Estimating Outstanding Claim Liabilities: The Role of Unobserved Risk Factors

By Spierdijk, Laura; Koning, Ruud H. | Journal of Risk and Insurance, December 2014 | Go to article overview

Estimating Outstanding Claim Liabilities: The Role of Unobserved Risk Factors


Spierdijk, Laura, Koning, Ruud H., Journal of Risk and Insurance


ABSTRACT

This article proposes a new method for estimating claim liabilities. Our approach is based on the observation from contract theory that there is information asymmetry between the insurer and the policyholder about the risks incurred by the latter. We show that unobserved heterogeneity allows for a form of experience learning that can reduce this asymmetry, which makes it easier for the insurer to distinguish between high-risk and low-risk claimants. We evaluate our approach in the context of disability insurance for self-employed and show that it results in more accurate best estimates of outstanding claim liabilities.

INTRODUCTION

Risk-based estimates of liabilities are the basis for determining evidence-based underwriting criteria and calculating insurance premiums. Moreover, the Solvency II Directive requires insurance companies to base loss reserves on risk-based estimates of liabilities (Sandstrom, 2011).

The actuarial literature describes two ways of estimating liabilities in the general insurance business. The first approach uses aggregate claim data, which makes it hard to relate person-specific risk factors to individual claim sizes (Zhao and Zhou, 2010). The second approach is based on a statistical model that captures the relation between individual claim sizes on the one hand and person-specific characteristics or other relevant risk factors on the other hand (e.g., Czado and Rudolph, 2002; Larsen, 2007; Zhao, Zhou, and Wang 2009; Antonio and Plat, 2010; Zhao and Zhou, 2010; Levantesi and Menzietti, 2012). The statistical model is used to estimate the claim size distribution of a single policyholder with certain risk factors, which provides input for the estimate of an individual liability. Subsequent aggregation of individual liabilities yields a risk-based liability at the aggregate portfolio level.

The economic literature has emphasized the importance of individual-specific unobserved heterogeneity (alternatively known as frailty) in modeling individual-specific risks such as unemployment and disability (Van den Berg, 2001). Unobserved heterogeneity is generally modeled as an individual-specific random effect that is uncorrelated with the model's observed risk factors. Ignoring unobserved heterogeneity may result in biased model coefficients; in survival models it may also lead to overestimation of the degree of negative duration dependence (Lancaster, 1990). Actuarial studies usually ignore unobserved heterogeneity (see also "Literature Review").

The goal of this research is to make a connection between the actuarial and economic literature by accounting for individual-specific unobserved heterogeneity in the estimation of insurance liabilities from individual claim data. Our approach is based on the observation from contract theory that there is information asymmetry between the insurer and the policyholder about the risks incurred by the latter (Chiappori and Salanie, 2003). We show that unobserved heterogeneity allows for a form of experience learning that can reduce this asymmetry, which makes it easier for the insurance company to distinguish between high-risk and low-risk claimants. The experience learning entails that we update the distribution of a claimant's unobserved risk factors on the basis of his or her claim history. This approach is expected to result in more accurate best estimates of outstanding claim liabilities.

The principle of experience learning is well known in the actuarial literature (see e.g., Herzog, 2010). In practice, it is widely applied in automobile insurance, where the information asymmetry between insurer and policyholder about the latter's riskiness is mitigated by means of a bonus-malus system (Ludovski and Young, 2010). The difference with our approach concerns the role of the unobserved risk factors, but we share the goal of reducing the information asymmetry between insurer and claimant by using the information contained in the claim history. …

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