Dependence between mortality and morbidity: is underwriting scoring really different for Life and Health products?
|
|
- Marlene Wiggins
- 8 years ago
- Views:
Transcription
1 Dependence between mortality and morbidity: is underwriting scoring really different for Life and Health products? Kudryavtsev Andrey St.Petersburg State University, Russia Postal address: Chaykovsky str. 62 St.Petersburg Russia Phone: Fax/phone: Abstract: Underwriting procedure is based on the extensive systems of underwriting scores. The rules of their estimation are included into special Underwriting Manuals. The aim of the paper is to show that underwriting scores are quite close to each other for life and health insurance products. It could be problematic for the portfolio construction and modelling. The paper is based on the special investigation having hold in Russia. The medical records and reviews were used to produce the averaging underwriting scores for life and health risks. The paper shows the high enough dependence between life and health underwriting scores. The dependence could not be explained only with mortality risks in permanent health (income protection) products as it is too high. Keywords: life risks, health risks, underwriting, dependence, copula
2 Dependence between mortality and morbidity: is underwriting scoring really different for Life and Health products? A. Kudryavtsev, St.Petersburg State University, Russia Summary Underwriting is a powerful tool of the rating for Life and Health products. The procedure of rating is based on the extensive systems of underwriting scores which mirror the medical and other risks influenced to mortality and morbidity. The rules how to score are included into special Underwriting Manuals. The aim of the paper is to show that underwriting scores are quite close to each other for different kinds of insurance products, say for life and health insurance. It could be problematic for the portfolio construction and modelling. The paper is based on the special investigation having hold in Russia. The medical records and reviews were used to produce the averaging underwriting scores for life and health risks. The paper shows the high enough dependence between life and health underwriting scores. The dependence could not be explained only with mortality risks in permanent health (income protection) products as it is too high. The fact means that actuaries and underwriters should be careful with portfolio construction and modelling. 1. Introduction Underwriting is a powerful tool of the rating for Life and Health products. The procedure of rating is based on the extensive systems of underwriting scores which mirror the medical and other risks influenced to mortality and morbidity. The rules how to score are included into special Underwriting Manuals mostly prepared by leading reinsurance companies. Every Underwriting Manual is a complex book or file based on deep statistical investigation. The aim of the paper is to show that underwriting scores are quite close to each other for different kinds of insurance products, say for life and health insurance. It could be problematic for the portfolio construction as a result of the sales strategy because risks in the portfolio are more dependent as they are thought by management and the higher degree of risk accumulation may take a place. The paper includes nor any critique of the statistical methods used for the construction of Underwriting Manuals neither any analysis of the methods of data collection. The idea is to compare underwriting scores for life and health risks of a sample population. The population is investigated from medical point of view. It helps to understand as a by-product how accurate is usual medical underwriting procedure in life and health risks estimating. So, the paper tries to answer rather the question how to use and interpret the underwriting scores than how to estimate them. 2. Methodology The investigation underlying the paper is based on the special study with data collection for all people living in one medical district of a small town in Central Russia Lyssye Gory in Saratov Region (downstream river Volga, south-east from Moscow). It presents typical agricultural province in Russia with some industrial development (in the case, small brick factory, small regional department of oil-drilled company etc.). So, it helped to collect data
3 representing an appropriate mix of both agriculture and industrial population. Some people studied in the investigation worked for the local municipal administration, in transportation (incl. railway station), in healthcare, education and in the police. The number of people studied was 769. The study took place in The basic aim of the study was mostly medical. It included two parts: deep medical investigation and survey about people s preferences in healthcare. For the purposes of the paper, only few appropriate data were used. The limitations were bound with the age interval chosen and the information which is useful for underwriting process. The age range has been limited with interval from 20 to 49 (including the latter age). The age definition used was last birthday. A result of choosing the interval was to shorten the number of people taken into account up to 520. The range were chosen for following reasons: Young people (younger than 20 year old) are presumably completely healthy (in the investigation mentioned above about 40 per cent of such people has standard life and health risks; only 10 