Selection and Application of Distorted Risk Measures

<p>This thesis develops and illustrates a methodology for the selection of probability distributions and distortion functions associated with risk scenarios resulting from military capability shortfalls. Distorted (or transformed) risk measures are analyzed and applied to account for loss scenarios that may occur with low frequency but result in catastrophic outcomes. After reviewing the rudimentary concepts of distortion four wellknown continuous distributions suitable for modeling risk scenarios are chosen using defined criteria. Based on subject matter expert inputs a simple method for assigning exactly one of the four distributions to any risk scenario is proposed. Four parametric distortion functions from the finance and insurance literature are then selected and applied to each of the chosen distributions. The distortion effects are examined analytically graphically and empirically and broad-based recommendations are recorded as to the instances when one distortion function might be preferred over others. An end-to-end notional problem -- in which a subset of available mitigation measures are selected to counteract a multi-faceted risk environment -- illustrates the means by which the proposed methodology may be used to affect future systems acquisition through the Capabilities Review and Risk Assessment (CRRA) process of the United States Air Force.</p><p>This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact and remains as true to the original work as possible. Therefore you will see the original copyright references library stamps (as most of these works have been housed in our most important libraries around the world) and other notations in the work.</p><p>This work is in the public domain in the United States of America and possibly other nations. Within the United States you may freely copy and distribute this work as no entity (individual or corporate) has a copyright on the body of the work.</p><p>As a reproduction of a historical artifact this work may contain missing or blurred pages poor pictures errant marks etc. Scholars believe and we concur that this work is important enough to be preserved reproduced and made generally available to the public. We appreciate your support of the preservation process and thank you for being an important part of keeping this knowledge alive and relevant.</p>