Paper: arXiv 2407.11761

Authors: Felix Fießinger, Mitja Stadje

Abstract

This paper studies the equity holders’ mean-variance optimal portfolio choice problem for (non-)protected participating life insurance contracts. We derive explicit formulas for the optimal terminal wealth and the optimal strategy in the multi-dimensional Black-Scholes model, showing the existence of all necessary parameters. In incomplete markets, we state Hamilton-Jacobi-Bellman equations for the value function. Moreover, we provide a numerical analysis of the Black-Scholes market. The equity holders on average increase their investment into the risky asset in bad economic states and decrease their investment over time.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical formulation for mean-variance portfolio optimization under non-concave payoff structures from participating life insurance contracts. While the mathematical derivation, existence proofs, and HJB framing in continuous time are highly advanced, the paper primarily relies on theoretical modeling and stylized numerical simulations in a Black-Scholes market rather than empirical backtesting on real historical market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Mean-Variance Optimal Portfolio for Participating Life Insurance] --> B[Market Context & Setup: Multi-Dim Black-Scholes Model]
    B --> C{Market Completeness?}
    C -- Complete Market --> D[Derive Explicit Formulas for Terminal Wealth & Optimal Strategy]
    C -- Incomplete Market --> E[Formulate Hamilton-Jacobi-Bellman Equations]
    D --> F[Numerical Analysis & Simulation]
    E --> F
    F --> G[Key Outcome: Equity holders increase risky investments in bad economic states & decrease them over time]

Cited References (42)

  1. Constrained non-concave utility maximization: An application to life insurance contracts with guarantees (2019)
  2. On the equivalence between Value-at-Risk-and Expected Shortfall-based risk measures in non-concave optimization (2024)
  3. Nonconcave optimal investment with value-at-risk constraint: An application to life insurance contracts (2020)
  4. Continuous-time mean-variance portfolio selection: A stochastic LQ framework (2000)
  5. Value-at-risk-based risk management: optimal policies and asset prices (2001)
  6. Continuous-time stochastic control and optimization with financial applications (2009)
  7. Optimal investment strategies for participating contracts (2017)
  8. On the equivalence between Value-at-Risk-and Expected Shortfall-based risk measures in non-concave optimization (2020) — link
and 34 more
  1. Weighted utility optimization of the participating endowment contract (2020)
  2. Optimal asset allocation for participating contracts under the VaR and PI constraint (2020)
  3. Portfolio Selection (1952) — link
  4. Portfolio Selection: Efficient Diversification of Investments (1959)
  5. Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature (2018)
  6. Optimum consumption and portfolio rules in a continuous-time model (1975)
  7. An analytic derivation of the efficient portfolio frontier (1972)
  8. Mean-variance portfolio selection with random parameters in a complete market (2002)
  9. Dynamic mean-variance portfolio selection with no-shorting constraints (2002)
  10. Utility maximization with a given pricing measure when the utility is not necessarily concave (2013)
  11. Optimal portfolio delegation when parties have different coefficients of risk aversion (2005)
  12. Non-concave utility maximization without the concavification principle (2019)
  13. A dynamic programming approach to constrained portfolios (2013)
  14. Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint — → 2309.01936
  15. A Unified Formula of the Optimal Portfolio for Piecewise HARA Utilities (2021) — link
  16. Optimal investment under VaR-regulation and minimum insurance (2018)
  17. Optimal dynamic trading strategies with risk limits (2008)
  18. European Insurance Overview 2023 (2023)
  19. On the risk of insurance liabilities: debunking some common pitfalls (1997)
  20. Policy characteristics and stakeholder returns in participating life insurance: which contracts can lead to a win-win? (2018)
  21. A proposal on how the regulator should set minimum interest rate guarantees in participating life insurance contracts (2015)
  22. Design and pricing of equity-linked life insurance under stochastic interest rates (2002)
  23. Analysis of participating life insurance contracts: A unification approach (2007)
  24. Non-Concave Utility Maximization with Transaction Costs — → 2307.02178
  25. Asset pricing: Revised edition (2009)
  26. Lifetime portfolio selection by dynamic stochastic programming (1975)
  27. Capital growth and the mean-variance approach to portfolio selection (1971)
  28. Dynamic mean-variance asset allocation (2010)
  29. A general theory of Markovian time inconsistent stochastic control problems (2010)
  30. Optimal reinsurance design under solvency constraints (2024)
  31. Optimal control of option portfolios and applications: Optimale Steuerung von Optionsportefeuilles und Anwendungen (1999)
  32. A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans (2019)
  33. Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework (2017)
  34. Financial modelling with jump processes (2004)

2 of 42 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.