per cent of the group have serious problems with their health). That age group really demonstrates the dependence between life and health risks as it is quite probable that there are no extra risks of both types. Old people (50+) are probably quite ill (in the investigation, about 50 per cent of them have serious problems with health and only 4,5 per cent have standard life and health risks). The dependence observed between life and health risks is basically explained with poor health (when both scores are growing with age although health score is raising faster). Only chosen age range (20 to 49) demonstrates balanced mixture of three groups (standard life and health risks, people with small problems with health, people with serious problems with health). So, the study of dependence is more interesting for them. Moreover, that age interval is more important for insurance practice. The results of medical investigations were used for the estimation of life and health risks under the usual underwriting procedure. Five basic risk factors were chosen for the procedure: 1) job/profession (including additional information about contacts with dust, chemical materials, ruining the usual sleeping time etc.); 2) height/weight index, 3) acute disease for the last 12 months before investigation and chronic disease (existing conditions); 4) addictions (tobacco smoking and alcohol drinking, there was nobody among investigated people who was addictive to narcotics); 5) heredity factors (indirectly estimated on the base of the information about the longevity and health status of close relatives). The factors were quantified with underwriting scores differently for life and health risks under usual underwriting procedures. From some different approach of the estimation of health risks, only one was chosen. The underwriting scoring was based on the Underwriting Manuals of three different companies: Skandia International Insurance Corporation, Munich Re and Cologne Re [1 4]. Those manuals have some differences in scoring procedures which could be explained with different reinsurance and underwriting experience and with the different statistical procedures used. Life and health risks were differently estimated the life risk as an extra mortality score (index) under whole life insurance contract, health risks as an extra claim score (index) for permanent health (income protection) insurance with 4 weeks of waiting periods. The latter was chosen as a middle term index of health which shows quite serious problem with health
4 (the term of illness more than a month), but not very rare cases like for periods of disability to work longer than 3 or 6 months. Every person investigated was estimated by the experienced underwriter with the rules taken from each manual. The estimation was quite conservative. In order to eliminate the differences in manual rules which are not explained by differences in health itself, individual score was equal to arithmetic average between company-specific scores (all three manuals for life score and Skandia and Cologne Re manuals for health score). Then, in order to eliminate the rest errors and subjectivism of estimation, the scores were classified into special boxes which represent typical standard and substandard classes (see table 1). Table 1. Rounding the individual scores Score interval Final score up to from 101 to from 136 to from 176 to from 226 to from 276 to more then 326 >300 Then two types of individual scores (life and health ones) were analysed and compared. Results and discussions The distribution of people investigated into life and health score boxes is shown in table 2. Although it is far from comonotonic (one-to-one functional) dependence, a kind of dependence is obvious. The coefficient of correlation is 0,6312 which is quite large (the actual t-test value is 24,6 that is much higher than the critical value that is quite close to 0). The dependence could not be explained only with mortality risks in permanent health (income protection) products as it is too high. Table 2. Frequency distribution of the rounded score for life and health risks Life Health score score >300 Total > Total Special interest in the context of practical applications may be paid to standard/substandard proportions. For this purpose, table 2 should be shortened to table 3.
5 Table 3. Standard/sub-standard proportions for life and health risks Life risks Health risks standard sub-standard Total standard sub-standard Total The actual value of χ 2 -test is 225,56 (that is much higher than the critical value that is equal to 3,84 with 1 d.f. and 5 per cent of probability). The data certainly show that there is large enough dependence between life and health scores even for age intervals where it is not highly expected from the point of view of health dynamics with age. This means that actuaries and underwriters should be more careful with assumptions about the existence of independence between different Life and Health products in context of ALM and similar concepts. The important result is that the proportion of standard risks is 27,5 per cent for life score and 22,69 per cent for health score. The odd of standard and sub-standard risks (1:3) is quite different from usual odd for life insurance portfolios (9:1). It could be explained with a) more conservative estimation under the investigation than one in insurance practice as a result of taking into account the sales strategy and underwriting strength avoiding underwriting for insurance