Portfolio optimization under solvency II: a multi-objective approach incorporating market views and real-world constraints

Abstract

We propose a new approach to handle the problem of portfolio optimization for non-life insurance company incorporating the solvency capital requirement (SCR), market views and their confident levels, several equality and inequality real-world constraints and transaction costs. We analyze two case studies: first, we consider a tri-objective optimization problem in which we minimize the Market SCR, the variance of the so-called basic own funds (BOF) and maximize the return of portfolio; secondly, we consider bi-objective optimization problem in which we minimize the variance of BOF and maximize the return of portfolio while considering the Market SCR as a constraint. We introduce a scenario-based framework in which the reference model is given by an internal model. By entropy pooling approach, we blended market views and their confident levels with the reference model to build the posterior distribution. The latter is used to compute the variance of BOF and the portfolio return. In both case studies, we obtain good results in term of risk-reward tradeoff and diversification.

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    The difference between company’s Assets and Liabilities.

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Acknowledgements

The author acknowledges the editor and two anonymous reviewers for their constructive feedback. It is his belief that the manuscript is substantially improved after making the suggested edits. A special thanks to author’s colleagues who allow him to write this paper. In particular, the author wishes to thank Daniele Della Rossa, for correcting and improving his English language, and Riccardo Casalini, aka Mister Validation, for several helpful conversation on the Solvency II Directive. Finally, the author would like to thank professor Andrea Pascucci, Sergio Polidoro and Paolo Foschi for some useful remarks.

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Correspondence to Marco Di Francesco.

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Appendix

Appendix

In this appendix, we report the two correlation matrices for Solvency II Standard Formula as reported in EIOPA (2014). In Table 12, we report the correlation matrix used to compute the SCR as the aggregate capital charge of these modules

Table 12 Solvency II: correlation matrix for solvency II standard formula

In Table 13, we report the correlation matrix used to compute the capital requirement for market risk (\(\text {Market}_{\text {SCR}}\)) as the aggregate capital charge of these sub module where the factor A is equal to 0 in the upward stress scenario and equal to 0.5 in the downward stress scenario.

Table 13 Solvency II: market correlation matrix for solvency II standard formula

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Di Francesco, M. Portfolio optimization under solvency II: a multi-objective approach incorporating market views and real-world constraints. Decisions Econ Finan (2021). https://doi.org/10.1007/s10203-021-00320-3

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Keywords

  • Portfolio theory
  • Solvency II
  • Multi-objective evolution algorithm
  • Real-world constraints
  • Non-life insurance company