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The manual organizes exam preparation through structured coverage of insurance and reinsurance coverages, including policy limit modifications, deductibles, coinsurance, and combinations. It then develops severity, frequency, and aggregate loss models with key distributions and risk measure concepts such as Value at Risk and Tail Value at Risk. It concludes with maximum likelihood estimation, covering complete and incomplete data cases and computational shortcuts.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/ambrose-los-study-manual-for-soa-exam-fam-3rd-edition-actuarial-mathematics/399168/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/ambrose-los-study-manual-for-soa-exam-fam-3rd-edition-actuarial-mathematics/399168.png","ImageObject",300,407,{"name":92,"@type":93},"Noah","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-09-27",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What topics are covered under coverage modifications in Exam FAM?","Question",{"text":113,"@type":114},"The manual covers policy limits, ordinary deductibles (including cost per loss, loss elimination ratios, and mean excess loss), franchise deductibles, coinsurance, and combinations of several coverage modifications.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which loss modeling frameworks are included in the severity, frequency, and aggregate models section?",{"text":118,"@type":114},"It includes severity models (moments, distribution tails, classes, and mixture distributions), frequency models (Poisson, Negative Binomial, Binomial, and related classes), and aggregate loss models such as the collective and individual risk models with key calculations and approximations.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the manual approach maximum likelihood estimation for the exam?",{"text":122,"@type":114},"It presents basics of MLE with complete individual data, complete grouped data, and incomplete data, followed by computational shortcuts and distribution-specific cases for different data completeness scenarios.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},399168,1790533416,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},8796095462418,"https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780","Ambrose Lo’s  \nStudy Manual for SOA Exam FAM (Fundamentals of Actuarial Mathematics)  \nAmbrose Lo, PhD, FSA, CERA  \n3rd Edition  \nCopyright © 2025 by Ambrose Lo  \nAll rights reserved. No part of this publication may be reproduced in any form or by any means without express permission of the copyright owner.  \nContents  \nPreface xiii  \nP.1 About Exam FAM .................................... xiii  \nP.2 About this Study Manual ................................ xix  \nI FAM-S 1  \n1 Insurance and Reinsurance Coverages 3  \n1.1 Coverage Modifications .................................. 4  \nModification 1: Policy Limits .............................. 5  \nModification 2 (a): Ordinary Deductibles ........................ 13  \nModification 2 (b): Franchise Deductibles ........................ 27  \nModification 3: Coinsurance ............................... 29  \nCombinations of Several Coverage Modifications .................... 31  \nPractice Problems for Section 1.1 ............................ 39  \nPolicy Limits ................................... 39  \nOrdinary Deductibles: Cost per Loss ...................... 46  \nOrdinary Deductibles: Loss Elimination Ratios ................ 59  \nOrdinary Deductibles: Mean Excess Loss .................... 68  \nFranchise Deductibles ............................... 79  \nMultiple Coverage Modifications ......................... 84  \nVariance of Cost per Loss ............................ 95  \n1.2 Reinsurance Coverages .................................. 100  \n1.2.1 Basics of Reinsurance ............................... 100  \n1.2.2 Reinsurance Pricing and Reserving ....................... 103  \nPractice Problems for Section 1.2 ............................ 109  \nBasics ....................................... 109  \nPricing and Reserving .............................. 112  \n2 Severity, Frequency, and Aggregate Models 119  \n2.1 Severity Models ...................................... 120  \n2.1.1 Moments ...................................... 120  \n2.1.2 Tails of Distributions ............................... 126  \n2.1.3 Classes of Distributions .............................. 128  \n2.1.4 Mixture Distributions .............................. 135  \nPractice Problems for Section 2.1 ............................ 146  \nMoments ...................................... 146  \nTails of Distributions ............................... 154  \nClasses of Distributions .............................. 156  \nMixture Distributions: General Cases ...................... 163  \nMixture Distributions: Case Studies ....................... 178  \n2.2 Frequency Models ..................................... 188  \n2.2.1 Poisson, Negative Binomial, and Binomial Distributions ............ 188  \n2.2.2 The (a, b, 0) Class of Distributions ........................ 198  \n2.2.3 The (a, b, 1) Class of Distributions ........................ 205  \nPractice Problems for Section 2.2 ............................ 219  \nPoisson ...................................... 219  \nNegative Binomial ................................ 228  \nBinomial ...................................... 234  \nThe (a, b, 0) Class of Distributions ........................ 238  \nThe (a, b, 1) Class of Distributions ........................ 245  \n2.3 Aggregate Loss Models .................................. 256  \n2.3.1 The Collective Risk Model ............................ 256  \n2.3.2 The Individual Risk Model ............................ 278  \nPractice Problems for Section 2.3 ............................ 281  \nConvolutions ................................... 281  \nCollective Risk Model: Exact Calculations ................... 284  \nCollective Risk Model: Moments of S ...................... 293  \nCollective Risk Model: Moments of S with Per-loss Coverage Modifications . 305  \nCollective Risk Model: Approximations ..................... 309  \nNet Stop-loss Premiums: Direct Calculations .................. 324  \nNet Stop-loss Premiums: Recursive Calculations ................ 334  \nIndividual Risk Model ..","cbCaipB0pBBoW4Tf","https://ap.wps.com/l/cbCaipB0pBBoW4Tf","pdf",1401628,69,"English","# Preface\n## About Exam FAM\n## About this Study Manual\n# Insurance and Reinsurance Coverages\n## Coverage Modifications\n## Reinsurance Coverages\n# Severity, Frequency, and Aggregate Models\n## Severity Models\n## Frequency Models\n## Aggregate Loss Models\n## Risk Measures\n# Maximum Likelihood Estimation","[{\"question\":\"What topics are covered under coverage modifications in Exam FAM?\",\"answer\":\"The manual covers policy limits, ordinary deductibles (including cost per loss, loss elimination ratios, and mean excess loss), franchise deductibles, coinsurance, and combinations of several coverage modifications.\"},{\"question\":\"Which loss modeling frameworks are included in the severity, frequency, and aggregate models section?\",\"answer\":\"It includes severity models (moments, distribution tails, classes, and mixture distributions), frequency models (Poisson, Negative Binomial, Binomial, and related classes), and aggregate loss models such as the collective and individual risk models with key calculations and approximations.\"},{\"question\":\"How does the manual approach maximum likelihood estimation for the exam?\",\"answer\":\"It presents basics of MLE with complete individual data, complete grouped data, and incomplete data, followed by computational shortcuts and distribution-specific cases for different data completeness scenarios.\"}]","Ambrose Lo’s Study Manual for SOA Exam FAM - 3rd Edition - Actuarial Mathematics | PDF",1790494110,174]