Country risk classification and multiriteria decision aid
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Country Risk Classification and Multiriteria Decision Aid. Xijun Wang January 26, 2004. Outline. Country Risk Classification Country Risk Classification Methods Utilities Additive Discrimination Multigroup Hierarchical Discrimination Dealing with Complex Factors Future Works.

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Outline
Outline

  • Country Risk Classification

  • Country Risk Classification Methods

  • Utilities Additive Discrimination

  • Multigroup Hierarchical Discrimination

  • Dealing with Complex Factors

  • Future Works


Country risk
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


Country risk classification
Country Risk Classification

  • Determine the risk level of a country based on various factors


Country risk classification methods
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


Utility function

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


Utilities additive discrimination 1

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


Utilities additive discrimination 2
Utilities Additive Discrimination (2)

Piecewise linear marginal utility function


Utilities additive discrimination 3
Utilities Additive Discrimination (3)

  • Learning model: minimizing total training classification error


A computation example
A Computation Example

  • Estimated Marginal Utility functions




Multigroup hierarchical discrimination 1

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?


Multigroup hierarchical discrimination 2
Multigroup Hierarchical Discrimination (2)

  • Learning Uk(c) and U¬k (c)

    • Minimizing the number of misclassifications?


Multigroup hierarchical discrimination 3
Multigroup Hierarchical Discrimination (3)

  • First, minimize total classification error, like in UTADIS


Multigroup hierarchical discrimination 4
Multigroup Hierarchical Discrimination (4)

  • Second, further minimize number of misclassifications


Multigroup hierarchical discrimination 5
Multigroup Hierarchical Discrimination (5)

  • Finally, make Uk and U¬k most distinguished on training examples, without changing the correctness of any training example


Dealing with complex factors
Dealing with Complex Factors

  • Non-monotone factors exists, such as birthrate, military expenditure

  • Allow unimodal utility function


Effect of unimodal factors
Effect of Unimodal Factors

  • Leave one out test





Conclusion and future works
Conclusion and Future Works military expenditure

  • 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


Thank You for Your Attention military expenditure


Birthrate
Birthrate military expenditure


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