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Dynamic surplus optimization with performance- and index-linked liabilities.

Sascha Desmettre1, Markus Wahl2, Rudi Zagst2

  • 1Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria.

European Actuarial Journal
|November 29, 2022
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Summary
This summary is machine-generated.

Liability-driven investment strategies face challenges. This study develops a flexible framework for optimizing portfolios with dynamic strategies and stochastic liabilities, finding that linked liabilities increase risky asset allocation while unhedgeable risks decrease it.

Keywords:
Asset-liability managementMartingale methodPerformance participationRandom utilityStochastic liabilitiesSurplus optimization

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Area of Science:

  • Finance
  • Actuarial Science
  • Quantitative Finance

Background:

  • The rise of liability-driven investment (LDI) strategies and retirement products with variable guarantees presents challenges for portfolio optimization.
  • Existing frameworks struggle to incorporate dynamic investment strategies and stochastic liabilities effectively.

Purpose of the Study:

  • To develop a general and flexible terminal surplus optimization framework in continuous time.
  • To allow for dynamic investment strategies and stochastic liabilities linked to market performance.
  • To derive optimal investment strategies for various liability models.

Main Methods:

  • Established a continuous-time terminal surplus optimization framework.
  • Developed closed-form solutions for optimal investment strategies under different liability models.
  • Conducted numerical examples to analyze key parameters.

Main Results:

  • Performance- or index-linked liabilities enable higher allocation to risky assets by closely aligning company wealth with liabilities.
  • Unhedgeable risks necessitate a reduced allocation to risky investments.
  • The relative risk aversion parameter influences investment decisions.

Conclusions:

  • Insurance companies should link product performance closely to wealth to enhance policyholder returns.
  • Minimizing unhedgeable risks is crucial for optimizing investment strategies.
  • The developed framework provides flexibility for dynamic LDI strategies.