to present notes on problems which they considered as important but unsolved. There was little response to this invitation, presumably because a problem, once it is well formulated, is almost solved.In this Note I do not present any new problems. In stead I try to outline a framework which may be useful for analysing different risk problems and seeing them in their proper perspective. In my view, a framework of this kind is urgently needed to place today's actuarial work on a sound foundation.2. In general an insurance contract will define two stochastic processes. We lose little by assuming that the processes are discrete, and describing them in the following manner:(i) The payment process: x0, x1 … xt …, where xt is the amount which the company pays to settle claims in period t, or at time t.(ii) The premium process: p0, p1 … pt …, where pt is the premium which the company receives in period t, or at time t.If the contract is concluded at time t = o, the Principle of Equivalence requires thatFor the typical short-term contract with premium payable in advance (i) will reduce to3. For a long-term insurance contract one usually requires that the inequalityshall hold for all τ. This means that the company must never be a net creditor of its customer.