<scp>Solvency, Capital Allocation, and Fair Rate of Return in Insurance</scp>

TLDR

The article investigates the relationship among solvency, capital allocation, and fair rate of return in insurance. A capital allocation method is developed using an economic definition of solvency and a complete markets arbitrage‑free model, illustrated with a single‑period discrete‑state example and yielding properties such as additive allocation consistent with balance‑sheet values. The impact of adding lines of business on capital allocation is briefly examined.

Abstract

Abstract In this article, we consider the links between solvency, capital allocation, and fair rate of return in insurance. A method to allocate capital in insurance to lines of business is developed based on an economic definition of solvency and the market value of the insurer balance sheet. Solvency, and its financial impact, is determined by the value of the insolvency exchange option. The allocation of capital is determined using a complete markets’ arbitrage‐free model and, as a result, has desirable properties, such as the allocated capital “adds up” and is consistent with the economic value of the balance sheet assets and liabilities. A single‐period discrete‐state model example is used to illustrate the results. The impact of adding lines of business is briefly considered.