Time-consistent and market-consistent actuarial valuations

Recent theoretical results establish that time-consistent valuations(i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-timelimits of well-known actuarial premium principles when such backwarditeration procedures are applied. We show that the iterated variancepremium principle converges to the non-linear exponential indifferencevaluation. Furthermore, we show that the iterated standard-deviationprinciple converges to an expectation under an equivalent martingalemeasure and that the Cost-of-Capital principle, which is widely usedby the insurance industry, converges to the same price as the standard-deviation principle. Finally, we study the converge of market-consistent extensions of these pricing principles.