Band 13, Heft 2 - New Solutions in Risk Management

Bayesian regularization, a relatively new method for estimating model parameters, shrinks estimates towards the overall mean by shrinking the parameters. It has been proven to lower estimation and prediction variances from those of MLE for linear models, such as regression or GLM. It has a goodness-of-fit measure, and can readily be applied using available software. This can be used for any type of actuarial linear modeling, but it is slightly more complicated for mortality and loss reserving models that use row, column, and diagonal effects for array data. These are called age-period-cohort, or APC models by statisticians. The problem is that the row, column and diagonal effects are not what should be shrunk. These models can easily become over-parameterized, and actuaries often reduce parameters with smooth curves or cubic splines. We discuss an alternative smoothing method that uses regularization, with its reduction in estimation errors, and illustrate both its classical and Bayesian forms and their application to APC modeling. Typical actuarial models and some generalizations are used as examples.

We analyze the recovery rates of 66,928 Japanese unsecured loans in default by ordered logistic regression. We divide the defaulted firms by sole proprietorships and industrial corporations and analyze the recovery rates for each type of firms. The recovery rate for sole proprietorships is larger than that for industrial corporations. Moreover, we model not only the recovery rate during five years at the time of default but also that evaluated at the time of loan appraisal for each type of firms, and we call them “loan model” and “after-default model” respectively. The significant factors with large regression coefficients are different for each model and each type of firms. We find that these are (1) guarantee by business owner’s family in two models for each type of firms, (2) firm age in two models for industrial corporations, (3) exposure rate at default in the after-default model for each type of firms, (4) obligor’s real-estate value minus debt amount, initial loan amount, and white tax return in the loan model for sole proprietorships. The values of Somers’ D for the after-default model are larger than those for the loan model because the exposure rate at default which has large estimates can be available at time of default. The values of Somers’ D for sole proprietorships are larger than those for industrial corporations. We divide all defaulted loans into four classes based on the score evaluated by the model, and validate the ratings of the actual recovery rates through three kinds of statistical tests. In addition, we conduct out-of-sample tests, and examine the usefulness of the model.

This study examines the consistency in risk aversion between hypothetical and actual choices in medical insurance. Utilizing a unique survey in which individuals in Japan are asked about their perception of a hypothetical necessary amount for hospitalization benefits and the actual insurance contract amount at the time of hospitalization, the study identifies that the gap between the hypothetical and actual domains is not constant. Even between two similar domains of hospital benefits selection, the gap is found to vary depending on respondents’ anxiety about future medical expenses, their level of financial literacy, and other personal attributes such as age and occupation. The results of this study strongly suggest a need for exercising caution when using the degree of risk aversion obtained by hypothetical questions, questionnaire surveys, and experiments to predict actual behavior.

For many decades, the analysis of underwriting-profitability regimes (i. e. successive “hard” and “soft” markets) has formed an important topic in insurance research. In the present article, we study the characteristics of firm-level underwriting results by applying both ordinary and Markov-switching autoregressive models to data from individual U.S. property-liability companies. The research employs both univariate and multivariate methods. Our analysis argues against the existence of distinct, firm-level underwriting regimes in the U.S. property-liability market, but offers evidence of cross-company interactions over time.