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 one-period variance premiumprinciple converges to
the non-linear exponential indifference valuation. Furthermore, we study the
convergence of the one-period standard-deviation principle and establish that
the Cost-of-Capital principle, which is widely used by the insurance industry,
converges to the same limit as the standard-deviation principle. Finally, we
study the connections between our time-consistent pricing operators, Good Deal
Bound pricing and pricing under model ambiguity.