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Economic Neutral Position: How to best replicate not fully replicable liabilities?

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  • Kunz, Andreas
  • Popp, Markus

Abstract

Financial undertakings often have to deal with liabilities of product type in the form “non-hedgeable claim size times value of a tradeable asset”, e.g. foreign property insurance claims in foreign currency multiplied by foreign exchange rate to convert to local currency. Which strategy of investing in the tradeable asset is risk minimal? We generalize the Gram–Charlier series for the sum of two dependent random variables, which allows us to expand the capital requirements for liabilities of product structure based on value-at-risk and expected shortfall. We derive a stable and fairly model independent approximation of the risk minimal asset allocation in terms of the claim size distribution and the moments of the asset return distribution. With the results, a correct and easy-to-implement modularization of capital requirements into a market risk and a non-hedgeable risk component becomes possible.

Suggested Citation

  • Kunz, Andreas & Popp, Markus, 2021. "Economic Neutral Position: How to best replicate not fully replicable liabilities?," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 53-67.
    • Handle: RePEc:eee:insuma:v:96:y:2021:i:c:p:53-67
    DOI: 10.1016/j.insmatheco.2020.10.006
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    References listed on IDEAS

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    1. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    2. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    3. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    4. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
    5. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    6. Morlais, Marie-Amelie, 2010. "A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1966-1995, September.
    7. Schweizer, Martin, 2001. "From actuarial to financial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 31-47, February.
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    More about this item

    Keywords

    Risk measure; Risk minimal asset allocation; Incomplete markets; Gram–Charlier series; Cornish–Fisher quantile approximation; Solvency II; Market risk; Replicating portfolio;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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