Time-Consistent Actuarial Valuations

Antoon Pelsser

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arXiv · 1109.1751

Time-Consistent Actuarial Valuations

Antoon Pelsser

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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.

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Antoon Pelsser. 2011-09-08. Time-Consistent Actuarial Valuations. https://arxiv.org/abs/1109.1751

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