Opportunity Cost in Insurance

ArXiv ID: 2511.13959 “View on arXiv”

Authors: Jan Maelger

Abstract

We develop a formalism for insurance profit optimisation for the in-force business constraint by regulatory and risk policy related requirements. This approach is applicable to Life, P&C and Reinsurance businesses and applies in all regulatory frameworks with a solvency requirement defined in the form of a solvency ratio, notably Solvency II and the Swiss Solvency Test. We identify the optimal asset allocation for profit maximisation within a pre-defined risk appetite and deduce the annual opportunity cost faced by the insurance company.

Keywords: Insurance profit optimisation, Solvency ratio, Solvency II, Asset allocation, Risk appetite, Insurance / Multi-asset

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is heavy on mathematical formalism, utilizing advanced calculus (KKT conditions, Lagrangians, Hessians) to derive an optimization framework for insurance profit. It lacks any empirical validation, backtests, or implementation details, focusing purely on theoretical model development.

  flowchart TD
    A["Research Goal:<br>Optimize insurance profit<br>under regulatory risk constraints"] --> B["Key Data & Inputs:<br>Asset classes, liabilities,<br>Solvency II/SST ratio requirements"]
    B --> C["Methodology:<br>Mathematical programming<br>for profit maximization"]
    C --> D{"Computation:<br>Optimal asset allocation<br>under risk appetite?"}
    D --> E["Key Findings:<br>1. Optimal allocation strategy<br>2. Deduced annual opportunity cost"]