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1 EDUCATION AND EXAMINATION COMMITTEE OF THE SOCIETY OF ACTUARIES RISK AND INSURANCE by Judy Feldman Anderson, FSA and Robert L. Brown, FSA Copyright 2005 by the Society of Actuaries The Education and Examination Committee provides study notes to persons preparing for the examinations of the Society of Actuaries. They are intended to acquaint candidates with some of the theoretical and practical considerations involved in the various subjects. While varying opinions are presented where appropriate, limits on the length of the material and other considerations sometimes prevent the inclusion of all possible opinions. These study notes do not, however, represent any official opinion, interpretations or endorsement of the Society of Actuaries or its Education and Examination Committee. The Society is grateful to the authors for their contributions in preparing the study notes. P - 2 1 - 0 5 P r i n t e d i n U . S . A . SECOND PRINTING
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2 RISK AND INSURANCE I. INTRODUCTION People seek security. A sense of security may be the next basic goal after food, clothing, and shelter. An individual with economic security is fairly certain that he can satisfy his needs (food, shelter, medical care, and so on) in the present and in the future. Economic risk (which we will refer to simply as risk) is the possibility of losing economic security. Most economic risk derives from variation from the expected outcome. One measure of risk, used in this study note, is the standard deviation of the possible outcomes. As an example, consider the cost of a car accident for two different cars, a Porsche and a Toyota. In the event of an accident the expected value of repairs for both cars is 2500. However, the standard deviation for the Porsche is 1000 and the standard deviation for the Toyota is 400. If the cost of repairs is normally distributed, then the probability that the repairs will cost more than 3000 is 31% for the Porsche but only 11% for the Toyota. Modern society provides many examples of risk. A homeowner faces a large potential for variation associated with the possibility of economic loss caused by a house fire. A driver faces a potential economic loss if his car is damaged. A larger possible economic risk exists with respect to potential damages a driver might have to pay if he injures a third party in a car accident for which he is responsible. Historically, economic risk was managed through informal agreements within a defined community. If someone’s barn burned down and a herd of milking cows was destroyed, the community would pitch in to rebuild the barn and to provide the farmer with enough cows to replenish the milking stock. This cooperative ( pooling ) concept became formalized in the insurance industry. Under a formal insurance arrangement, each insurance policy purchaser ( policyholder ) still implicitly pools his risk with all other policyholders. However, it is no longer necessary for any individual policyholder to know or have any direct connection with any other policyholder.
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This note was uploaded on 03/29/2010 for the course STATISTICS 50 taught by Professor Diaz during the Spring '10 term at California State University , Monterey Bay.

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