Paper: arXiv 2504.12851

Authors: Felix Fießinger, Mitja Stadje

Abstract

We adapt Leland’s dynamic capital structure model to the context of an insurance company selling participating life insurance contracts explaining the existence of life insurance contracts which provide both a guaranteed payment and surplus participation to the policyholders. Our derivation of the optimal participation rate reveals its pronounced sensitivity to the contract duration and the associated tax rate. Moreover, the asset substitution effect, which describes the tendency of equity holders to increase the riskiness of a company’s investment decisions, decreases when adding surplus participation.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical adaptation of Leland’s structural capital model to participating life insurance contracts, deriving closed-form/analytical results for optimal participation and bankruptcy thresholds. However, it is largely a theoretical and numerical calibration paper with limited empirical data testing or backtesting. The mathematical derivation and novel application to mitigate asset substitution effects are the primary strengths.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain & Optimize Surplus Participation in Life Insurance] --> B[Model Framework: Adapt Leland's Dynamic Capital Structure Model]
    B --> C[Inputs: Contract Duration, Tax Rates & Investment Volatility]
    C --> D[Compute Optimal Capital Structure & Surplus Participation Rate]
    D --> E[Outcome 1: Participation Rate Highly Sensitive to Duration & Tax Rate]
    D --> F[Outcome 2: Surplus Participation Reduces Asset Substitution Effect]

Cited References (66)

  1. Brownian Motion and Stochastic Flow Systems (1990)
  2. The Leland–Toft optimal capital structure model under Poisson observations (2020)
  3. Structural Models of the Firm under State-Dependent Volatility and Jump Process Asset Dynamics (2012)
  4. Breaking down the barriers (1991)
  5. Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads (1996)
  6. Annual Report 2023 (2023)
  7. Annual Report 2023 (2023)
  8. European Insurance Overview 2023 (2023)
and 58 more
  1. Options, Futures, and Other Derivatives (2017)
  2. Corporate debt value, bond covenants, and optimal capital structure (1994)
  3. Theory of rational option pricing (1973)
  4. Super contact and related optimality conditions (1991)
  5. A simplified treatment of the theory of optimal regulation of Brownian motion (1991)
  6. On Cox processes and credit risky securities (1998)
  7. Agency costs, risk management, and capital structure (1998)
  8. An EBIT-based model of dynamic capital structure (2001)
  9. Performance-sensitive debt (2010)
  10. Mean-Variance Optimization for Participating Life Insurance Contracts — → 2407.11761
  11. Nonconcave optimal investment with value-at-risk constraint: An application to life insurance contracts (2020)
  12. Optimal investment strategies for participating contracts (2017)
  13. Weighted utility optimization of the participating endowment contract (2020)
  14. Optimal asset allocation for participating contracts under the VaR and PI constraint (2020)
  15. Optimal investment under VaR-regulation and minimum insurance (2018)
  16. On the risk of insurance liabilities: debunking some common pitfalls (1997)
  17. Policy characteristics and stakeholder returns in participating life insurance: which contracts can lead to a win-win? (2018)
  18. A proposal on how the regulator should set minimum interest rate guarantees in participating life insurance contracts (2015)
  19. Design and pricing of equity-linked life insurance under stochastic interest rates (2002)
  20. Analysis of participating life insurance contracts: A unification approach (2007)
  21. The impact of surplus distribution on the risk exposure of with profit life insurance policies including interest rate guarantees (2007)
  22. The interaction of guarantees, surplus distribution, and asset allocation in with-profit life insurance policies (2007)
  23. Analyzing the effect of low interest rates on the surplus participation of life insurance policies with different annual interest rate guarantees (2015)
  24. Constrained non-concave utility maximization: An application to life insurance contracts with guarantees (2019)
  25. Horses and rabbits? Trade-off theory and optimal capital structure (2005)
  26. Personal taxes, endogenous default, and corporate bond yield spreads (2006)
  27. Taxation, agency conflicts, and the choice between callable and convertible debt (2008)
  28. The term structure of lease rates with endogenous default triggers and tenant capital structure: theory and evidence (2011)
  29. The cost and timing of financial distress (2012)
  30. Contingent capital with a capital-ratio trigger (2012)
  31. Credit market frictions and capital structure dynamics (2015)
  32. Dynamic debt maturity (2016)
  33. Contingent capital, tail risk, and debt-induced collapse (2017)
  34. Capital structure and the substitutability versus complementarity nature of leases and debt (2019)
  35. Short-term debt and incentives for risk-taking (2020)
  36. The bank as grim reaper: Debt composition and bankruptcy thresholds (2021)
  37. The information value of distress (2024)
  38. The pricing of options and corporate liabilities (1973)
  39. Theory of the Firm (1976)
  40. On the pricing of corporate debt: The risk structure of interest rates (1974)
  41. A rationale for debt maturity structure and call provisions in the agency theoretic framework (1980)
  42. From intertemporal smoothing to intergenerational risk sharing: The effects of different Return Smoothing Mechanisms in Life Insurance
  43. Intertemporal smoothing and intergenerational risk sharing: The impact on objective utility and subjective attractiveness of retirement savings products (2024)
  44. Life insurance liabilities at market value: an analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework (2002)
  45. Market value of life insurance contracts under stochastic interest rates and default risk (2005)
  46. Guarantees in With-Profit and Unitized With-Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option (2006)
  47. Early default risk and surrender risk: Impacts on participating life insurance policies (2018)
  48. Does default risk in coupons affect the valuation of corporate bonds?: A contingent claims model (1993)
  49. Capital structure and the cost of capital (2005)
  50. A simple approach to valuing risky fixed and floating rate debt (1995)
  51. Debt maturity and the leverage ratcheting effect (2019)
  52. Optimal debt and profitability in the trade-off theory (2018)
  53. Dynamic risk management: investment, capital structure, and hedging in the presence of financial frictions (2015)
  54. Rethinking Dynamic Capital Structure Models with Roll-Over Debt (2014)
  55. Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk (2009)
  56. Optimal investment for participating insurance contracts under VaR-Regulation (2019) — link
  57. Does option compensation increase managerial risk appetite? (2000)
  58. Optimal Capital Structure for Life Insurance Companies Offering Surplus Participation — → 2504.12851

2 of 66 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.