Abstract
In this paper, we consider the strategic asset allocation of an insurance company. This task can be seen as a special case of portfolio optimization. In the 1950s, Markowitz proposed to formulate portfolio optimization as a bicriteria optimization problem considering risk and return as objectives. However, recent developments in the field of insurance require four and more objectives to be considered, among them the so-called solvency ratio that stems from the Solvency II directive of the European Union issued in 2009. Moreover, the distance to the current portfolio plays an important role. While the literature on portfolio optimization with three objectives is already scarce, applications in the financial context with four and more objectives have not yet been solved so far by multi-objective approaches based on scalarizations. However, recent algorithmic improvements in the field of exact multi-objective methods allow the incorporation of many objectives and the generation of well-spread representations within few iterations. We describe the implementation of such an algorithm for a strategic asset allocation with four objective functions and demonstrate its usefulness for the practitioner. Our approach is in operative use in a German insurance company. Our partners report a significant improvement in their decision-making process since, due to the proper integration of the new objectives, the software proposes portfolios of much better quality than before within short running time.
Highlights
Insurance companies have to manage and invest large amounts of money, both from their equity and from premia paid by customers
Our approach is in operative use in a German insurance company
The Solvency II directive, introduced by the European Union1 in the aftermath of the financial crisis to strengthen the financial stability of the insurance sector, stipulates higher capital requirements for investment in high-risk assets
Summary
Insurance companies have to manage and invest large amounts of money, both from their equity and from premia paid by customers. The goal is to maximize the expected value of this utility via finding the optimal admissible trading strategy Another fundamental approach is to choose a measure of risk and directly maximize the expected return, constrained by the amount of risk the investor is willing to accept. Escobar et al (2019) investigate the implications of the market risk module of Solvency II on investment strategies in an expected utility framework In all these approaches, the SCR is used as a constraint. Kellner et al (2019) present a multi-objective optimization model with four objectives which are all linear apart from one that is quadratic To solve this problem the authors reduce it to three objectives and compute the exact Pareto front following the approach of Hirschberger et al (2013).
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