Applications of Statistics in the Field of General Insurance: An Overview

This is an expository paper on applications of statistics in the field of general insurance, also called non‐life insurance. Unlike life insurance where advanced statistical techniques have long been part of financial mathematics and actuarial applications, their use is only relatively recent in non‐life insurance. The business model of insurance companies, especially those active in non‐life insurance, has seen dramatic changes over the last 15 years. The aim of this paper is to convince the readers that especially today non‐life insurance is not only an exciting ground to apply existing modern statistical tools but also a fertile environment for new and challenging statistical developments. The activities of an insurance company can be viewed as an industrial process where data management and data analysis play a key role. That is why a fundamental understanding of data‐related issues (such as data quality, variability, analysis and correct interpretation) is so essential to the insurance business. These are exactly the tasks where professional statisticians excel. Also, a better understanding of the field of general insurance by statisticians will promote fruitful exchanges between actuaries and statisticians, thereby helping to bring actuarial and statistical professional societies closer to each other. Selected examples are used to cover the essential aspects of general insurance, and all of them are based on the author's experience. The paper concludes with some remarks on the role of statisticians working in general insurance.     

Coherent Distortion Risk Measures and Higher-Order Stochastic Dominances

Abstract

We show that the only coherent distortion risk measure that is consistent with respect to 3-convex order and hence with stochastic dominance of order 3 is the expected value, thus generalizing previous results of Hurlimann and solving a problem posed by Yamai and Yoshiba.     

A Simple Model of Insurance Market Dynamics

Abstract

This paper constructs and studies a simple but realistic model of an insurance market. The model has a minimalist construction in the sense that the number of parameters defining it is strictly limited and the elimination of any one of them would destroy its realism. There are 11 essential parameters. Each of the parameters has a physical interpretation. Some determine competitive effects within the market, some barriers to entry, and so on. The effect of each on various aspects of the market is examined in the presence of simulated loss experience. The aspects of the market considered include stability of premium rates, profitability, and market concentration. Some of the parameters are capable of use as regulatory controls. Two parameters, in addition to the original 11, are explicit price controls. Despite its simplicity, the model displays considerably complex behavior. Some results are intuitive, but some are not. For this reason, regulatory controls need to be applied with great caution lest they induce perverse effects, possibly even the reverse of those intended. The effect of the parameters on market behavior is first studied in the absence of catastrophic events from the loss experience. Subsequently, the effect of a single such event is studied.     

The growth path of the dynamic Asian economies

The rapid and sustained growth of several Asian economies led researchers, policymakers, and decision‐makers in the world of international business to search for a plausible Asian model of growth. Numerous explanations of the dynamic growth in Asia have been put forward, including the ‘new structuralist’ approach proposed by Lin (2012). This paper examines the various explanations of what these countries did to unleash their growth potential. Industrial policy and market intervention are two such explanations. While the dynamic Asian economies did not flout the Washington Consensus, they adapted it in different ways. The policies that they followed under the Beijing Consensus allowed them to proactively follow pro‐business policies. They also exploited the concepts of economic statism or state capitalism, which became an integral part of what became known as the ‘Asia model’.     

Pricing a Heterogeneous Portfolio Based on a Demand Function

Abstract

Consider a portfolio containing number of risk classes. Each class has its own demand function, which determines the number of insureds in this class as a function of the premium. The insurer determines the premiums based on the number of insureds in each class. The “market” reacts by updating the number of the policyholders, then the insurer updates the premium, and so on. We show that this process has an equilibrium point, and then we characterize this point.     

Building the Legitimacy of Whistleblowers: A Multi‐Case Discourse Analysis

Evidence suggests that society still does not view whistleblowers as wholly legitimate—despite legal protections now offered in some jurisdictions, such as the United States. Drawing on a discourse analysis (i.e., an examination of statements), we investigate the well‐publicized stories of seven whistleblowers from 69 sources, including books, first‐ and second‐hand interviews, websites, and videos. Our focus is to examine how whistleblower discourses can build legitimacy by more tightly defining the whistleblower role and demonstrating its alignment with social norms. Using whistleblower self‐narratives, we identify four narrative patterns: (i) Trigger(s)—the event(s) leading to whistleblowing; (ii) Personality traits—whistleblower's morality, resourcefulness, and determination; (iii) Constraints—barriers requiring regulatory and organizational change; and (iv) Consequences—the longer term positive impact of the whistleblowing act. These patterns rely on symbolic, analogical, and metaphorical framing to allow others to better understand the role of whistleblowers and enlist their support. Exploring a data set of 1,621 press articles, we find indications that these narrative patterns resonate in the media—which provide a form of support and may be instrumental in legitimizing the whistleblower role. Grounded on these results, we develop a legitimacy construction model of the whistleblower role, that is, a representation of how role legitimacy is produced and sustained. From this model, we identify a number of important areas for future research.     

