Insurance-Finance Arbitrage

TL;DR

This paper introduces the concept of insurance-finance arbitrage, analyzing the conditions under which insurance contracts are consistent with financial market trading, and establishes a fundamental theorem linking arbitrage absence to a special probability measure.

Contribution

It formalizes insurance-finance arbitrage, extends the fundamental theorem of asset pricing to insurance contexts, and develops a framework incorporating mortality risk and market dependence.

Findings

Established a fundamental theorem on the absence of insurance-finance arbitrage.

Defined insurance-finance-consistent probability measures.

Developed a tractable valuation framework using filtration enlargement.

Abstract

Most insurance contracts are inherently linked to financial markets, be it via interest rates, or -- as hybrid products like equity-linked life insurance and variable annuities -- directly to stocks or indices. However, insurance contracts are not for trade except sometimes as surrender to the selling office. This excludes the situation of arbitrage by buying and selling insurance contracts at different prices. Furthermore, the insurer uses private information on top of the publicly available one about financial market. This paper provides a study of the consistency of insurance contracts in connection with trades in the financial market with explicit mention of the information involved. By defining strategies on an insurance portfolio and combining them with financial trading strategies, we arrive at the notion of insurance-finance arbitrage (IFA). In analogy to the classical fundamental theorem of asset pricing, we give a fundamental theorem on the absence of IFA, leading to the existence of an insurance-finance-consistent probability. In addition, we study when this probability gives the expected discounted cash-flows required by the EIOPA best estimate. The generality of our approach allows to incorporate many important aspects, like mortality risk or general levels of dependence between mortality and stock markets. Utilizing the theory of enlargements of filtrations, we construct a tractable framework for insurance-finance consistent valuation.