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CAS Exam 7 Study Notes: Risk Margins, Stochastic Reserve Models, and Enterprise Risk Management
2018-05-13
I've uploaded the last three of my Exam 7 Study Note files, covering the following topics:
- Assessment of Risk Margins, based on a paper by Karl Marshall, Scott Collings, Matt Hodson, and Conor O'Dowd.
- Stochastic Loss Reserving, based on three readings: Obtaining Predictive Distributions for Reserves Which Incorporate Expert Opinion by R.J. Verrall, Using the ODP Bootstrap Model: A Practitioner's Guide by M. Shapland, and Stochastic Loss Reserving Using Bayesian MCMC Models by G. Meyers.
- Enterprise Risk Management, based on a reading by Brehm, Gluck, Kreps, Major, Mango, Shaw, Venter, White, and Witcraft.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Unpaid Claims by Layer
2018-04-17
My notes on unpaid claims by layer of loss are now available. These notes synthesize the ideas in two syllabus readings. The first, A Model for Reserving Workers Compensation High Deductibles by Jerome Siewert, describes how to relate unlimited development loss development factors to limited and excess development factors. The second, Claims Development by Layer: The Relationship Between Claims Development Patterns, Trend, and Claim Size Models by Rajesh Sahasrabuddhe, generalizes these ideas to include adjustments for accident year and calendar year trends.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Premium Asset for Retro Policies
2018-04-12
I've uploaded my notes on premium estimation for retrospectively rated policies, which are based on a paper by Michael Teng and Miriam Perkins, and includes a discussion by Sholom Feldblum. The notes demonstrate how to estimate future premium on retrospectively-rated policies through the calculation of premium development to loss development (PDLD) ratios.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Loss Reserving for Reinsurance
2018-04-10
I've uploaded my notes on loss reserving for reinsurance, which are based on a section on reinsurance loss reserving that appears in Foundations of Casualty Actuarial Science by G. S. Patrik. The notes describe some concerns that are specific to reinsurance reserving, and provide details on the Stanard-Buhlmann method, which is often used for long-tailed lines of reinsurance.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Benktander Method and Optimal Credibility
2018-04-09
I've uploaded my notes on the Benktander method and optimal credibility. These notes are based on two papers from the syllabus. The first, Credible Claims Reserves: The Benktander Method by Thomas Mack illustrates how to apply the methods to a single accident year. The second, Credible Loss Ratio Claims Reserves: The Benktander, Neuhaus, and Mack Methods Revisited, addresses the question of how to apply the methods to an entire development triangle, by taking credibility-weighted averages of the individual loss ratio claims reserve and the collective loss ratio claims reserve.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Testing Assumption of the Chain Ladder Method
2018-04-08
I've uploaded my study notes on the topic of testing assumption underlying the chain ladder method. These notes are based on a combination of two closely-related papers, Measuring the Variability of Chain Ladder Reserve Estimates by Thomas Mack, and Testing the Assumptions of Age-to-Age Factors by Gary Venter. The topics addressed include testing the variance assumption underlying the method, testing for calendar year or accident year correlations, and comparing the "direct linear relationship" assumption of the chain ladder method against alternative emergence patterns, such as a linear-plus-constant pattern or a Bornhuetter-Ferguson or Cape Cod emergence pattern.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Maximum Likelihood Approaches in Reserving
2018-03-28
I've uploaded my study notes based on LDF Curve-fitting and Stochastic Reserving: A Maximum Likelihood Approach by David Clark. This paper describes how to fit a smooth curve to the historical loss emergence pattern, under both the Loss Development Factor and Cape Cod reserving methods, and how to obtain estimates for the variance of the reserves resulting from use of this method. In the notes, I demonstrate how to use R to maximize the likelihood functions corresponding to Clark's models and replicate the examples from his paper.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: Loss Development Using Credibility
2018-02-28
I've uploaded my notes on Loss Development Using Credibility, a paper by Eric Brosius. The paper explains how to use linear regression to predict ultimate claim values based on the amount reported as of a given date, and demonstrates that the result has an equivalent interpretation as a credibility-weighted average of the ultimate loss estimates from the link ratio and budgeted loss methods. The notebook illustrates how to replicate the examples from the paper using R. Of particular interest, it shows how to use R to simulate the results of a Poisson process as a means to generate data to illustrate the methodology.
Keywords: Actuarial Science, Exam 7, Study Note
CAS Exam 7 Study Notes: P&C Insurance Company Valuation
2018-02-21
As part of my preparation for Exam 7 of the Casualty Actuarial Society, I'm writing my study notes in R notebooks, using R code to illustrate the concepts in the readings. As a result, the notes will sometimes address more than the bare minimum that is needed to pass an exam, but will contain additional information that can be used to put the ideas into practice using contemporary statistical software. Some of the notebooks may be of interest, independent of the subject matter, of illustrations of R techniques.
The first instalment is P&C Company Valuation, based on a reading by Richard Goldfarb. It addresses learning objectives B1-B3 on the exam, explaining several methods for determining the value of an insurance company. Of particular interest is that it shows how R can be used to quickly perform sensitivity testing over a range of assumptions, and visualize the results.
Keywords: Actuarial Science, Exam 7, Study Note