We investigate the credit risk model previously introduced by Hatchett and K\"uhn  under more general assumptions . We show that the model is exactly solvable in the N\rightarrow \infty limit and  that the exact solution is described by a message-passing approach outlined by Karrer and Newman, generalized to include heterogeneous agents and couplings. We provide comparisons with simulations in the case of a scale-free graph .
We investigate the credit risk model defined in Hatchett K\"{u under more general assumptions , in particular using a general degree distribution for sparse graphs. Expanding upon earlier results, we show that the model is exactly solvable in the N\rightarrow \infty limit and demonstrate that the exact solution is described by the message-passing approach outlined by Karrer and Newman, generalized to include heterogeneous agents and couplings. We provide comparisons with simulations of graph ensembles with power-law degree distributions .
R
previously introduced by Hatchett and K\"uhn
defined in Hatchett
A
K\"{u
R
. We
, in particular using a general degree distribution for sparse graphs. Expanding upon earlier results, we
A
demonstrate
R
a
the
R
in the case of a scale-free graph
of graph ensembles with power-law degree distributions