Credibility Using Copulas

Abstract

Credibility is a form of insurance pricing that is widely used, particularly in North America. The theory of credibility has been called a “cornerstone” in the field of actuarial science. Students of the North American actuarial bodies also study loss distributions, the process of statistical inference of relating a set of data to a theoretical (loss) distribution. In this work, we develop a direct link between credibility and loss distributions through the notion of a copula, a tool for understanding relationships among multivariate outcomes.

This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross section of risk classes (towns) with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time; specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution; like the univariate tdistributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.

We present an illustrative example of Massachusetts automobile claims, and compare our new credibility estimates with those currently existing in the literature.     

Weighted Pricing Functionals With Applications to Insurance

Abstract

We explore the role of weighted distributions in pricing insurance risks. In particular, we relate the distributions to actuarial and economic premium calculation principles and in this way provide a unifying methodology for constructing new principles and analyzing known ones.     

Corporate strategy financialized: Conjuncture,arbitrage and earnings capacity in the S&P500

The conjuncture that ushered in the era of shareholder value served to embed capital market expectations into corporate governance aligning management and shareholder interests. Market arbitrage focussed on modifying contractual relations with stakeholders to extract a (higher) return on invested capital. In this article we focus on cash earnings on capital employed generated by the S&P 500 survivor group of firms covering the period 1990–2008. We use this financial data to construct three complementary perspectives on corporate financial performance: firm, firm-relative and macro. Within this framework the financial numbers and perspectives are analogous to a ‘hall of mirrors’ where ambiguity and contradiction are in play frustrating straightforward performative narratives that connect purpose with financial transformation an era of shareholder value.     

Perfectly competitive bilateral exchange without discounting

In a random-matching economy of traders who maximize cumulative consumption (overtaking criterion), the stationary, Markov, Bayesian-perfect equilibrium is studied. At such equilibrium, two results hold: (1) perfect substitutability between current and future consumption implies a no-surplus condition; and (2) by the no-surplus condition, there is a nominal price at which all trades must occur. These results strengthen the seminal results of Ostroy (1973) regarding monetary bilateral exchange in two ways: the incentive compatibility of the equilibrium trading pattern is established and a less roundabout trading pattern enhances welfare by enabling consumption to occur more frequently.     

全球化：前景、潜力与问题

本文扼要阐述了经济全球化发展的前景和潜力,并运用李嘉图模型对全球化可能导致的经济损害作出论证分析进而说明,尽管经济学家在极大程度上趋向于将全球化视为基本良性的现象,但全球化仍然对某些国家（包括发达国家）带来经济损害,及对部分人群可能造成极其痛苦的后果。不过,源自于全球化的不断增长的竞争压力,会加强创新和增长,从长远来看,的确对每个国家有利。     

Peer effects in the diffusion of water‐saving agricultural technologies

We investigate the role of peer effects in the diffusion of an important water‐saving irrigation technology: low energy precise application (LEPA). Using detailed irrigation behavior data for growers in the High Plains Aquifer region of Kansas covering 1990–2014, we find clear evidence of peer influence in adoption of LEPA, net of environmental factors. Specifically, an additional neighboring LEPA installation within 1 km increases the probability of adoption by about 0.3 percentage points, on average, and this effect diminishes with distance. Our empirical estimates indicate that in the absence of peer effects, LEPA adoption would have been about 10% lower (1,000–1,600 fewer installations) per year. In addition, we find that growers install LEPA in response to higher energy prices.     

Enacting risk reduction: an examination of the volitional stages of smoking cessation within Scotland

This study examines an extended version of the Theory of Planned Behaviour (TPB) in the context of nicotine replacement therapy (NRT) as an aid to smoking cessation. An attempt is made to address the intention–behaviour gap identified in the literature by specifically focusing on the role and interrelationships of volitional stages, namely intention, planning and anticipated effort. A convenience sample of 207 female smokers, aged 16–36, provided information about their views, attitudes and volitional behaviour regarding the use of NRT as an aid to smoking cessation. Results of this study show the TPB to be pertinent, accounting for 41% of the variance in intention to use NRT as an aid to smoking cessation. Furthermore, behavioural intention is found to mediate the relationship between the TPB antecedents (attitude, subjective norm and perceived behavioural control) and each of the two volitional elements, planning and anticipated effort. The implications of these findings are discussed.