The Tail Stein's Identity with Applications to Risk Measures

In this article, we examine a generalized version of an identity made famous by Stein, who constructed the so-called Stein's Lemma in the special case of a normal distribution. Other works followed to extend the lemma to the larger class of elliptical distributions. The lemma has had many applications in statistics, finance, insurance, and actuarial science. In an attempt to broaden the application of this generalized identity, we consider the version in the case where we investigate only the tail portion of the distribution of a random variable. Understanding the tails of a distribution is very important in actuarial science and insurance. Our article therefore introduces the concept of the “tail Stein's identity” to the case of any random variable defined on an appropriate probability space with a Lebesgue density function satisfying certain regularity conditions. We also examine this “tail Stein's identity” to the class of discrete distributions. This extended identity allows us to develop recursive formulas for generating tail conditional moments. As examples and illustrations, we consider several classes of distributions including the exponential family, and we apply this result to demonstrate how to generate tail conditional moments. This holds a large promise for applications in risk management.     

我国养老保险精算管理研究——基于国际养老保险精算平衡制度的借鉴

本文在分析养老保险精算管理的政策背景、现实意义的基础上,比较研究了发达 国家养老保险精算管理的基本制度,结合我国养老保险精算管理现实状况,在借鉴国外先进经 验的基础上,提出完善我国养老保险精算管理制度的政策建议。文章认为,我国应当借鉴发达 国家做法,建立健全养老保险精算法治框架,以精算管理推进养老保险改革和制度完善,强化 养老保险精算运行的基础保障,并合理划定财政责任,促使养老保险自求平衡。     

Pricing Double-Trigger Reinsurance Contracts: Financial Versus Actuarial Approach

This article discusses various approaches to pricing double‐trigger reinsurance contracts—a new type of contract that has emerged in the area of ‘‘alternative risk transfer.’’ The potential coverage from this type of contract depends on both underwriting and financial risk. We determine the reinsurer's reservation price if it wants to retain the firm's same safety level after signing the contract, in which case the contract typically must be backed by large amounts of equity capital (if equity capital is the risk management measure to be taken). We contrast the financial insurance pricing models with an actuarial pricing model that has as its objective no lessening of the reinsurance company's expected profits and no worsening of its safety level. We show that actuarial pricing can lead the reinsurer into a trap that results in the failure to close reinsurance contracts that would have a positive net present value because typical actuarial pricing dictates the type of risk management measure that must be taken, namely, the insertion of additional capital. Additionally, this type of pricing structure forces the reinsurance buyer to provide this safety capital as a debtholder. Finally, we discuss conditions leading to a market for double‐trigger reinsurance contracts.     

“营业税改征增值税”对地方经济的影响分析——以吉林省延边州为例

自从“营改增”税收模式在2012年1月1日上海试运行以来，其动态一直处于各界人士的关注当中。随着“营改增”税收制度的不断完善，目前延边州1万多户企业单位成为了“营改增”试点，随着我国社会经济持续发展，“营改增”作为我国税制改革与增值税改革发展的必然趋势，这种税收模式将越来越被人所认同，并愿意接受和实施该税收制度。当该税收制度实行的程度越深，对地方经济的影响也会越来越大，以下我们就浅谈该税收模式对延边州地方经济的影响及建议。     

Compound mixed Poisson distributions I

The concept of compound mixed Poisson distributions in actuarial science is used to represent such variables as the total amount of claims or losses payable by an insurer. In this paper, comprehensive collections of approximate forms are derived for the compound mixed Poisson distribution. The calculations involve use of several special functions and their properties. We believe that the results will serve as an important reference in actuarial science.     

