Probability Metrics Approach to Financial Risk Measures

A Probability Metrics Approach to Financial Risk Measures relates the field of probability metrics and risk measures to one another and applies them to finance for the first time.§Helps to answer the question: which risk measure is best for a given problem?§Finds new relations between existing classes of risk measures§Describes applications in finance and extends them where possible§Presents the theory of probability metrics in a more accessible form which would be appropriate for non-specialists in the field§Applications include optimal portfolio choice, risk theory, and numerical methods in finance§Topics requiring more mathematical rigor and detail are included in technical appendices to chaptersIs the behavior of the stocks in our portfolio close to their behavior during the most recent crisis? How close is the strategy of hedge fund A to the strategy of hedge fund B? In which proportions do we invest in a given universe of stocks so that the resulting portfolio matches as much as possible the strategy of fund C?§All of these questions are essential to finance and they have one feature in common: measuring distances between random quantities. Problems of this kind have been explored for many years in areas other than finance. In A Probability Metrics Approach to Financial Risk Measures, the field of probability metrics and risk measures are related to one another and applied to finance for the first time, revealing groundbreaking new classes of risk measures, finding new relations between existing classes of risk measures, and providing answers to the question of which risk measure is best for a given problem. Applications include optimal portfolio choice, risk theory, and numerical methods in finance.