Solvency, Capital Allocation, and Fair Rate of Return in Insurance

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. Copyright The Journal of Risk and Insurance, 2006.

Enterprise Risk Management, Insurer Value Maximisation, and Market Frictions

“…We now extend the model analyzed in Sherris [26] and Sherris and van der Hoek [27] by explicitly including frictional costs. Capital is assumed to be costly to hold and at time 1 frictional costs are incurred in the form of deadweight losses from taxes, agency costs of capital, and costs of financial distress.…”

“…We take a similar approach to construct a representative insurer, however, our objective is to determine optimal capitalization and insurer profit margins allowing for varying frictional costs and, importantly, including policyholder demand elasticity and a preference for financial quality in the model. We follow Doherty and Garven [9] and Sherris [26] in the construction of the balance sheet, ignoring frictional costs. We then develop a market value based balance sheet incorporating frictional costs of capital.…”

“…Equity is the difference between the assets and the liabilities allowing for the value of the default put option. This balance sheet is similar to Sherris [26] and Sherris and van der Hoek [27] except that the model formally includes production costs and assumes premium income is determined by price and quantity sold by line.…”

Capital Allocation in the Insurance Sector

“…Denault 2001;Csóka et al 2009, Csóka andPintér 2016), option pricing (e.g. Myers -Read 2001;Sherris 2006;Kim -Hardy 2007) or other statistical approaches (e.g. Kalkberener 2005; Homburg -Scherpereel 2008;Buch -Dorfleitner 2008).…”

Multivariate TVaR-Based Risk Decomposition for Vector-Valued Portfolios

“…Our approach allows a conservative risk protection, which is in line with desirable changes, as a consequence of the recent financial crisis and catastrophic events. Sherris [1] studies how to distribute the expected policyholder deficit to each business line under a complete market condition. Kim and Hardy [2] study the allocation principle on policyholders' deficit.…”