policies with small sum assured etc., b) self-selection of potential clients with poor health, c) full informational support in the investigation vs. informational deficit in practice of insurance. Explanations (a) and (b) are not problematic as they show only the differences between insurance practice and the artificial investigation. But explanation (c), if it is correct, may be a sign of an underestimation of life and health risks by underwriters under the data shortage and long-term forecasting uncertainty. In the case, there is a huge amount of latent crosssubsidiary in life and health insurance portfolios. The next step is to study life and health dependence among sub-standard risks. Correlation coefficient is 0,84 which is even more than for all risks. The idea is to develop more formal model than simple statistical coefficient, say, copulas [5 7]. First of all, one needs to find marginal distributions (although conditional ones given risk is sub-standard). It is possible to use the last column of table 2 (without the above value of 143) for life scores frequencies and the last row of the table (without the left-hand value of 118) for health scores. The last two boxes (300 and >300 ) for health risk scores should be combined. Both distributions were fitted using Maximum Likelihood method. The best goodness-of-fit (measured with χ 2 -test) was achieved on Log-Normal distribution in both cases. The results are shown in table 4. Table 4. Frequency distribution of the rounded score for life and health risks Values for life risks health risks Distribution parameter μ 3,761 4,545 Distribution parameter σ 1,043 2,088 Degrees of freedom 4 3 χ 2 -test 8,81 1,39 p-value 0,066 0,709
6 1 1 As a first choice, the normal copula could be used: C( u, v) = Φ ( Φ ( u), Φ ( )), 2 v where Φ 2 (, ) is the bivariate Normal distribution function with zero vector of expected values and covariation matrix 1 α, α 1 α is the correlation coefficient (in our case 0,84), Φ 1 ( ) is the inverse function to standard Normal distribution function. As marginal distributions in our case are Log-Normal, the copula simply gives the bivariate Log-Normal distribution. Other copulas tend to bring more complex formulas. Such models may be quite simple tools for portfolio modelling in the context of ALM or similar concepts. Conclusions The example shows the high enough dependence between life and health underwriting scores. The dependence could not be explained only with mortality risks in permanent health (income protection) products as it is too high. The fact means that actuaries and underwriters should be careful with portfolio construction and modelling. Moreover, copula technique may give quite simple tool for modeling with dependence. Another important question which has been brought up with the report is whether a kind of underestimation of life and health risks exists in underwriting process as a result of informational deficit and uncertainty. The further investigation of underwriting procedures should be organized. Bibliographies 1. Life and Disability Underwriting Manual. In 2 Vol. Skandia International Insurance Corporation. Life Reassurance. 2. Life Underwriting Manual. Munich Reinsurance Company. [Münchener Rückversicherungs-Gesellschaft AG]. 3. Medical Underwriting Guidelines. In 2 Vol. [Hong Kong]: The Cologne Re, [Kölnische Rückversicherungs-Gesellschaft AG]. 4. Occupational Rating Guide. Munich Reinsurance Company [Münchener Rückversicherungs-Gesellschaft AG]. 5. Carrière J.F. Copulas. In: Encyclopedia of Actuarial Science. Vol. 1, p Frees G.V., Valdez E.A. Understanding Relationship Using Copulas. North American Actuarial Journal. Vol. 2, No. 1, p Venter G. Tails of Copulas. ASTIN Colloquium. Tokyo, Japan. August 22-25, 1999.
The Chi-Square Test. STAT E-50 Introduction to Statistics
STAT -50 Introduction to Statistics The Chi-Square Test The Chi-square test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed
More informationAssociation Between Variables
Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi
More informationSimple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
More informationStudy Guide for the Final Exam
Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make
More informationAdvanced Statistical Analysis of Mortality. Rhodes, Thomas E. and Freitas, Stephen A. MIB, Inc. 160 University Avenue. Westwood, MA 02090
Advanced Statistical Analysis of Mortality Rhodes, Thomas E. and Freitas, Stephen A. MIB, Inc 160 University Avenue Westwood, MA 02090 001-(781)-751-6356 fax 001-(781)-329-3379 trhodes@mib.com Abstract
More informationCalculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation
Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.
More informationFinancial Simulation Models in General Insurance
Financial Simulation Models in General Insurance By - Peter D. England Abstract Increases in computer power and advances in statistical modelling have conspired to change the way financial modelling is
More informationThe Study of Chinese P&C Insurance Risk for the Purpose of. Solvency Capital Requirement
The Study of Chinese P&C Insurance Risk for the Purpose of Solvency Capital Requirement Xie Zhigang, Wang Shangwen, Zhou Jinhan School of Finance, Shanghai University of Finance & Economics 777 Guoding
More information" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
More informationINTERNATIONAL MEDICAL UNDERWRITING APPROACHES AND THE IMPACT ON PROFITABILITY. Aree K. Bly, F.S.A., M.A.A.A. Milliman, Inc.
