Mean-field Libor market model and valuation of long term guarantees

Paper: arXiv 2310.09022

Authors: Florian Gach, Simon Hochgerner, Eva Kienbacher, Gabriel Schachinger

Abstract

Existence and uniqueness of solutions to the multi-dimensional mean-field Libor market model (introduced by [7]) is shown. This is used as the basis for a numerical asset-liability management (ALM) model capable of calculating future discretionary benefits in accordance with Solvency~II regulation. This ALM model is complimented with aggregated life insurance data to perform a realistic numerical study. This yields numerical evidence for heuristic assumptions which allow to derive estimators of lower and upper bounds for future discretionary benefits. These estimators are applied to publicly available life insurance data.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents rigorous mathematical foundations for a multi-dimensional mean-field Libor market model, proving existence and uniqueness. It effectively bridges advanced stochastic calculus with practical actuarial applications under Solvency II, backed by numerical studies using real life insurance data.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Multi-Dim Mean-Field LMM & Valuate Long-Term Guarantees under Solvency II] --> B[Prove Existence & Uniqueness of Solutions for Mean-Field LMM]
    B --> C[Build Numerical ALM Model with Aggregated Life Insurance Data]
    C --> D[Simulate Future Discretionary Benefits & Analyze Numerical Evidence]
    D --> E[Derive Estimators for Lower and Upper Benefit Bounds]
    E --> F[Key Outcome: Applied Estimators to Public Life Insurance Data for Realistic Valuation]