Two-dimensional ruin probability for subexponential claim size

We analyse the asymptotics of ruin probabilities of two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions when the initial reserves of both companies tend to infinity and generic claim size is subexponential

Extremes of multidimensional Gaussian processes

This paper considers extreme values attained by a centered, multidimensional Gaussian process $X(t)= (X_1(t),\ldots,X_n(t))$ minus drift $d(t)=(d_1(t),\ldots,d_n(t))$, on an arbitrary set $T$. Under mild regularity conditions, we establish the asymptotics of $$\log\mathbb P\left(\exists{t\in T}:\bigcap_{i=1}^n\left\{X_i(t)-d_i(t)>q_iu\right\}\right),$$ for positive thresholds $q_i>0$, $i=1,\ldots,n$, and $u\to\infty$. Our findings generalize and extend previously known results for the single-dimensional and two-dimensional cases. A number of examples illustrate the theory

The two defaults scenario for stressing credit portfolio loss distributions

The impact of a stress scenario of default events on the loss distribution of a credit portfolio can be assessed by determining the loss distribution conditional on these events. While it is conceptually easy to estimate loss distributions conditional on default events by means of Monte Carlo simulation, it becomes impractical for two or more simultaneous defaults as then the conditioning event is extremely rare. We provide an analytical approach to the calculation of the conditional loss distribution for the CreditRisk+ portfolio model with independent random loss given default distributions. The analytical solution for this case can be used to check the accuracy of an approximation to the conditional loss distribution whereby the unconditional model is run with stressed input probabilities of default (PDs). It turns out that this approximation is unbiased. Numerical examples, however, suggest that the approximation may be seriously inaccurate but that the inaccuracy leads to overestimation of tail losses and hence the approach errs on the conservative side.Comment: 20 pages, 1 figure, 2 table

Quasi-product forms for L

We study stochastic tree fluid networks driven by a multidimensional

Extremes of multidimensional Gaussian processes

This paper considers extreme values attained by a centered, multidimensional Gaussian process t) = (X_1(t), ..., X_n(t)) minus drift d(t) = (d_1(t), ..., d_n(t)), on an arbitrary set T. Under mild regularity conditions, we establish the asymptotics of the logarithm of the probability that for some t in T, we have that (for all i = 1, ..., n) X_i(t) - d_i(t) > q_i u, for positive thresholds q_i > 0 and u large. Our findings generalize and extend previously known results for the single-dimensional and two-dimensional case. A number of examples illustrate the theory