A framework for the valuation of insurance liabilities by production cost

Abstract

This paper sets out a framework for the valuation of insurance liabilities that is intended to be economically realistic, elementary, reasonably practically applicable, and as a special case to provide a basis for the valuation in regulatory solvency systems such as Solvency II and the SST. The valuation framework is based on the cost of producing the liabilities to an insurance company that is subject to solvency regulation (regulatory solvency capital requirements) and insolvency laws (consequences of failure) in finite discrete time. Starting from the replication approach of classical no-arbitrage theory, the framework additionally considers the nature and cost of capital (expressed by a ``financiability condition"), that the liabilities may be required to be fulfilled only ``in sufficiently many cases" (expressed by a ``fulfillment condition"), production using ``fully illiquid" assets in addition to tradables, and the asymmetry between assets and liabilities. We identify necessary and sufficient conditions on the capital investment under which the framework recovers the market prices of tradables, investigate extending production to take account of insolvency, implications of using illiquid assets in the production, and show how Solvency II and SST valuation can be derived with specific assumptions.