We study, in a Hilbert framework, some abstract parabolic variational inequalities, governed by reflecting subgradients with multiplicative perturbation, of the following type: y´(t)+ Ay(t)+0.t Θ(t,y(t)) ∂φ(y(t))∋f(t,y(t)),y(0) = y0,t ∈[0,T] where A is a linear self-adjoint operator, ∂φ is the subdifferential operator of a proper lower semicontinuous convex function φ defined on a suitable Hilbert space, and Θ is the perturbing term which acts on the set of reflecting directions, destroying the...

We investigate the properties of a rating migration process assuming that it is given by subordination of a discrete time Markov chain and a Cox process. The problem of pricing of defaultable bonds with fractional recovery of par value with rating migration and credit default swaps is considered. As an example of applications of our results, we give an explicit solution to the pricing problem in a model with short rate and intensity processes given by the solution of a two-dimensional Ornstein-Uhlenbeck...

In this paper we formulate a general model of the continuous double auction. We (recursively) describe the distribution of the model. As a useful by-product, we give a (recursive) analytic description of the distribution of the process of the best quotes (bid and ask).