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The Iterated Cte

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  • Mary Hardy
  • Julia Wirch

Abstract

In this paper we present a method for defining a dynamic risk measure from a static risk measure, by backwards iteration. We apply the method to the conditional tail expectation (CTE) risk measure to construct a new, dynamic risk measure, the iterated CTE (ICTE). We show that the ICTE is coherent, consistent, and relevant according to the definitions of Riedel (2003), and we derive formulae for the ICTE for the case where the loss process is lognormal. Finally, we demonstrate the practical implementation of the ICTE to an equity-linked insurance contract with maturity and death benefit guarantees.

Suggested Citation

  • Mary Hardy & Julia Wirch, 2004. "The Iterated Cte," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(4), pages 62-75.
    • Handle: RePEc:taf:uaajxx:v:8:y:2004:i:4:p:62-75
    DOI: 10.1080/10920277.2004.10596171
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    Cited by:

    1. Devolder, Pierre & Piscopo, Gabriella, 2012. "Solvency analysis of defined benefit pension schemes," LIDAM Discussion Papers ISBA 2012030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Dan A. Iancu & Marek Petrik & Dharmashankar Subramanian, 2015. "Tight Approximations of Dynamic Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 655-682, March.
    3. Pierre Devolder & Adrien Lebègue, 2016. "Compositions of Conditional Risk Measures and Solvency Capital," Risks, MDPI, vol. 4(4), pages 1-21, December.
    4. Brahim Brahimi, 2012. "Involving copula functions in Conditional Tail Expectation," Papers 1205.4345, arXiv.org, revised Apr 2014.
    5. Takayuki Osogami, 2012. "Iterated risk measures for risk-sensitive Markov decision processes with discounted cost," Papers 1202.3755, arXiv.org.
    6. Rassoul, Abdelaziz, 2013. "Kernel-type estimator of the conditional tail expectation for a heavy-tailed distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 698-703.
    7. D. Madan & M. Pistorius & M. Stadje, 2017. "On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation," Finance and Stochastics, Springer, vol. 21(4), pages 1073-1102, October.

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