Portfolio optimization under Solvency II

  • Marcos Escobar
  • Paul Kriebel
  • Markus Wahl
  • Rudi Zagst
S.I.: Risk in Financial Economics


In the current low interest-rate and highly-regulated environment investing capital efficiently is one of the most important challenges insurance companies face. Certain quantitative parts of regulatory requirements (e.g. Solvency II capital requirements) result in constraints on the investment strategies. This paper mathematically describes the implications of Solvency II constraints on the investment strategies of insurance companies in an expected utility framework with a focus on the market risk module. For this constrained expected utility problem, we define a two-step approach that leads to closed-form approximations for the optimal investment strategies. This proposal circumvents the technical difficulties encountered when applying the convex duality approach or the theory of viscosity solutions. The investment strategies found using the two-step approach can be understood as the optimal investment strategies for constraint problems according to Solvency II. The impact of such constraints on the asset allocation and the performance of these strategies is assessed in a numerical case study.


Portfolio optimization Investment strategies Regulatory constraints Market risk Solvency II 



Markus Wahl and Rudi Zagst greatfully acknowledge the support of Allianz Global Investors for this research.


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Authors and Affiliations

  1. 1.Department of Statistical and Actuarial SciencesWestern UniversityLondonCanada
  2. 2.Chair of Mathematical FinanceTechnical University of MunichGarching-HochbrückGermany

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