Time-Consistent and Market-Consistent Actuarial Valuations

Abstract

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-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show that the iterated variance premium principle converges to the non-linear exponential indifference valuation. Furthermore, we show that the iterated standard-deviation principle converges to an expectation under an equivalent martingale measure and that the Cost-of-Capital principle, which is widely used by 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.