Antonio Heras

Rough Sets and the role of the monetary policy in financial stability (macroeconomic problem) and the prediction of insolvency in insurance sector (microeconomic problem)

Abstract This paper faces two questions related with financial stability. The first one is a macroeconomic problem in which we try to further investigate the role of monetary policy in explaining banking sector fragility and, ultimately, systemic banking crisis. It analyses a large sample of countries in the period 1981–1999. We find that the degree of central bank independence is one of the key variables to explain financial crisis. However, the effects of the degree of independence are not linear. Surprisingly, either a high degree of independence or a high degree of dependence are compatible with a situation of financial stability, while intermediate levels of independence are more likely associated with financial crisis. It seems that it is the uncertainty related with a non-clear allocation of monetary policy responsibilities that contributes to financial crisis episodes. The second one is a microeconomic problem: the prediction of insolvency in insurance companies. This question has been a concern of several parties stemmed from the perceived need to protect general public and to minimize the costs associated such as the effects on state insurance guaranty funds or the responsibilities for management and auditors. We have developed a bankruptcy prediction model for Spanish non-life insurance companies and the results obtained are very encouraging in comparison with previous analysis. This model could be used as an early warning system for supervisors in charge of the soundness of these entities and/or in charge of the financial system stability. Most methods applied in the past to tackle these two problems are techniques of statistical nature and, variables employed in these models do not usually satisfy statistical assumptions what complicates the analysis. We propose an approach to undertake these questions based on Rough Set Theory.

Duality theory for infinite-dimensional multiobjective linear programming

Abstract The purpose of this paper is to study the relationship between an arbitrary-dimensional multiobjective linear program and its dual program. Dual solutions are obtained which, under certain conditions, measure the sensitivity of the proper primal solutions.

Asymptotic Fairness of Bonus-Malus Systems and Optimal Scales of Premiums

In this paper we try to evaluate the asymptotic fairness of bonus-malus systems, assuming the simplest case when there is no hunger for bonus. The asymptotic fairness has to be understood as the bonus-malus system ability in assessing the individual risks in the long run. Firstly we define the asymptotic fairness of a bonus-malus system following an expression that can be found in J. Lemaire [1985]: Automobile Insurance. Actuarial Models. Dordrecht: Kluwer-Nijhoff Publishing, p. 168. Secondly, we define a measure of the global asymptotic fairness considering the structure function of the risk group. Finally we try to calculate, for each set of transition rules and a given structure function, the scale of premiums that brings the global asymptotic fairness closest to the ideal situation where each insured pays in the long run a premium corresponding to its own claim frequency. This is possible thanks to the application of a multiobjective optimization technique named Goal Programming.

Duality theory and slackness conditions in multiobjective linear programming

Abstract The aim of this paper is to develop a duality theory for linear multiobjective programming verifying similar properties as in the scalar case. We use the so-called “strongly proper optima” and we characterize such optima and its associated dual solutions by means of some complementary slackness conditions. Moreover, the dual solutions can measure the sensitivity of the primal optima.

An Application of Linear Programming to Bonus Malus System Design

The purpose of this paper is to show how linear programming methodology can help us to design Bonus-Malus premium scales with some interesting theoretical and practical attributes. Examples of these properties are the financial equilibrium of the system, the monotonicity and proper variability of the premium scale, and the improvement of some efficiency measures such as the RSAL and the elasticity of the system. We will conclude that the use of the linear programming methodology makes possible a high degree of interaction between the designer and the mathematical model.

Conditional Tail Expectation and Premium Calculation

In this paper we calculate premiums which are based on the minimization of the Expected Tail Loss or Conditional Tail Expectation (CTE) of absolute loss functions. The methodology generalizes well known premium calculation procedures and gives sensible results in practical applications. The choice of the absolute loss becomes advisable in this context since its CTE is easy to calculate and to understand in intuitive terms. The methodology also can be applied to the calculation of the VaR and CTE of the loss associated with a given premium.

An application of two-stage quantile regression to insurance ratemaking

Abstract Two-part models based on generalized linear models are widely used in insurance rate-making for predicting the expected loss. This paper explores an alternative method based on quantile regression which provides more information about the loss distribution and can be also used for insurance underwriting. Quantile regression allows estimating the aggregate claim cost quantiles of a policy given a number of covariates. To do so, a first stage is required, which involves fitting a logistic regression to estimate, for every policy, the probability of submitting at least one claim. The proposed methodology is illustrated using a portfolio of car insurance policies. This application shows that the results of the quantile regression are highly dependent on the claim probability estimates. The paper also examines an application of quantile regression to premium safety loading calculation, the so-called Quantile Premium Principle (QPP). We propose a premium calculation based on quantile regression which inherits the good properties of the quantiles. Using the same insurance portfolio data-set, we find that the QPP captures the riskiness of the policies better than the expected value premium principle.

The Multiobjective Nature of Bonus-Malus Systems in Insurance Companies

The so-called Problem of Optimal Premium Calculation deals with the selection of the appropriate premiums to be paid by the insurance policies. At first sight, this seems to be a statistical estimation problem: we should estimate the mean claim amount, which in actuarial terms is known as the net premium. Nevertheless, several extensions of this problem are clearly multi-objective decision problems. For example, when we allow the company to modify the premiums paid by the policyholders according to their past claim experience, there are several ways of designing the resulting Bonus-Malus System (BMS), and they usually involve several different objectives.