INTERNATIONAL MEDICAL UNDERWRITING APPROACHES AND THE IMPACT ON PROFITABILITY Aree K. Bly, F.S.A., M.A.A.A. Milliman, Inc. 1099 18 th St., Suite 3100, Denver, CO, 80202-1931 Tel.: (1) 303 299-9400 Fax:
More informationActuarial Risk Management
ARA syllabus Actuarial Risk Management Aim: To provide the technical skills to apply the principles and methodologies studied under actuarial technical subjects for the identification, quantification and
More informationTwo Related Samples t Test
Two Related Samples t Test In this example 1 students saw five pictures of attractive people and five pictures of unattractive people. For each picture, the students rated the friendliness of the person
More informationOdds ratio, Odds ratio test for independence, chi-squared statistic.
Odds ratio, Odds ratio test for independence, chi-squared statistic. Announcements: Assignment 5 is live on webpage. Due Wed Aug 1 at 4:30pm. (9 days, 1 hour, 58.5 minutes ) Final exam is Aug 9. Review
More informationChapter 3 RANDOM VARIATE GENERATION
Chapter 3 RANDOM VARIATE GENERATION In order to do a Monte Carlo simulation either by hand or by computer, techniques must be developed for generating values of random variables having known distributions.
More informationFinal. Actuarial Standards Board. July 2011. Document 211070. Ce document est disponible en français 2011 Canadian Institute of Actuaries
Final Final Standards Standards of Practice for the Valuation of Insurance Contract Liabilities: Life and Health (Accident and Sickness) Insurance (Subsection 2350) Relating to Mortality Improvement (clean
More informationPricing variable annuity product in Hong Kong -- a starting point for practitioners
Pricing variable annuity product in Hong Kong -- a starting point for practitioners Abstract With regard to its rapid emergence in Hong Kong, this paper aims to perform a pricing exercise for a sample
More informationt Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon
t-tests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com
More informationSTATISTICA Formula Guide: Logistic Regression. Table of Contents
: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary
More informationModelling the Scores of Premier League Football Matches
Modelling the Scores of Premier League Football Matches by: Daan van Gemert The aim of this thesis is to develop a model for estimating the probabilities of premier league football outcomes, with the potential
More informationSUMAN DUVVURU STAT 567 PROJECT REPORT
SUMAN DUVVURU STAT 567 PROJECT REPORT SURVIVAL ANALYSIS OF HEROIN ADDICTS Background and introduction: Current illicit drug use among teens is continuing to increase in many countries around the world.
More informationPricing Alternative forms of Commercial insurance cover. Andrew Harford
Pricing Alternative forms of Commercial insurance cover Andrew Harford Pricing alternative covers Types of policies Overview of Pricing Approaches Total claim cost distribution Discounting Cash flows Adjusting
More informationAdditional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
More informationNormality Testing in Excel
Normality Testing in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com
More informationBivariate Statistics Session 2: Measuring Associations Chi-Square Test
Bivariate Statistics Session 2: Measuring Associations Chi-Square Test Features Of The Chi-Square Statistic The chi-square test is non-parametric. That is, it makes no assumptions about the distribution
More informationHierarchical Insurance Claims Modeling
Hierarchical Insurance Claims Modeling Edward W. (Jed) Frees, University of Wisconsin - Madison Emiliano A. Valdez, University of Connecticut 2009 Joint Statistical Meetings Session 587 - Thu 8/6/09-10:30
More informationCopula Simulation in Portfolio Allocation Decisions
Copula Simulation in Portfolio Allocation Decisions Gyöngyi Bugár Gyöngyi Bugár and Máté Uzsoki University of Pécs Faculty of Business and Economics This presentation has been prepared for the Actuaries
More informationCapital requirements for health insurance under Solvency II
Capital requirements for health insurance under Solvency II Medical Expense Insurance: Actuarial Aspects and Solvency Afternoon Seminar at the AG Insurance Chair in Health Insurance, KU Leuven 25 April
More information1. How different is the t distribution from the normal?
Statistics 101 106 Lecture 7 (20 October 98) c David Pollard Page 1 Read M&M 7.1 and 7.2, ignoring starred parts. Reread M&M 3.2. The effects of estimated variances on normal approximations. t-distributions.
More informationLAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.
More informationStats Review Chapters 9-10
Stats Review Chapters 9-10 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More informationTwo Correlated Proportions (McNemar Test)
Chapter 50 Two Correlated Proportions (Mcemar Test) Introduction This procedure computes confidence intervals and hypothesis tests for the comparison of the marginal frequencies of two factors (each with
More informationPricing Alternative forms of Commercial Insurance cover
Pricing Alternative forms of Commercial Insurance cover Prepared by Andrew Harford Presented to the Institute of Actuaries of Australia Biennial Convention 23-26 September 2007 Christchurch, New Zealand
More informationStatistical Analysis of Life Insurance Policy Termination and Survivorship
Statistical Analysis of Life Insurance Policy Termination and Survivorship Emiliano A. Valdez, PhD, FSA Michigan State University joint work with J. Vadiveloo and U. Dias Session ES82 (Statistics in Actuarial
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationSection 13, Part 1 ANOVA. Analysis Of Variance
Section 13, Part 1 ANOVA Analysis Of Variance Course Overview So far in this course we ve covered: Descriptive statistics Summary statistics Tables and Graphs Probability Probability Rules Probability
More informationPEER REVIEW HISTORY ARTICLE DETAILS VERSION 1 - REVIEW. Elizabeth Comino Centre fo Primary Health Care and Equity 12-Aug-2015
PEER REVIEW HISTORY BMJ Open publishes all reviews undertaken for accepted manuscripts. Reviewers are asked to complete a checklist review form (http://bmjopen.bmj.com/site/about/resources/checklist.pdf)
More informationPreliminary Report on. Hong Kong Assured Lives Mortality and Critical Illness. Experience Study 2000-2003
Preliminary Report on Hong Kong Assured Lives Mortality and Critical Illness Experience Study 2000-2003 Actuarial Society of Hong Kong Experience Committee ASHK - Hong Kong Assured Lives Mortality and
More informationREINSURANCE PROFIT SHARE
REINSURANCE PROFIT SHARE Prepared by Damian Thornley Presented to the Institute of Actuaries of Australia Biennial Convention 23-26 September 2007 Christchurch, New Zealand This paper has been prepared
More informationMortality Assessment Technology: A New Tool for Life Insurance Underwriting
Mortality Assessment Technology: A New Tool for Life Insurance Underwriting Guizhou Hu, MD, PhD BioSignia, Inc, Durham, North Carolina Abstract The ability to more accurately predict chronic disease morbidity
More informationApplication of Credibility Theory to Group Life Pricing
Prepared by: Manuel Tschupp, MSc ETH Application of Credibility Theory to Group Life Pricing Extended Techniques TABLE OF CONTENTS 1. Introduction 3 1.1 Motivation 3 1.2 Fundamentals 1.3 Structure 3 4
More informationIs it statistically significant? The chi-square test
UAS Conference Series 2013/14 Is it statistically significant? The chi-square test Dr Gosia Turner Student Data Management and Analysis 14 September 2010 Page 1 Why chi-square? Tests whether two categorical
More informationChapter 9 Experience rating
0 INTRODUCTION 1 Chapter 9 Experience rating 0 Introduction The rating process is the process of deciding on an appropriate level of premium for a particular class of insurance business. The contents of
More informationLeast Squares Estimation
Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN-13: 978-0-470-86080-9 ISBN-10: 0-470-86080-4 Editors Brian S Everitt & David
More informationStochastic Analysis of Long-Term Multiple-Decrement Contracts
Stochastic Analysis of Long-Term Multiple-Decrement Contracts Matthew Clark, FSA, MAAA, and Chad Runchey, FSA, MAAA Ernst & Young LLP Published in the July 2008 issue of the Actuarial Practice Forum Copyright
More informationGRF_115_0A_G: Outstanding Claims Liabilities - Insurance Risk Charge - Australia by Class of Business (G)
GRF_115_0A_G: Outstanding Claims Liabilities - Insurance Risk Charge - Australia by Class of Business (G) These instructions must be read in conjunction with the general instruction guide. Explanatory
More informationChi Square Tests. Chapter 10. 10.1 Introduction
Contents 10 Chi Square Tests 703 10.1 Introduction............................ 703 10.2 The Chi Square Distribution.................. 704 10.3 Goodness of Fit Test....................... 709 10.4 Chi Square
More informationSOA Annual Symposium Shanghai. November 5-6, 2012. Shanghai, China
