Time-Consistent and Market-Consistent Evaluations

Abstract:     
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 a continuous stock prices process 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.

Number of Pages in PDF File: 40

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

JEL Classification: D81, G12, G22, G23

working papers series