On the market-consistent valuation of health insurance liabilities

Paper: arXiv 2604.18243

Authors: Simon Hochgerner, Jonas Ingmanns, Nicole Kastanek

Abstract

We are concerned with the market-consistent valuation of lifelong health insurance products, which are subject to adjustments derived from the actuarial equivalence principle and driven by (medical) inflation. Such products are well-established in the European national markets, and the dynamics of the adjustment mechanism is well-understood from an actuarial perspective. However, the question of market-consistent valuation (as is necessary for Solvency II reporting) has not previously been addressed. This gap has led to a situation where some practitioners use stochastic models while others rely on deterministic methods to assign market-consistent values (Best Estimates) to the same type of health insurance liabilities. The purpose of this note is to fill this gap by showing that the Best Estimate of a lifelong health insurance policy depends on the choice of model for the interest and inflation rates. That is, the Best Estimate is not uniquely determined by the currently prevailing term structures of nominal and real spot rates, whence a deterministic calculation is theoretically unjustified. Furthermore, we construct a valuation portfolio such that the Best Estimate valuation decouples into calculations of 1.) deterministic coefficients derived from policy data and 2.) the prices of basis financial instruments that are independent of the individual policy data. Using this decomposition, the policies do not have to be tracked individually along each generated stochastic path. This allows for a more efficient evaluation of the Best Estimate for a large stock of policies with a stochastic model.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical bridge between actuarial science and market-consistent financial valuation under Solvency II by decomposing health insurance liabilities into basis financial instruments. However, it is largely a theoretical note that lacks empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Market-consistent valuation (Best Estimate) for lifelong health insurance liabilities under Solvency II"] --> B["Inputs: Policy data, nominal & real spot rate term structures, interest & inflation models"]
    
    B --> C["Theoretical Analysis: Prove Best Estimate depends on stochastic model choice (deterministic methods unjustified)"]
    
    C --> D["Methodology: Construct a Valuation Portfolio decoupling policy data from financial instruments"]
    
    D --> E["Computation: 1. Calculate deterministic policy coefficients<br/>2. Price policy-independent basis instruments"]
    
    E --> F["Outcomes: Highly efficient stochastic valuation for large policy stocks; fills regulatory valuation gap"]

Cited References (21)

1. Measuring medical inflation for health insurance portfolios in Belgium (2019) — link
2. Zillmerung und Rückkaufswert – ein kritischer Blick auf die rechtliche Bewertung (2016) — link
3. Lifelong Health Insurance Covers With Surrender Values: Updating Mechanisms In The Presence Of Medical Inflation (2017)
4. Once covered, forever covered: The actuarial challenges of the Belgian private health insurance system (2019) — link
5. Updating mechanism for lifelong insurance contracts subject to medical inflation (2017) — link
6. I nterest R ate M odels – T heory and P ractice (2006)
7. Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market (1995) — link
8. On the Pricing of Contingent Claims under Constraints (1996) — link

0 of 21 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.