Time-Consistent Actuarial Valuations

TL;DR

This paper explores the continuous-time limits of actuarial premium principles under time-consistent valuation methods, revealing convergence to exponential indifference valuation and connections to industry-practiced principles.

Contribution

It demonstrates the convergence of variance and standard-deviation premium principles to exponential indifference valuation in continuous time, linking theoretical and practical valuation methods.

Findings

Variance premium converges to exponential indifference valuation.

Standard-deviation principle converges to the same limit as Cost-of-Capital.

Connections established between time-consistent valuations, Good Deal Bound pricing, and model ambiguity.

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 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.