David J. Nye

The Stochastic Characteristics of Property-Liability Insurance Company Underwriting Profits

Research on property-liability insurance often depends on the assumptions that combined ratios are normally distributed and/or uncorrelated with yield rates on common stocks. This study examines 206 combined ratio time series for nine major lines of insurance in order to gauge the accuracy of these assumptions. The normality hypothesis is accepted for approximately one-half the series, many are highly correlated with the industry-wide combined ratio, and almost none are significantly correlated with equity yields. An important implication is that mean-variance models should not be used in insurance research without validating the normality assumption or determining the impact of departures from normality. Managerial and public policy research on property-liability insurance often depends on assumptions about the stochastic characteristics of the profit margins for various types of insurance. These assumptions are of two principal types: (1) assumptions about the distributional properties of the profit margins, and (2) assumptions about the systematic risk inherent in various types of insurance. The first type of assumption is common in portfolio optimization research. Kahane [ 13], for example, has developed a quadratic programming model for use in determining the optimal product mix of a multiple line propertyliability insurer. This model will be valid if profits in the various product lines are normally distributed or if quadratic utility functions are appropriate. As quadratic utility functions are considered undesirable by many researchers, the usefulness of the model may hinge on the validity of the normality assumption. Decision making models developed by Thompson, Matthews, and Li [2 1 ], by Hammond, Shapiro, and Shilling [ 10], and by other researchers also depend on this assumption.

A NOTE ON STOP LOSS PREMIUMS

This note uses a covariance model of insurance pricing to examine stop loss premiums. The premium is equal to the expected loss plus a term proportional to the covariance between the loss and another random variable Y which represents an index. Under this model premiums are additive. Three further properties of the stop loss premium are proposed and the conditions for the stop loss premium to have these properties are derived.

Reinsurance retention levels for property/liability firms: A managerial portfolio selection framework

Abstract This paper presents a managerial portfolio selection model which analyzes the reinsurance decision of the ceding insurer. Alternative goal functions for management are assumed and then comparative statics, as well as illustrative numerical examples are used to develop testable implications concerning the optimal proportional reinsurance retention level for property/liability insurance firms.

An Insurance Approach to Risk Analysis of Debt Home Equity Conversion Programs

The use of home equity conversion debt creates a compounding obligation against the home that makes collateral deficiency a potentially dominant risk. Using an insurance methodology, an examination of this risk and its impact upon the potential for home equity conversion is conducted. The paper includes a consideration of how deficiency risk and maximum potential benefits are affected by the interaction of household characteristics with demographic and economic factors. Copyright American Real Estate and Urban Economics Association.