SOA Annual Symposium Shanghai November 5-6, 2012 Shanghai, China Session 5a: Some Research Results on Insurance Risk Models with Dependent Classes of Business Kam C. Yuen Professor Kam C. Yuen The University
More informationPeople have thought about, and defined, probability in different ways. important to note the consequences of the definition:
PROBABILITY AND LIKELIHOOD, A BRIEF INTRODUCTION IN SUPPORT OF A COURSE ON MOLECULAR EVOLUTION (BIOL 3046) Probability The subject of PROBABILITY is a branch of mathematics dedicated to building models
More informationBowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition
Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology Step-by-Step - Excel Microsoft Excel is a spreadsheet software application
More informationOrdinal Regression. Chapter
Ordinal Regression Chapter 4 Many variables of interest are ordinal. That is, you can rank the values, but the real distance between categories is unknown. Diseases are graded on scales from least severe
More informationING Insurance Economic Capital Framework
ING Insurance Economic Capital Framework Thomas C. Wilson Chief Insurance Risk Officer Kent University, September 5, 2007 www.ing.com Objectives of this session ING has been using economic capital internally
More informationTRINITY COLLEGE. Faculty of Engineering, Mathematics and Science. School of Computer Science & Statistics
UNIVERSITY OF DUBLIN TRINITY COLLEGE Faculty of Engineering, Mathematics and Science School of Computer Science & Statistics BA (Mod) Enter Course Title Trinity Term 2013 Junior/Senior Sophister ST7002
More informationVariables Control Charts
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. Variables
More informationPREMIUM AND BONUS. MODULE - 3 Practice of Life Insurance. Notes
4 PREMIUM AND BONUS 4.0 INTRODUCTION A insurance policy needs to be bought. This comes at a price which is known as premium. Premium is the consideration for covering of the risk of the insured. The insured
More information1 July 2008-30 June 2009
NAVY AND MARINE CORPS PUBLIC HEALTH CENTER Fleet and Marine Corps Health Risk Assessment 1 July 8-3 June 9 Navy Population Health Report Annual Report The Fleet and Marine Corps Health Risk Appraisal is
More informationData Analysis Tools. Tools for Summarizing Data
Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool
More informationFleet and Marine Corps Health Risk Assessment, 1 January 31 December, 2014
Fleet and Marine Corps Health Risk Assessment, 1 January 31 December, 2014 Executive Summary The Fleet and Marine Corps Health Risk Appraisal is a 22-question anonymous self-assessment of many of the most
More informationFactors Affecting Demand Management in the Supply Chain (Case Study: Kermanshah Province's manufacturing and distributing companies)
International Journal of Agriculture and Crop Sciences. Available online at www.ijagcs.com IJACS/2013/6-14/994-999 ISSN 2227-670X 2013 IJACS Journal Factors Affecting Demand Management in the Supply Chain
More informationAspects in Development of Statistic Data Analysis in Romanian Sanitary System
Aspects in Development of Statistic Data Analysis in Romanian Sanitary System DANA SIMIAN 1, CORINA SIMIAN 1, OANA DANCIU 2, LAVINIA DANCIU 3 1 Faculty of Sciences University Lucian Blaga Sibiu Str. Ion
More informationHow To Buy Health Insurance
Post Retirement Health Insurance KC Cheung, FSA Regional Product Actuary Swiss Re, Life & Health Session Number: MBR10 Post-Retirement Health My Challenges What is post retirement healthcare? Post retirement
More informationMultiple logistic regression analysis of cigarette use among high school students
Multiple logistic regression analysis of cigarette use among high school students ABSTRACT Joseph Adwere-Boamah Alliant International University A binary logistic regression analysis was performed to predict
More informationUNDERSTANDING THE TWO-WAY ANOVA
UNDERSTANDING THE e have seen how the one-way ANOVA can be used to compare two or more sample means in studies involving a single independent variable. This can be extended to two independent variables
More informationCALCULATIONS & STATISTICS
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents
More informationChi-square test Fisher s Exact test
Lesson 1 Chi-square test Fisher s Exact test McNemar s Test Lesson 1 Overview Lesson 11 covered two inference methods for categorical data from groups Confidence Intervals for the difference of two proportions
More informationPricing the Critical Illness Risk: The Continuous Challenge.
