The law of large numbers for self-exciting correlated defaults (Q436290)

A model of correlated defaults is proposed. The model presumes that in a large collection of defaultable entities, the intensity of each individual default depends on factors specific to the individual entity, and on a common factor. The model allow a part of the common factor to have a self-exciting nature, reflecting the general``health'' of the market. This self-exciting factor takes the form of an ``average loss process''.NEWLINENEWLINEAssuming the all the factors are diffusion processes, the authors show that the proposed self-exciting model is well-posed. The limit of the average default loss, if exists, can be characterized vie fixed point theorem Under certain monotonicity conditions the existence of the fixed point is proved.NEWLINENEWLINEIn a special case, a CLT for the average number of defaults is proved also.