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Cost-of-capital valuation with risky assets

Author

Listed:
  • Hansjorg Albrecher
  • Filip Lindskog
  • Herv'e Zumbach

Abstract

Cost-of-capital valuation is a well-established approach to the valuation of liabilities and is one of the cornerstones of current regulatory frameworks for the insurance industry. Standard cost-of-capital considerations typically rely on the assumption that the required buffer capital is held in risk-less one-year bonds. The aim of this work is to analyze the effects of allowing investments of the buffer capital in risky assets, e.g.~in a combination of stocks and bonds. In particular, we make precise how the decomposition of the buffer capital into contributions from policyholders and investors varies as the degree of riskiness of the investment increases, and highlight the role of limited liability in the case of heavy-tailed insurance risks. We present a combination of general theoretical results, explicit results for certain stochastic models and numerical results that emphasize the key findings.

Suggested Citation

  • Hansjorg Albrecher & Filip Lindskog & Herv'e Zumbach, 2025. "Cost-of-capital valuation with risky assets," Papers 2511.00895, arXiv.org.
    • Handle: RePEc:arx:papers:2511.00895
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    References listed on IDEAS

    as
    1. Karim Barigou & Jan Dhaene, 2019. "Fair valuation of insurance liabilities via mean-variance hedging in a multi-period setting," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(2), pages 163-187, February.
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    3. Pablo Koch-Medina & Cosimo Munari, 2020. "Market-Consistent Prices," Springer Books, Springer, number 978-3-030-39724-1, January.
    4. Engler, Nils & Lindskog, Filip, 2025. "Approximations of multi-period liability values by simple formulas," Insurance: Mathematics and Economics, Elsevier, vol. 123(C).
    5. Pablo Koch-Medina & Cosimo Munari, 2020. "Market-Consistent Prices for General Payoffs," Springer Books, in: Market-Consistent Prices, chapter 17, pages 303-316, Springer.
    6. Pablo Koch-Medina & Cosimo Munari, 2020. "Market-Consistent Prices for Replicable Payoffs," Springer Books, in: Market-Consistent Prices, chapter 15, pages 261-278, Springer.
    7. Pablo Koch-Medina & Cosimo Munari, 2020. "Market-Consistent Prices for American Options," Springer Books, in: Market-Consistent Prices, chapter 19, pages 343-411, Springer.
    8. 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.
    9. Salzmann, Robert & Wüthrich, Mario V., 2010. "Cost-of-Capital Margin for a General Insurance Liability Runoff," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 415-451, November.
    10. Pablo Koch-Medina & Cosimo Munari, 2020. "Market-Consistent Prices for Payoff Streams," Springer Books, in: Market-Consistent Prices, chapter 18, pages 317-342, Springer.
    11. Engsner, Hampus & Lindholm, Mathias & Lindskog, Filip, 2017. "Insurance valuation: A computable multi-period cost-of-capital approach," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 250-264.
    12. Hansjörg Albrecher & Karl‐Theodor Eisele & Mogens Steffensen & Mario V. Wüthrich, 2022. "On the cost‐of‐capital rate under incomplete market valuation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 1139-1158, December.
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    14. Engsner, Hampus & Lindskog, Filip & Thøgersen, Julie, 2023. "Multiple-prior valuation of cash flows subject to capital requirements," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 41-56.
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    16. Pablo Koch-Medina & Cosimo Munari, 2020. "Market-Consistent Prices for General Payoffs," Springer Books, in: Market-Consistent Prices, chapter 8, pages 147-157, Springer.
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