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Why Credibility Theory? Wang, Di Supervisor: Zhou, Jian School of management, Shanghai University 1/17

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Allais paradox 1 Statement of the Problem 2 Mathematical proof of inconsistency Experiment 1 Experiment School of management, Shanghai University 2

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Statement of the Problem The Allais paradox arises when comparing participants' choices in two different experiments, each of which consists of a choice between two gambles, A and B. The payoffs for each gamble in each experiment are as follows: Experiment 1Experiment 2 Gamble 1AGamble 1BGamble 2AGamble 2B Winnin gs Chance Winnin gs Chance Winnin gs Chance Winnin gs Chance $1 million 100% $1 million 89%Nothing89% Nothing90% Nothing1% $1 million 11% $5 million 10% $5 million 10% School of management, Shanghai University 3

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Mathematical proof of inconsistency Using the values above and a utility function U(W), where W is wealth, we can demonstrate exactly how the paradox manifests. Because the typical individual prefers 1A to 1B and 2B to 2A, we can conclude that the expected utilities of the preferred is greater than the expected utilities of the second choices. Experiment 1: 1.00U($1M) > 0.89U($1M) U($0M) + 0.1U($ 5M) Experiment 2: 0.89U($0M) U($1M) < 0.9U($ 0M) + 0.1U($5M ） We can know from the experiment that: Probability and Expect Utility Theory may not work in Some circumstances School of management, Shanghai University 4

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Divakaran Liginlala,*, Terence T. Owb ， Modeling attitude to risk in human decision processes: An application of fuzzy measures ， Fuzzy Sets and Systems 157 (2006) 3040 – 3054 Several models of the human decision process have been proposed, classical examples of which are utility theory and prospect theory. In recent times, the theory of fuzzy measures and integrals has emerged as an alternative meriting further investigation. For instance, of the nearly 196 articles on fuzzy measures published in the journal “Fuzzy Sets and Systems” since 1981, only 14 describe practical applications. fuzzy measures and integrals represents a starting point of a nonadditive expected utility theory School of management, Shanghai University 5

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Table 1 provides a chronological listing of selected applications reported until the year 2005 along with the methodology and the type of integral used in each case. For instance, of the nearly 196 articles on fuzzy measures published in the journal “Fuzzy Sets and Systems” since 1981, only 14 describe practical applications. nonadditive expected utility theory (i) " is additive if "(A & B) = "(A) + "(B). (ii) " is superadditive if "(A & B)""(A) + "(B). (iii) " is subadditive if "(A & B)!"(A) + "(B) School of management, Shanghai University 6

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Jae H. Min a, Young-Chan Lee b,*, A practical approach to credit scoring, A practical approach to credit scoring, Expert Systems with Applications 35 (2008) 1762–1770 So far, a variety of methods such as linear probability and multivariate conditional probability models, the recursive partitioning algorithm, artificial intelligence approaches multi-criteria decision-making (MCDM), mathematical programming approaches have been proposed to support the credit decision School of management, Shanghai University 7

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Arijit Laha, Building contextual classifiers by integrating fuzzy rule based classification technique and k-nn method for credit scoring, Advanced Engineering Informatics 21 (2007) 281–291 Credit-risk evaluation is a very challenging and important problem in the domain of financial analysis. Statistical and neural network based approaches are among the most popular paradigms. However, most of these methods produce so-called ‘‘hard’’ classifiers, those generate decisions without any accompanying confidence measure School of management, Shanghai University 8

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application scoring: where the task is to classify credit applicants into ‘‘good’’ and ‘‘bad’’ risk groups. 1.financial information 2.demographic information behavioral scoring 1.payment history information the accuracy of the estimation techniques decreases with increased dimensions of the feature space School of management, Shanghai University 9

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especially those incorporating fuzzy set theoretic approach, termed as ‘‘soft’’ classifiers. These classifiers,along with the classification decision produce a confidence other words, they have natural ability of handling uncertainty Domain experts The simplest way of tackling the above issues is to take the help of a domain expert and create the fuzzy rules to represent his/her domain knowledge School of management, Shanghai University 10

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Gia Sirbiladze1, Irina Khutsishvili2, COMBINED DECISION PRECISING FUZZY TECHNOLOGY FOR CREDIT RISK EVALUATION OF BANK INVESTMENTS, The Third International Conference “Problems of Cybernetics and Informatics”, September 6-8, 2010, Baku, Azerbaijan. Section #6 “Decision Making for Social- Economic Systems” When a juridical person submits business-plan to the investment fund or the bank with the aim of receiving a credit, experts perform applicant's business analysis. In particular, they check up on certain factors that are essential to grant a credit School of management, Shanghai University 11

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heuristic methods the objective and expert data possibilistic discrimination analysis The classic version of the fuzzy discrimination analysis uses so called frequency tabular-numeric knowledge base. Psychometric since one can hardly hope for the availability of statistical information data bases School of management, Shanghai University 12

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Yue Jiaoa, Yu-Ru Syaub, E. Stanley Leec, Modelling credit rating by fuzzy adaptive network, Mathematical and Computer Modelling 45 (2007) 717–731 Various factors are used to determine the credit worth of a financial enterprise. Vagueness may be caused by many different situations such as the difficult in defining precision, in deciding which variable is important, and how to define the variables and, sometimes, even how to define the problem. Due to these problems, the modern computer cannot be used effectively and the judgment of human experts form an essential part of the overall evaluation School of management, Shanghai University 13

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Essays in the theory of risk bearing 2.Exposition of the Theory of Choice Under Uncertainty 3.The Theory of Risk Aversion 8.Uncertainty and the Welfare Economics of Medical Care 11.Uncertainty and the Evaluation of Public Investments School of management, Shanghai University 14

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Uncertainty and the Welfare Economics of Medical Care Patients are uncertain about the effectiveness of medical treatment Another uncertainty may be quite different from that of his physician School of management, Shanghai University 15

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Uncertainty and the Evaluation of Public Investments Discount with time and risk Discount rate Subjective probability School of management, Shanghai University 16

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Thank you! School of management, Shanghai University 17

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