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Time-Consistent and Market-Consistent Evaluations

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  • Mitja Stadje
  • Antoon Pelsser

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.

Suggested Citation

  • Mitja Stadje & Antoon Pelsser, 2011. "Time-Consistent and Market-Consistent Evaluations," Papers 1109.1749, arXiv.org, revised Dec 2013.
  • Handle: RePEc:arx:papers:1109.1749
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    Cited by:

    1. Madan, Dilip & Pistorius, Martijn & Stadje, Mitja, 2016. "Convergence of BSΔEs driven by random walks to BSDEs: The case of (in)finite activity jumps with general driver," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1553-1584.
    2. Pelsser, Antoon & Salahnejhad Ghalehjooghi, Ahmad, 2016. "Time-consistent actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 97-112.
    3. Dhaene, Jan & Stassen, Ben & Barigou, Karim & Linders, Daniël & Chen, Ze, 2017. "Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 14-27.
    4. repec:wsi:ijtafx:v:20:y:2017:i:08:n:s0219024917500509 is not listed on IDEAS
    5. Martijn Pistorius & Mitja Stadje, 2016. "On Dynamic Deviation Measures and Continuous-Time Portfolio Optimisation," Papers 1604.08037, arXiv.org.
    6. repec:eee:insuma:v:74:y:2017:i:c:p:20-30 is not listed on IDEAS

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