{"product_id":"a-probability-metrics-approach-to-financial-risk-measures-hardback-9781405183697","title":"A Probability Metrics Approach to Financial Risk Measures (Hardback) 9781405183697","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eA Probability Metrics Approach to Financial Risk Measures\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003e\u003cp\u003e\"The authors should be applauded for providing a unique and very readable account of probability metrics and the application of this specialized field to financial problems.\"\u003cbr\u003e—\u003cb\u003eProfessor Carol Alexander, Henley Business School at Reading\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\"This self-contained book covering the important field of probability metrics is a wonderful addition to the literature in financial economics. What makes it unique is that it presents this area at a level accessible to those without extensive prior experience-academic and practitioner alike.\"\u003cbr\u003e—\u003cb\u003ePetter Kolm, New York University\u003c\/b\u003e\u003c\/p\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eSvetlozar T. Rachev (Author), Stoyan V. Stoyanov (Author), Frank J. Fabozzi (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781405183697, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 21 January 2011\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e392 pages\u003cbr\u003e23.9 x 16 x 2.5 cm, 0.703 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003ci\u003eA Probability Metrics Approach to Financial Risk Measures\u003c\/i\u003e relates the field of probability metrics and risk measures to one another and applies them to finance for the first time.  \u003cul\u003e \u003cli\u003eHelps to answer the question: which risk measure is best for a given problem?\u003c\/li\u003e \u003cli\u003eFinds new relations between existing classes of risk measures\u003c\/li\u003e \u003cli\u003eDescribes applications in finance and extends them where possible\u003c\/li\u003e \u003cli\u003ePresents the theory of probability metrics in a more accessible form which would be appropriate for non-specialists in the field\u003c\/li\u003e \u003cli\u003eApplications include optimal portfolio choice, risk theory, and numerical methods in finance\u003c\/li\u003e \u003cli\u003eTopics requiring more mathematical rigor and detail are included in technical appendices to chapters\u003c\/li\u003e \u003c\/ul\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAbout the Authors xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Probability Metrics 1\u003c\/p\u003e \u003cp\u003e1.2 Applications in Finance 2\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Probability Distances and Metrics 7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 9\u003c\/p\u003e \u003cp\u003e2.2 Some Examples of Probability Metrics 9\u003c\/p\u003e \u003cp\u003e2.2.1 Engineer’s metric 10\u003c\/p\u003e \u003cp\u003e2.2.2 Uniform (or Kolmogorov) metric 10\u003c\/p\u003e \u003cp\u003e2.2.3 Lévy metric 11\u003c\/p\u003e \u003cp\u003e2.2.4 Kantorovich metric 14\u003c\/p\u003e \u003cp\u003e2.2.5 Lp-metrics between distribution functions 15\u003c\/p\u003e \u003cp\u003e2.2.6 Ky Fan metrics 16\u003c\/p\u003e \u003cp\u003e2.2.7 Lp-metric 17\u003c\/p\u003e \u003cp\u003e2.3 Distance and Semidistance Spaces 19\u003c\/p\u003e \u003cp\u003e2.4 Definitions of Probability Distances and Metrics 24\u003c\/p\u003e \u003cp\u003e2.5 Summary 28\u003c\/p\u003e \u003cp\u003e2.6 Technical Appendix 28\u003c\/p\u003e \u003cp\u003e2.6.1 Universally measurable separable metric spaces 29\u003c\/p\u003e \u003cp\u003e2.6.2 The equivalence of the notions of p. (semi-)distance on P2 and on X 35\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Choice under Uncertainty 40\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 41\u003c\/p\u003e \u003cp\u003e3.2 Expected Utility Theory 44\u003c\/p\u003e \u003cp\u003e3.2.1 St Petersburg Paradox 44\u003c\/p\u003e \u003cp\u003e3.2.2 The von Neumann–Morgenstern expected utility theory 46\u003c\/p\u003e \u003cp\u003e3.2.3 Types of