Time-Consistent and Market-Consistent Evaluations

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call ‘two step market evaluation.’ This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

Keywords: Actuarial valuation principles, financial risk, market-consistency, time-consistency

JEL Classification: G10, G11, G12, G13

Suggested Citation: Suggested Citation

Stadje, Mitja and Pelsser, Antoon A. J., Time-Consistent and Market-Consistent Evaluations (January 7, 2014). CentER Working Paper Series No. 2014-002, Available at SSRN: https://ssrn.com/abstract=1856538 or http://dx.doi.org/10.2139/ssrn.1856538