We propose a new model for the dynamics of the aggregate credit portfolio loss. The model is Markovian in two dimensions with the state variables being the total accumulated loss Lt and the stochastic default intensity λt. The dynamics of the default intensity are governed by the equation...

We present the SPA framework, a novel approach to the modeling of the dynamics of portfolio default losses. In this framework, models are specified by a two-layer process. The first layer models the dynamics of portfolio loss distributions in the absence of information about default times. This...

Let (Xn) be a strictly stationary random sequence and Mn=max{X1,...,Xn}. Suppose that some of the random variables X1,X2,... can be observed and denote by the maximum of observed random variables from the set {X1,...,Xn}. We determine the limiting distribution of random vector under some...

Let (Xn) be a sequence of possibly dependent random variables with the same marginal distribution function F, such that 1-F(x)=x-[alpha]L(x), [alpha]0, where L(x) is a slowly varying function. In this paper the Hill estimator of the exponent of regular variation based on a sample with missing...

A formula is derived for the 'effective' skew in a stochastic volatility model with a time-dependent local volatility function. The formula relates the total amount of skew generated by the model over a given time period to the time-dependent slope of the instantaneous local volatility function....

Let ξ(t) be a standard stationary Gaussian process with covariance function r(t), and η(t), another smooth random process. We consider the probabilities of exceedances of ξ(t)η(t) above a high level u occurring in an interval [0,T] with T0. We present asymptotically exact results for...

The maximum MT of the storage process Y(t)=sups[greater-or-equal, slanted]t(X(s)-X(t)-c(s-t)) in the interval [0,T] is dealt with, in particular, for growing interval length T. Here X(s) is a fractional Brownian motion with Hurst parameter, 0<H<1. For fixed T the asymptotic behaviour of MT was analysed by Piterbarg (Extremes 4(2) (2001) 147) by determining an approximation for the probability P MT>u for u--[infinity]. Using this expression the...</h<1.>

For certain Gaussian processes X(t) with trend -ct[beta] and variance V2(t), the ruin time is analyzed where the ruin time is defined as the first time point t such that X(t)-ct[beta]=u. The ruin time is of interest in finance and actuarial subjects. But the ruin time is also of interest in...