防御性现实主义:进攻性现实主义时代的悲剧

作者旨在回答一个重要的问题:防御性现实主义在进攻性现实主义时代的命运如何?这个问题可以分解为两个小问题:进攻性现实主义时代下的防御性现实主义国家面临哪些生存压力?这些生存压力对防御性现实主义国家会造成哪些影响?作者认为,在进攻性现实主义时代,防御性现实主义国家面临五种生存压力:防御性现实主义国家是进攻性现实主义国家进攻的诱因;防御性现实主义国家经常遭遇进攻性现实主义国家的攻击;防御性现实主义国家被进攻性现实主义国家包围;防御性现实主义国家几乎无法和进攻性现实主义国家合作;防御性现实主义国家的军力通常在整体上或在关键指标上落后于进攻性现实主义国家。在这些生存压力之下,防御性现实主义国家的生存质量堪忧,在重要的物质利益和国家的自主性两项指标上的表现难如人意。作者采取了案例分析的方法,以中国宋朝和波兰为例,论证了进攻性现实主义时代的防御性现实主义困境。     

亚洲工厂及关联度分析

依据亚洲零部件贸易数据,作者采用了依存比率的方法对亚洲工厂的规模、工厂内部以及同美国之间的相互依存关系进行了研究。研究结果发现,亚洲工厂的规模超过北美洲和欧洲工厂,成为了世界上最大的工厂。亚洲零部件内部贸易额及比重超过了欧盟,这说明亚洲生产的一体化程度更高。从零部件进出口规模角度看,亚洲地区的经济体均高度依赖亚洲工厂的活动,而亚洲工厂对中国的依存度则最高,对日本的依赖程度只排在第三位,这说明中国是亚洲工厂的核心平台。美国在亚洲贸易中的重要性主要体现为中国的最终产品出口对美国市场存在严重依赖,而亚洲主要经济体对中国市场的出口已经超过对美国的出口,亚洲工厂对于美国的依赖程度并不高,远远低于亚洲工厂对中国内地和中国香港的依赖。相反,美国对亚洲工厂的依赖程度则远高于亚洲工厂对美国的依赖。     

Markov Aging Process and Phase-Type Law of Mortality

Abstract

In this article, we propose a finite-state Markov process with one absorbing state to model human mortality. A health index called physiological age is introduced and modeled by the Markov process. Under this model the time of death follows a phase-type distribution. The model possesses many desirable analytical properties useful for mortality analysis. Closed-form expressions are available for many quantities of interest including the conditional survival probabilities of the time of death and the actuarial present values of the whole life insurance and annuity. The heterogeneity or frailty effect of a cohort can be expressed explicitly. The model is also able to explain some stylized facts of observed mortality data. We fit the model to some Swedish population cohort data and life tables compiled by the U.S. Social Security Administration. The fitting results are very satisfactory.     

Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty

Abstract

In this article we investigate three related investment-consumption problems for a risk-averse investor: (1) an investment-only problem that involves utility from only terminal wealth, (2) an investment-consumption problem that involves utility from only consumption, and (3) an extended investment-consumption problem that involves utility from both consumption and terminal wealth. Although these problems have been studied quite extensively in continuous-time frameworks, we focus on discrete time. Our contributions are (1) to model these investmentconsumption problems using a discrete model that incorporates the environment risk and mortality risk, in addition to the market risk that is typically considered, and (2) to derive explicit expressions of the optimal investment-consumption strategies to these modeled problems. Furthermore, economic implications of our results are presented. It is reassuring that many of our findings are consistent with the well-known results from the continuous-time models, even though our models have the additional features of modeling the environment uncertainty and the uncertain exit time.