Time-Consistent and Market-Consistent Evaluations

TL;DR

This paper introduces a new two-step market evaluation method for financial payoffs that combines actuarial and financial techniques, ensuring time and market consistency, with theoretical characterizations and practical implications.

Contribution

It proposes the two-step market evaluation procedure, extending actuarial principles with market consistency, and provides axiomatic and dynamic characterizations.

Findings

The two-step evaluation preserves actuarial structure.

It is uniquely characterized by time and market consistency.

Applicable in Brownian-Poisson models with g-expectations.

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.