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On capital allocation for a risk measure derived from ruin theory

Author

Listed:
  • Delsing, G.A.
  • Mandjes, M.R.H.
  • Spreij, P.J.C.
  • Winands, E.M.M.

Abstract

This paper addresses allocation methodologies for a risk measure inherited from ruin theory. Specifically, we consider a dynamic value-at-risk (VaR) measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given threshold. We introduce an intuitively appealing, novel allocation method, with a focus on its application to capital reserves which are determined through the dynamic VaR measure. Various desirable properties of the presented approach are derived including a limit result when considering a large time horizon and the comparison with the frequently used gradient allocation method. In passing, we introduce a second allocation method and discuss its relation to the other allocation approaches. A number of examples illustrate the applicability and performance of the allocation approaches.

Suggested Citation

  • Delsing, G.A. & Mandjes, M.R.H. & Spreij, P.J.C. & Winands, E.M.M., 2022. "On capital allocation for a risk measure derived from ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 76-98.
    • Handle: RePEc:eee:insuma:v:104:y:2022:i:c:p:76-98
    DOI: 10.1016/j.insmatheco.2022.02.001
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    More about this item

    Keywords

    Risk capital allocation; Gradient allocation method; Value-at-risk (VaR); Ruin probability; Insurance risk;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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