An Analysis of Risk, Insurance, and Actuarial Research: Citations From 1996 to 2000

This article evaluates the relative significance of research published in 16 risk, insurance, and actuarial journals by examining the frequency of citations in these risk, insurance, and actuarial journals and 16 of the leading finance journals during the years 1996 through 2000. First, the article provides the frequency with which each sample risk, insurance, and actuarial journal cites itself and the other sample journals so as to communicate the degree to which each journal's published research has had an influence on the other sample journals. Then the article divides the 16 journals into two groups: (1) the risk and insurance journal group, and (2) the actuarial journal group, and ranks them within their group based on their total number of citations, including and excluding self‐citations. A ranking within each group is based on the journals’ influence on a per article published basis. Finally, this study observes and reports on the most frequently cited articles from the sample risk, insurance, and actuarial journals.     

Contingent means in multi-life models

Multi-life models are useful in actuarial science for studying life contingency. Contingent probabilities are well-understood by most actuaries and are discussed extensively in the existing actuarial literature. However, the mean of a life in a multi-life model involving order of deaths is often found to be rather challenging to interpret by most actuaries who do not understand measure-theoretic probability. Standard textbooks on actuarial science or statistics do not elaborate on the correct interpretation of contingent means, leaving the actuaries at risk of making a blunder. This paper presents the correct interpretation both heuristically and rigorously using a non-measure-theoretic language, so that actuaries will be aware of some common misconceptions and avoid pitfalls in their work. The primary audience of this paper is practicing actuaries, actuarial students and actuarial educators. So we have given several actuarial applications. We hope that applied statisticians also will find this paper useful.     

Principal Applications of Bayesian Methods in Actuarial Science

Abstract

Bayesian ideas were introduced into actuarial science in the late 1960s in the form of empirical credibility methods for premium setting. The advance of the Bayesian methodology was slow due to its subjective nature and to the computational difficulties associated with the full Bayesian analysis. This paper offers a brief survey of Bayesian solutions to some actuarial problems and discusses the current state of research.     

Basic concepts in life assurance mathematics

Abstract

1. Introduction.

In this paper the basic concepts of the life insurance mathematics will be discussed. Due to the fact that the importance of the probability calculus as a hasis for the actuarial science has repeatedly been disclaimed in recent literature (See e.g. Ernst ZWinggi (1]), the present author feels that there is a justification for reconsidering the fundamental ideas of the actuarial science.     

Preferences representation in actuarial sciences

Abstract

The paper presents a generalization of Bernoulli's principle and of Von Neumann-Morgenstern's theorem with a view to lending more realism to the representation of preferences in actuarial sciences.     

Extending composite loss models using a general framework of advanced computational tools

ABSTRACT

Composite models have a long history in actuarial science because they provide a flexible method of curve-fitting for heavy-tailed insurance losses. The ongoing research in this area continuously suggests methodological improvements for existing composite models and considers new composite models. A number of different composite models have been previously proposed in the literature to fit the popular data set related to Danish fire losses. This paper provides the most comprehensive analysis of composite loss models on the Danish fire losses data set to date by evaluating 256 composite models derived from 16 parametric distributions that are commonly used in actuarial science. If not suitably addressed, inevitable computational challenges are encountered when estimating these composite models that may lead to sub-optimal solutions. General implementation strategies are developed for parameter estimation in order to arrive at an automatic way to reach a viable solution, regardless of the specific head and/or tail distributions specified. The results lead to an identification of new well-fitting composite models and provide valuable insights into the selection of certain composite models for which the tail-evaluation measures can be useful in making risk management decisions.     

指数保险有效性实证分析

运用Miranda模型研究发现,农户个体产量波动与所在区域产量波动存在高度正相关性,基于区域产量保险的保费率低于传统农业保险的保费率,这有利于刺激指数保险的需求。由于指数保险克服了传统农业保险市场中的逆向选择与道德风险问题,降低了交易成本,从而指数保险能够降低农户的保费支出并有效管理农业生产风险。     

Pareto-Optimal Insurance Policies in the Models with a Premium Based on the Actuarial Value

This article analyzes the problem of designing Pareto‐optimal insurance policies when both the insurer and the insured are risk averse and the premium is calculated as a function of the actuarial value of the insurer's risk. Two models are considered: in the first, the set of admissible policies is constrained by a given size of the premium; in the second, the premium size is not constrained so that it varies with the actuarial value of a policy chosen by the agents. For both cases a characterization of the Pareto‐optimal policies is derived. The corresponding optimality equations for the Pareto‐optimal policies are obtained and compared with the results on the classical risk exchange model.     

