Time-Consistent and Market-Consistent Actuarial Valuations

21 Pages Posted: 12 Feb 2010

See all articles by Antoon Pelsser

Antoon Pelsser

Maastricht University; Netspar

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Date Written: February 11, 2010

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.

Keywords: Actuarial pricing, time-consistent, market-consistent, BSDE

JEL Classification: G13, C61

Suggested Citation

Pelsser, Antoon A. J., Time-Consistent and Market-Consistent Actuarial Valuations (February 11, 2010). Available at SSRN: https://ssrn.com/abstract=1551323 or http://dx.doi.org/10.2139/ssrn.1551323

Antoon A. J. Pelsser (Contact Author)

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://https://sites.google.com/site/apelsseraca/

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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