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On the Sensitivity of Premiums and Reserves to Changes in Valuation Elements

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  • Vladimir Kalashnikov
  • Ragnar Norberg

Abstract

Upon differentiating the Thiele differential equations and the equivalence condition with respect to some parameter appearing in the equations, one obtains differential equations for the derivatives of the state-wise reserves and the premium level with respect to the parameter. The solution to these equations measures the impact on premiums and reserves of a change in the parameter. Typically only numerical results can be obtained, but the method applies quite generally to multi-state policies and to virtually any parameter, and so represents a panacea in (the vast majority of) situations where analytical results are out of reach. Extensions to higher order derivatives and higher order conditional moments are straightforward. A difference method for computation is devised, and numerical results are reported for some practical cases.

Suggested Citation

  • Vladimir Kalashnikov & Ragnar Norberg, 2003. "On the Sensitivity of Premiums and Reserves to Changes in Valuation Elements," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2003(3), pages 238-256.
    • Handle: RePEc:taf:sactxx:v:2003:y:2003:i:3:p:238-256
    DOI: 10.1080/03461230110106408
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