Financial Economics and Actuarial Practice

Abstract

Starting in the United Kingdom and continuing through the U.S. and Canadian actuarial professions, proponents of financial economics have been forcefully promoting a review of traditional actuarial practices and training. In particular, the financial theories first proposed by Modigliani and Miller and subsequently developed by others have been used to highlight serious weaknesses in typical actuarial thinking. In summary, it is claimed that much actuarial advice wrongly specifies value, that guidelines and standards need radical revision, and that traditional actuarial intuition suffers in comparison to newer modes of thought adopted by other professions.

This paper examines concepts from both financial economics and actuarial science as applied to defined benefit schemes using a simple discounted cash-flow framework as a reference point. The general finding is that many standard modes of actuarial thought are, in fact, indefensible when examined with the tools and techniques of financial economics. The call for revision of actuarial training and practices is credible and necessary.

However, the paper also touches upon areas where a heavy-handed application of finance theory could be misguided due to limitations in the simple financial economic models presented. It concludes that financial economics should be carefully integrated into actuarial thought rather than appended to existing actuarial theory or inserted as a wholesale replacement.     

Stochastic loss reserving: A new perspective from a Dirichlet model

Forecasting the outstanding claim liabilities to set adequate reserves is critical for a nonlife insurer's solvency. Chain–Ladder and Bornhuetter–Ferguson are two prominent actuarial approaches used for this task. The selection between the two approaches is often ad hoc due to different underlying assumptions. We introduce a Dirichlet model that provides a common statistical framework for the two approaches, with some appealing properties. Depending on the type of information available, the model inference naturally leads to either Chain–Ladder or Bornhuetter–Ferguson prediction. Using claims data on Worker's compensation insurance from several U.S. insurers, we discuss both frequentist and Bayesian inference.     

Skewed distributions in finance and actuarial science: a review

That the returns on financial assets and insurance claims are not well described by the multivariate normal distribution is generally acknowledged in the literature. This paper presents a review of the use of the skew-normal distribution and its extensions in finance and actuarial science, highlighting known results as well as potential directions for future research. When skewness and kurtosis are present in asset returns, the skew-normal and skew-Student distributions are natural candidates in both theoretical and empirical work. Their parameterization is parsimonious and they are mathematically tractable. In finance, the distributions are interpretable in terms of the efficient markets hypothesis. Furthermore, they lead to theoretical results that are useful for portfolio selection and asset pricing. In actuarial science, the presence of skewness and kurtosis in insurance claims data is the main motivation for using the skew-normal distribution and its extensions. The skew-normal has been used in studies on risk measurement and capital allocation, which are two important research fields in actuarial science. Empirical studies consider the skew-normal distribution because of its flexibility, interpretability, and tractability. This paper comprises four main sections: an overview of skew-normal distributions; a review of skewness in finance, including asset pricing, portfolio selection, time series modeling, and a review of its applications in insurance, in which the use of alternative distribution functions is widespread. The final section summarizes some of the challenges associated with the use of skew-elliptical distributions and points out some directions for future research.     

S -Convex Extrema,Taylor-Type Expansions and Stochastic Approximations

The present work studies s -convex orders using a remarkable probabilistic generalization of Taylor's theorem obtained by Massey & Whitt (1993) and further discussed by Lin (1994). We propose two methods for approximating a given risk with known first moments by means of s -convex extremal distributions. The goodness of those approximations is explored using stop-loss distances. Several applications show the interest of this approach in actuarial sciences.     

