Let $𝐗=(X,Y)$ be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let ${𝐗}_t=\left[(X-t,Y-t)\right|X>t,Y>t]$ denotes the corresponding pair of residual lifetimes after time $t$, with $t\ge 0$. This note deals with stochastic comparisons between $𝐗$ and ${𝐗}_t$: we provide sufficient conditions for their comparison in usual stochastic and lower orthant orders. Some of the results and examples presented here are quite unexpected, since they show that there is not a direct correspondence between univariate...

The following problem in risk theory is considered. An insurance company, endowed with an initial capital a > 0, receives insurance premiums and pays out successive claims from two kind of risks. The losses occur according to a marked point process. At any time the company may broaden or narrow down the offer, which entails the change of the parameters of the underlying risk process. These changes concern the rate of income, the intensity of the renewal process and the distribution of claims....