Insurance: solvency and valuation

Doktorsavhandling, 2015

This thesis concerns mathematical and statistical concepts useful to assess an insurer's risk of insolvency. We study company internal claims payment data and publicly available market data with the aim of estimating (the right tail of) the insurer's aggregate loss distribution. To this end, we also develop a framework for market-consistent valuation of insurance liabilities. Moreover, we discuss Solvency II, the risk-based regulatory regime in the European Union, in some detail. In Paper I, we construct a multidimensional simulation model that could be used to get a better understanding of the stochastic nature of insurance claims payments, and to calculate solvency capital requirements. The assumptions made in the paper are based on an analysis of motor insurance data from the Swedish insurance company Folksam. In Paper II, we investigate risks related to the common industry practice of engaging in interest-rate swaps to increase the duration of assets. Our main focus is on foreign-currency swaps, but the same risks are present in domestic-currency swaps if there is a spread between the swap-zero-rate curve and the zero-rate curve used for discounting insurance liabilities. In Paper III, we study data from the yearly reports the four major Swedish non-life insurers have sent to the Swedish Financial Supervisory Authority (FSA). Our aim is to find the marginal distributions of, and dependence between, losses in the five largest lines of business. In Paper IV, we study the valuation of stochastic cash flows that exhibit dependence on interest rates. We focus on insurance liability cash flows linked to an index, such as a consumer price index or wage index, where changes in the index value can be partially understood in terms of changes in the term structure of interest rates. %We focus primarily on the case when a deep and liquid market for index-linked bonds is absent, or when the market price data are unreliable. Papers I and III are based on data that are difficult to get hold of for people in academia. The FSA reports are publicly available, but actuarial experience is needed to find and interpret them. These two papers contribute to a better understanding of the stochastic nature of insurance claims by providing data-driven models, and analyzing their usefulness and limitations. Paper II contributes by highlighting what may happen when an idea that is theoretically sound (reducing interest-rate risk with swaps) is applied in practice. Paper IV contributes by explicitly showing how the dependence between interest rates and inflation can be modeled, and hence reducing the insurance liability valuation problem to estimation of pure insurance risk.