Time-consistent and market-consistent evaluations

A. Pelsser, M.A. Stadje

Research output: Contribution to journalArticleScientificpeer-review

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 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.
Original languageEnglish
Pages (from-to)25-65
JournalMathematical Finance
Volume24
Issue number1
Early online date7 Feb 2013
DOIs
Publication statusPublished - 2014

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Keywords

  • Actuarial valuation principles
  • financial risk
  • market-consistency
  • time-consistency

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