Country Risk Classification and Multiriteria Decision Aid

1. Country Risk Classification and Multiriteria Decision Aid Xijun Wang January 26, 2004

2. Outline • Country Risk Classification • Country Risk Classification Methods • Utilities Additive Discrimination • Multigroup Hierarchical Discrimination • Dealing with Complex Factors • Future Works

3. Country Risk • The overall risk of loaning money to foreign companies. • How much is debt delayed and how much is the return? • Help financial institutions in decision-making • Measurements • Risk levels C1, C2 ,…, Cq, • Evaluation factors • Population structure, education, political and social status, economics, financial status

5. Country Risk Classification • Determine the risk level of a country based on various factors

6. Country Risk Classification Methods • Early used statistical methods: Bayesian discrimination, • Simple to implement • Not widely used due to unrealistic statistics assumptions • Recent approaches based on optimization: Multicriteria decision-aid methods • No statistics assumption • Background knowledge incorporated

7. Cq Ck C1 U(c) μq-1 μk μk-1 μ1 Utility Function • Utility function U(c) is an indicator of the risk level of a country • Risk level of country a is higher than of b, then U(a)<U(b) • Borderlines to separate different risk levels

8. Cq Ck C1 σ+(c) U(c) μq-1 μk μk-1 μ1 Cq Ck C1 σ-(c) U(c) μq-1 μk μk-1 μ1 Utilities Additive Discrimination (1) • Learning the utility function and the thresholds in the function space. • But, in practice, we might not find threshholds and utility functions that can predict all the country risk levels correctly

9. Utilities Additive Discrimination (2) Piecewise linear marginal utility function

10. Utilities Additive Discrimination (3) • Learning model: minimizing total training classification error

11. A Computation Example • Estimated Marginal Utility functions

12. Weights of Factor Groups

13. Examples and their Utilities

14. C¬k Ck Uk(c) U¬k(c) Multigroup Hierarchical Discrimination (1) • Hierarchical classification process • Is it in level C1? • If not, is it in level C2? • … • Suppose we have • Uk(c): similarity measure of c to countries in Ck • U¬k(c): similarity measure of c to countries in C¬k=Ck+1…Cq • Is c in Ck or C¬k?  Is Uk(c)> U¬k(c) or not?

15. Multigroup Hierarchical Discrimination (2) • Learning Uk(c) and U¬k (c) • Minimizing the number of misclassifications?

16. Multigroup Hierarchical Discrimination (3) • First, minimize total classification error, like in UTADIS

17. Multigroup Hierarchical Discrimination (4) • Second, further minimize number of misclassifications

18. Multigroup Hierarchical Discrimination (5) • Finally, make Uk and U¬k most distinguished on training examples, without changing the correctness of any training example

19. Dealing with Complex Factors • Non-monotone factors exists, such as birthrate, military expenditure • Allow unimodal utility function

20. Effect of Unimodal Factors • Leave one out test

21. Estimated Marginal Utility functions of birthrate and military expenditure

22. Weights of Factor Groups

23. Examples and their risk level

24. Conclusion and Future Works • Discussed two MCDA methods for country risk classification • UTADIS • MHDIS • Discussed an extension of MCDA models • Unimodal factors • Future work • Trade-off between correctness and computation effort for models with unimodal factors

25. Thank You for Your Attention

26. Birthrate