Pricing the Critical Illness Risk: The Continuous Challenge. To be presented at the 6 th Global Conference of Actuaries, New Delhi 18 19 February 2004 Andres Webersinke, ACTUARY (DAV), FASSA, FASI 9 RAFFLES
More informationMaking insurance less sexy
Life Conference 2011: Workshop B6 Jim Murphy, Milliman Making insurance less sexy 21 November 2011 2010 The Actuarial Profession www.actuaries.org.uk Agenda Background to ECJ gender ruling Use of gender
More informationWeb-based Supplementary Materials for Bayesian Effect Estimation. Accounting for Adjustment Uncertainty by Chi Wang, Giovanni
1 Web-based Supplementary Materials for Bayesian Effect Estimation Accounting for Adjustment Uncertainty by Chi Wang, Giovanni Parmigiani, and Francesca Dominici In Web Appendix A, we provide detailed
More informationMULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS
MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MSR = Mean Regression Sum of Squares MSE = Mean Squared Error RSS = Regression Sum of Squares SSE = Sum of Squared Errors/Residuals α = Level of Significance
More informationChapter 23. Inferences for Regression
Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily
More informationSystematic risk modelisation in credit risk insurance
Systematic risk modelisation in credit risk insurance Frédéric Planchet Jean-François Decroocq Ψ Fabrice Magnin α ISFA - Laboratoire SAF β Université de Lyon - Université Claude Bernard Lyon 1 Groupe EULER
More informationBenchmark Rates for XL Reinsurance Revisited: Model Comparison for the Swiss MTPL Market
Benchmark Rates for XL Reinsurance Revisited: Model Comparison for the Swiss MTPL Market W. Hürlimann 1 Abstract. We consider the dynamic stable benchmark rate model introduced in Verlaak et al. (005),
More informationOutline. Topic 4 - Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares
Topic 4 - Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test - Fall 2013 R 2 and the coefficient of correlation
More informationActuary s Guide to Reporting on Insurers of Persons Policy Liabilities. Senior Direction, Supervision of Insurers and Control of Right to Practice
Actuary s Guide to Reporting on Insurers of Persons Policy Liabilities Senior Direction, Supervision of Insurers and Control of Right to Practice September 2015 Legal deposit - Bibliothèque et Archives
More informationStatistical Functions in Excel
Statistical Functions in Excel There are many statistical functions in Excel. Moreover, there are other functions that are not specified as statistical functions that are helpful in some statistical analyses.
More informationSolvency Assessment and Management Third South African Quantitative Impact Study (SA QIS3)
CONTACT DETAILS Physical Address: Riverwalk Solvency Assessment and Management Third South African Quantitative Impact Study (SA QIS3) Draft Technical Specifications Part 4 of 6: SCR Life Underwriting
More informationVALUATION OF LIFE INSURANCE POLICIES MODEL REGULATION (Including the Introduction and Use of New Select Mortality Factors)
Table of Contents Model Regulation Service October 2009 VALUATION OF LIFE INSURANCE POLICIES MODEL REGULATION (Including the Introduction and Use of New Select Mortality Factors) Section 1. Section 2.
More informationBecause. life. happens
Because life happens You can t predict the future but you can protect it John and Christa, both 34 years old and parents of five-year-old Jack, live a life typical of many middle-income Canadian families.
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationA Log-Robust Optimization Approach to Portfolio Management
A Log-Robust Optimization Approach to Portfolio Management Dr. Aurélie Thiele Lehigh University Joint work with Ban Kawas Research partially supported by the National Science Foundation Grant CMMI-0757983
More informationSession 54 PD, Credibility and Pooling for Group Life and Disability Insurance Moderator: Paul Luis Correia, FSA, CERA, MAAA
Session 54 PD, Credibility and Pooling for Group Life and Disability Insurance Moderator: Paul Luis Correia, FSA, CERA, MAAA Presenters: Paul Luis Correia, FSA, CERA, MAAA Brian N. Dunham, FSA, MAAA Credibility
More informationActuarial Society of India
Actuarial Society of India EXAMINATION 30 th October 2006 Subject ST1 Health and Care Insurance Specialist Technical Time allowed: Three hours (14.15* pm 17.30 pm) INSTRUCTIONS TO THE CANDIDATE 1. Enter
More informationA LOGNORMAL MODEL FOR INSURANCE CLAIMS DATA
REVSTAT Statistical Journal Volume 4, Number 2, June 2006, 131 142 A LOGNORMAL MODEL FOR INSURANCE CLAIMS DATA Authors: Daiane Aparecida Zuanetti Departamento de Estatística, Universidade Federal de São
More informationCOMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.
