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.

Cited by in corpus (7)

• Pricing equity-linked life insurance contracts with multiple risk factors by neural networks
• Insurance valuation: A two-step generalised regression approach
• A bridge between Local GAAP and Solvency II frameworks to quantify Capital Requirement for demographic risk
• Representation Results for Law Invariant Recursive Dynamic Deviation Measures and Risk Sharing
• Insurance-Finance Arbitrage
• On Dynamic Deviation Measures and Continuous-Time Portfolio Optimisation
• On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation