We present a simple model of firm rating evolution and resulting bankruptcies, taking into account two sources of defaults: individual dynamics of economic development and ordering interactions between firms. We show that such a defined model leads to phase transition, which results in collective defaults. Our results mean that, in the case when the individual firm dynamics favors dumping of rating changes, there is an optimal strengthof firms' interactions from the risk point of view . For small interaction strength parameters  there are many independent bankruptcies of individual companies. For large parameters  there are giant collective defaults of firm clusters  .
We present a simple model of firm rating evolution . We consider two sources of defaults: individual dynamics of economic development and Potts-like interactions between firms. We show that such a defined model leads to phase transition, which results in collective defaults. The existence of the collective phase depends on the mean interaction strength . For small interaction strength parameters , there are many independent bankruptcies of individual companies. For large parameters , there are giant collective defaults of firm clusters . In the case when the individual firm dynamics favors dumping of rating changes, there is an optimal strength of the firm's interactions from the systemic risk point of view .
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and resulting bankruptcies, taking into account
. We consider
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ordering
Potts-like
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Our results mean that, in the case when the individual firm dynamics favors dumping of rating changes, there is an optimal strengthof firms' interactions from the risk point of view
The existence of the collective phase depends on the mean interaction strength
A
,
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,
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. In the case when the individual firm dynamics favors dumping of rating changes, there is an optimal strength of the firm's interactions from the systemic risk point of view