utility functions 48\u003c\/p\u003e \u003cp\u003e3.3 Stochastic Dominance 51\u003c\/p\u003e \u003cp\u003e3.3.1 First-order stochastic dominance 52\u003c\/p\u003e \u003cp\u003e3.3.2 Second-order stochastic dominance 53\u003c\/p\u003e \u003cp\u003e3.3.3 Rothschild–Stiglitz stochastic dominance 55\u003c\/p\u003e \u003cp\u003e3.3.4 Third-order stochastic dominance 56\u003c\/p\u003e \u003cp\u003e3.3.5 Efficient sets and the portfolio choice problem 58\u003c\/p\u003e \u003cp\u003e3.3.6 Return versus payoff 59\u003c\/p\u003e \u003cp\u003e3.4 Probability Metrics and Stochastic Dominance 63\u003c\/p\u003e \u003cp\u003e3.5 Cumulative Prospect Theory 66\u003c\/p\u003e \u003cp\u003e3.6 Summary 70\u003c\/p\u003e \u003cp\u003e3.7 Technical Appendix 70\u003c\/p\u003e \u003cp\u003e3.7.1 The axioms of choice 71\u003c\/p\u003e \u003cp\u003e3.7.2 Stochastic dominance relations of order n 72\u003c\/p\u003e \u003cp\u003e3.7.3 Return versus payoff and stochastic dominance 74\u003c\/p\u003e \u003cp\u003e3.7.4 Other stochastic dominance relations 76\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 A Classification of Probability Distances 83\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 86\u003c\/p\u003e \u003cp\u003e4.2 Primary Distances and Primary Metrics 86\u003c\/p\u003e \u003cp\u003e4.3 Simple Distances and Metrics 90\u003c\/p\u003e \u003cp\u003e4.4 Compound Distances and Moment Functions 99\u003c\/p\u003e \u003cp\u003e4.5 Ideal Probability Metrics 105\u003c\/p\u003e \u003cp\u003e4.5.1 Interpretation and examples of ideal probability metrics 107\u003c\/p\u003e \u003cp\u003e4.5.2 Conditions for boundedness of ideal probability metrics 112\u003c\/p\u003e \u003cp\u003e4.6 Summary 114\u003c\/p\u003e \u003cp\u003e4.7 Technical Appendix 114\u003c\/p\u003e \u003cp\u003e4.7.1 Examples of primary distances 114\u003c\/p\u003e \u003cp\u003e4.7.2 Examples of simple distances 118\u003c\/p\u003e \u003cp\u003e4.7.3 Examples of compound distances 131\u003c\/p\u003e \u003cp\u003e4.7.4 Examples of moment functions 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Risk and Uncertainty 146\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 147\u003c\/p\u003e \u003cp\u003e5.2 Measures of Dispersion 150\u003c\/p\u003e \u003cp\u003e5.2.1 Standard deviation 151\u003c\/p\u003e \u003cp\u003e5.2.2 Mean absolute deviation 153\u003c\/p\u003e \u003cp\u003e5.2.3 Semi-standard deviation 154\u003c\/p\u003e \u003cp\u003e5.2.4 Axiomatic description 155\u003c\/p\u003e \u003cp\u003e5.2.5 Deviation measures 156\u003c\/p\u003e \u003cp\u003e5.3 Probability Metrics and Dispersion Measures 158\u003c\/p\u003e \u003cp\u003e5.4 Measures of Risk 159\u003c\/p\u003e \u003cp\u003e5.4.1 Value-at-risk 160\u003c\/p\u003e \u003cp\u003e5.4.2 Computing portfolio VaR in practice 165\u003c\/p\u003e \u003cp\u003e5.4.3 Back-testing of VaR 172\u003c\/p\u003e \u003cp\u003e5.4.4 Coherent risk measures 175\u003c\/p\u003e \u003cp\u003e5.5 Risk Measures and Dispersion Measures 179\u003c\/p\u003e \u003cp\u003e5.6 Risk Measures and Stochastic Orders 181\u003c\/p\u003e \u003cp\u003e5.7 Summary 182\u003c\/p\u003e \u003cp\u003e5.8 Technical Appendix 183\u003c\/p\u003e \u003cp\u003e5.8.1 Convex risk measures 183\u003c\/p\u003e \u003cp\u003e5.8.2 Probability metrics and deviation measures 184\u003c\/p\u003e \u003cp\u003e5.8.3 Deviation measures and probability quasi-metrics 187\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Average Value-at-Risk 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 192\u003c\/p\u003e \u003cp\u003e6.2 Average Value-at-Risk 193\u003c\/p\u003e \u003cp\u003e6.2.1 AVaR for stable distributions 200\u003c\/p\u003e \u003cp\u003e6.3 AVaR Estimation from a Sample 204\u003c\/p\u003e \u003cp\u003e6.4 Computing Portfolio AVaR in Practice 207\u003c\/p\u003e \u003cp\u003e6.4.1 The multivariate normal assumption 207\u003c\/p\u003e \u003cp\u003e6.4.2 The historical method 208\u003c\/p\u003e \u003cp\u003e6.4.3 The hybrid method 208\u003c\/p\u003e \u003cp\u003e6.4.4 The Monte Carlo method 209\u003c\/p\u003e \u003cp\u003e6.4.5 Kernel methods 211\u003c\/p\u003e \u003cp\u003e6.5 Back-testing of AVaR 218\u003c\/p\u003e \u003cp\u003e6.6 Spectral Risk Measures 220\u003c\/p\u003e \u003cp\u003e6.7 Risk Measures and Probability Metrics 223\u003c\/p\u003e \u003cp\u003e6.8 Risk Measures Based on Distortion Functionals 226\u003c\/p\u003e \u003cp\u003e6.9 Summary 227\u003c\/p\u003e \u003cp\u003e6.10 Technical Appendix 228\u003c\/p\u003e \u003cp\u003e6.10.1 Characteristics of conditional loss distributions 228\u003c\/p\u003e \u003cp\u003e6.10.2 Higher-order AVaR 232\u003c\/p\u003e \u003cp\u003e6.10.3 The minimization formula for AVaR 234\u003c\/p\u003e \u003cp\u003e6.10.4 ETL vs AVaR 237\u003c\/p\u003e \u003cp\u003e6.10.5 Kernel-based estimation of AVaR 242\u003c\/p\u003e \u003cp\u003e6.10.6 Remarks on spectral risk measures 245\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Computing AVaR through Monte Carlo 252\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 253\u003c\/p\u003e \u003cp\u003e7.2 An Illustration of Monte Carlo Variability 256\u003c\/p\u003e \u003cp\u003e7.3 Asymptotic Distribution, Classical Conditions 259\u003c\/p\u003e \u003cp\u003e7.4 Rate of Convergence to the Normal Distribution 262\u003c\/p\u003e \u003cp\u003e7.4.1 The effect of tail thickness 263\u003c\/p\u003e \u003cp\u003e7.4.2 The effect of tail truncation 268\u003c\/p\u003e \u003cp\u003e7.4.3 Infinite variance distributions 271\u003c\/p\u003e \u003cp\u003e7.5 Asymptotic Distribution, Heavy-tailed Returns 277\u003c\/p\u003e \u003cp\u003e7.6 Rate of Convergence, Heavy-tailed Returns 283\u003c\/p\u003e \u003cp\u003e7.6.1 Stable Paretian distributions 283\u003c\/p\u003e \u003cp\u003e7.6.2 Student’s t distribution 286\u003c\/p\u003e \u003cp\u003e7.7 On the Choice of a Distributional Model 290\u003c\/p\u003e \u003cp\u003e7.7.1 Tail behavior and return frequency 290\u003c\/p\u003e \u003cp\u003e7.7.2 Practical implications 295\u003c\/p\u003e \u003cp\u003e7.8 Summary 297\u003c\/p\u003e \u003cp\u003e7.9 Technical Appendix 298\u003c\/p\u003e \u003cp\u003e7.9.1 Proof of the stable limit result 298\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Stochastic Dominance Revisited 304\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 306\u003c\/p\u003e \u003cp\u003e8.2 Metrization of Preference Relations 308\u003c\/p\u003e \u003cp\u003e8.3 The Hausdorff Metric Structure 310\u003c\/p\u003e \u003cp\u003e8.4 Examples 314\u003c\/p\u003e \u003cp\u003e8.4.1 The L´evy quasi-semidistance and first-order stochastic dominance 315\u003c\/p\u003e \u003cp\u003e8.4.2 Higher-order stochastic dominance 317\u003c\/p\u003e \u003cp\u003e8.4.3 The H-quasi-semidistance 320\u003c\/p\u003e \u003cp\u003e8.4.4 AVaR generated stochastic orders 322\u003c\/p\u003e \u003cp\u003e8.4.5 Compound quasi-semidistances 324\u003c\/p\u003e \u003cp\u003e8.5 Utility-type Representations 325\u003c\/p\u003e \u003cp\u003e8.6 Almost Stochastic Orders and Degree of Violation 328\u003c\/p\u003e \u003cp\u003e8.7 Summary 330\u003c\/p\u003e \u003cp\u003e8.8 Technical Appendix 332\u003c\/p\u003e \u003cp\u003e8.8.1 Preference relations and topology 332\u003c\/p\u003e \u003cp\u003e8.8.2 Quasi-semidistances and preference relations 334\u003c\/p\u003e \u003cp\u003e8.8.3 Construction of quasi-semidistances on classes of investors 335\u003c\/p\u003e \u003cp\u003e8.8.4 Investors with balanced views 338\u003c\/p\u003e \u003cp\u003e8.8.5 Structural classification of probability distances 339\u003c\/p\u003e \u003cp\u003eIndex 357\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Economics [\u003ca title=\"See our other books on Economics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Economics%20%5BKC%5D%22\"\u003eKC\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-Blackwell","offers":[{"title":"Brand New","offer_id":52437791146264,"sku":"9781405183697","price":133.56,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781405183697.jpg?v=1784940759","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/a-probability-metrics-approach-to-financial-risk-measures-hardback-9781405183697","provider":"Freshly Printed Books","version":"1.0","type":"link"}