Commentary: New Currents in Science: The Challenge of Quality,examining the discrepancies and incongruities between Japanese techno-scientific policy and the citizens’ science movement in post-3/11 Japan

This commentary is inspired by my participation in the conference on post normal science: New Currents in Science: The Challenges of Quality, 2016, Ispra.First, I will describe Japanese commitment to PNS, which consists of a part of the long history of the Japanese response to European citizens' science/technology movement, in the framework of the introduction of Post-Normal Science in East Asia.Then I will re-examine the relationship between techno-science and democracy after 3/11 Japan, where triple disaster has radically changed the relationship between science/technology and society, and hence the very nature of Japan as a democratic society. Japan had been returning to an authoritarian state and technocratic nation in the aftermath of 3/11. As for the citizens' sphere, since 3/11, Japanese society has been badly divided; in fact, the current division of Japanese society is as bad as that of the Trumpian US.I have applied several conceptual tools to analyze this post-3/11 situation of Japan, that it was created by a combination of 'disaster capitalism' (a concept described by Naomi Klein (2008)), and 'normalcy bias'. The new political climate in post-3/11 Japan results in part from the politics of emergency, and partly from the manipulation and distortion of democracy.From the viewpoint of democracy and science, cases of thyroid cancer in Fukushima and its surroundings are a serious and even pathetically painful issue. One hundred seventy two children in and around Fukushima have already had their thyroids removed in surgical operations. But any suggestion of causality between the Fukushima incident and thyroid cancer is officially rejected. It is announced by the authority's voice that "radioactivity risk is safe, take it, because risk creates chance", like the proclamation given in the novel 1984 by George Orwell. Behind this is another historical psychology, that Japan has overcome Hiroshima and Nagasaki and made a great success in economic development. Post 3/11 Japan is judged as not a good place to discuss science and technology in a deliberate manner supported by a reasonable democracy with mutual understanding and value-free examination of techno-science in action. But, in this time of serious social divide and political populism, can PNS and a citizens' science approach now lead the way to fill in the gap? Are there any lessons from PNS that can be applied to post3/11 Japan? The question is still open.     

The Role of the Auditor in Modern Society: An Exploratory Essay

This paper examines competing proprietary and political cost arguments for incentives facing managers of different types of Australian and UK pension fund, to voluntarily disclose pension liability information in annual reports sent to their participants. For Australian defined benefit pension funds, the disclosure reveals the fund's actuarial surplus or deficit, which conveys information to participants about the pension fund's ability to generate future cash flows. Tests are conducted on the voluntary reporting practices of a sample of 119 Australian and 100 UK pension funds, using variables which prior research suggests affects their financial valuation and performance. The empirical results support predictions that managerial discretionary disclosure carries proprietary cost implications for Australian defined benefit pension funds, as proxied by their investment risk and funding ratio, and political cost implications for Australian defined contribution and UK defined benefit pension funds, as proxied by their size.     

Biological and Psychobehavioral Correlates of Credit Scores and Automobile Insurance Losses: Toward an Explication of Why Credit Scoring Works

The most important new development in the past two decades in the personal lines of insurance may well be the use of an individual's credit history as a classification and rating variable to predict losses. However, in spite of its obvious success as an underwriting tool, and the clear actuarial substantiation of a strong association between credit score and insured losses over multiple methods and multiple studies, the use of credit scoring is under attack because there is not an understanding of why there is an association. Through a detailed literature review concerning the biological, psychological, and behavioral attributes of risky automobile drivers and insured losses, and a similar review of the biological, psychological, and behavioral attributes of financial risk takers, we delineate that basic chemical and psychobehavioral characteristics (e.g., a sensation‐seeking personality type) are common to individuals exhibiting both higher insured automobile loss costs and poorer credit scores, and thus provide a connection which can be used to understand why credit scoring works. Credit scoring can give information distinct from standard actuarial variables concerning an individual's biopsychological makeup, which then yields useful underwriting information about how they will react in creating risk of insured automobile losses.