# Applying Game Theory to a financial risk analysis

## Applying Game Theory to a financial risk analysis

Financial ratios are one of the first variables which need to be considered when approaching a rating analysis. Why? Financial theory points out which are the ratios’ values that need to be studied to understand the risk of the company evaluated.

Ratios can be divided into different areas, for example solvency, profitability, liquidity, etc.

And the lowest financial risk is pointed out by the company showing the best ratios.Unfortunately, this isn’t easy to define mathematically and not so many analysts are aware of (and are able to) apply custom modeling to finance.

### How do you define “good” financial ratios, and what does this mean?

If X is the company, the ratios will be as follows:

*F _{i}(X), i = 1, .., n*

Where *n* is the number of the ratios we consider.

There’s a general problem here: losing precision. We are able to say that company X, to be considered “good” (showing a high Rating class) needs to have all ratios maximum:

*max F _{i}(X) = 1, .., n*

And here the problem begins: the formulation outlined above is a multi-objective optimization problem.

A way to solve it, is to use Game Theory.

To develop a model for credit rating evaluation, we necessarily relied on algorithms that use the Game Theory, specifically, choosing among different Game Theories (several possibilities, Nash, Stackelberg, Pareto, etc.)As we developed our Rating mathodology, we chose to apply the theory that best suited technologies and results: the Pareto Theory.

So, the company that meets the optimum point according to Pareto, is the one that has a “high” Rating class.