277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies
More informationRISK MANAGEMENT IN LIFE INSURANCE
RISK MANAGEMENT IN LIFE INSURANCE ASSAL 2015 Regional Training Seminar for Insurance Supervisors of Latin America Augusto Diaz-Leante / SVP Iberia & Latin America Agenda Risk Management in Life Insurance
More informationThe different types of cost of alcohol
A number of studies have attempted to calculate the cost of alcohol to society. This is tricky for two reasons. First, because many of the costs are difficult to estimate accurately. Second, because there
More informationHealth & Care INCOME PROTECTION AND CRITICAL ILLNESS RESERVING SURVEY RESULTS AND DISCUSSION OF ISSUES ARISING. Prepared by:
INCOME PROTECTION AND CRITICAL ILLNESS RESERVING SURVEY RESULTS AND DISCUSSION OF ISSUES ARISING Prepared by: H&C Reserving Working Party May 2008 Contents PAGE 1. Introduction 1 2. Summary Results and
More informationMBA 611 STATISTICS AND QUANTITATIVE METHODS
MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain
More informationConfidence intervals
Confidence intervals Today, we re going to start talking about confidence intervals. We use confidence intervals as a tool in inferential statistics. What this means is that given some sample statistics,
More informationConcepts in Investments Risks and Returns (Relevant to PBE Paper II Management Accounting and Finance)
Concepts in Investments Risks and Returns (Relevant to PBE Paper II Management Accounting and Finance) Mr. Eric Y.W. Leung, CUHK Business School, The Chinese University of Hong Kong In PBE Paper II, students
More informationChapter 23. Two Categorical Variables: The Chi-Square Test
Chapter 23. Two Categorical Variables: The Chi-Square Test 1 Chapter 23. Two Categorical Variables: The Chi-Square Test Two-Way Tables Note. We quickly review two-way tables with an example. Example. Exercise
More informationOverview Classes. 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7)
Overview Classes 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7) 2-4 Loglinear models (8) 5-4 15-17 hrs; 5B02 Building and
More informationModule 2 Probability and Statistics
Module 2 Probability and Statistics BASIC CONCEPTS Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The standard deviation of a standard normal distribution
More informationCaregiving Impact on Depressive Symptoms for Family Caregivers of Terminally Ill Cancer Patients in Taiwan
Caregiving Impact on Depressive Symptoms for Family Caregivers of Terminally Ill Cancer Patients in Taiwan Siew Tzuh Tang, RN, DNSc Associate Professor, School of Nursing Chang Gung University, Taiwan
More informationBridging the Gap LTC Combination Products
Bridging the Gap LTC Combination Products Session 28 : Current Topics in Mortality Tony Laudato, Vice President and Actuary Hannover Life Reassurance Company of America Valuation Actuary Symposium Indianapolis,
More informationNon Linear Dependence Structures: a Copula Opinion Approach in Portfolio Optimization
Non Linear Dependence Structures: a Copula Opinion Approach in Portfolio Optimization Jean- Damien Villiers ESSEC Business School Master of Sciences in Management Grande Ecole September 2013 1 Non Linear
More informationThe Distribution of Aggregate Life Insurance Claims
The Distribution of ggregate Life Insurance laims Tom Edwalds, FS Munich merican Reassurance o. BSTRT This paper demonstrates the calculation of the moments of the distribution of aggregate life insurance
More informationJava Modules for Time Series Analysis
Java Modules for Time Series Analysis Agenda Clustering Non-normal distributions Multifactor modeling Implied ratings Time series prediction 1. Clustering + Cluster 1 Synthetic Clustering + Time series
More informationPNB Life Insurance Inc. Risk Management Framework
1. Capital Management and Management of Insurance and Financial Risks Although life insurance companies are in the business of taking risks, the Company limits its risk exposure only to measurable and
More information