A cohort-based Partial Internal Model for demographic risk

Paper: arXiv 2307.03090

Authors: Francesco Della Corte, Gian Paolo Clemente, Nino Savelli

Abstract

We investigate the quantification of demographic risk in a framework consistent with the market-consistent valuation imposed by Solvency II. We provide compact formulas for evaluating inflows and outflows of a portfolio of insurance policies based on a cohort approach. In this context, we maintain the highest level of generality in order to consider both traditional policies and equity-linked policies: therefore, we propose a market-consistent valuation of the liabilities. In the second step we evaluate the Solvency Capital Requirement of the idiosyncratic risk, linked to accidental mortality, and the systematic risk one, also known as trend risk, proposing a formal closed formula for the former and an algorithm for the latter. We show that accidental volatility depends on the intrinsic characteristics of the policies of the cohort (Sums-at-Risk), on the age of the policyholders and on the variability of the sums insured; trend risk depends both on accidental volatility and on the longevity forecasting model used.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 4.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a solid mathematical formulation for demographic risk within Solvency II using a cohort approach and closed-form/algorithmic solutions. However, it leans heavily theoretical with limited empirical backtesting provided in the abstract summary.

Research Flowchart

  flowchart TD
    A["Research Goal: Quantify Demographic Risk <br>under Solvency II Market-Consistent Framework"] --> B["Inputs: Portfolio Cohort Data <br>& Longevity Forecasting Models"]
    B --> C["Step 1: Market-Consistent Valuation <br>of Policy Liabilities (Inflows/Outflows)"]
    C --> D["Step 2: Evaluate Solvency Capital Requirement (SCR)"]
    D --> E["Idiosyncratic Risk (Accidental Mortality):<br>Closed Formula"]
    D --> F["Systematic Risk (Trend Risk):<br>Algorithmic Model"]
    E & F --> G["Key Outcomes: Accidental volatility driven by Sums-at-Risk & age; <br>Trend risk depends on volatility & longevity model"]