We say that a random variable X taking nonnegative integers has selective lack-of-memory (SLM) property with selector s if P(X ≥ n + s/X ≥ n) = P(X ≥ s) for n = 0,1,.... This property is characterized in an elementary manner by probabilities pₙ = P(X=n). An application in car insurance is presented.

We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an information-based approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The "best-estimate ultimate loss process" is given by the conditional expectation of the ultimate loss. We derive explicit expressions for the...

Let $L$ be a parabolic second order differential operator on the domain $\overline{\Pi }=\left[0,T\right]\times ℝ.$ Given a function $\widehat{u}:ℝ\to R$ and $\widehat{x}\>0$ such that the support of $\widehat{u}$ is contained in $(-\infty ,-\widehat{x}]$, we let $\widehat{y}:\overline{\Pi }\to ℝ$ be the solution to the equation:$$L\widehat{y}=0,\widehat{y}{|}_{\left\{0\right\}\times ℝ}=\widehat{u}.$$Given positive bounds $0\<x_0\<x_1,$ we seek a function $u$ with support in $\left[x_0,x_1\right]$ such that the corresponding solution $y$ satisfies:$$y(t,0)=\widehat{y}(t,0)\forall t\in \left[0,T\right].$$We prove in this article that, under some regularity conditions on the coefficients of $L,$ continuous solutions are unique and dense in the sense that $\widehat{y}{|}_{[0,T]\times \left\{0\right\}}$ can be $C^0$-approximated, but an exact solution does not...

Let L be a parabolic second order differential operator on the domain $\overline{\Pi }=\left[0,T\right]\times ℝ.$ Given a function $\widehat{u}:ℝ\to R$ and $\widehat{x}>0$ such that the support of û is contained in $(-\infty ,-\widehat{x}]$, we let $\widehat{y}:\overline{\Pi }\to ℝ$ be the solution to the equation: $$L\widehat{y}=0,\widehat{y}{|}_{\left\{0\right\}\times ℝ}=\widehat{u}.$$ Given positive bounds $0<x_0<x_1,$ we seek a function u with support in $\left[x_0,x_1\right]$ such that the corresponding solution y satisfies: $$y(t,0)=\widehat{y}(t,0)\forall t\in \left[0,T\right].$$ We prove in this article that, under some regularity conditions on the coefficients of L, continuous solutions are unique and dense in the sense that $\widehat{y}{|}_{[0,T]\times \left\{0\right\}}$ can be C0-approximated, but an exact solution...

Our research is centred on the stochastic structure of matched open populations, subjected to periodical reclassifications. These populations are divided into sub-populations. In our application we considered two populations of customers of a bank: with and without account manager. Two or more of such population are matched when there is a 1-1 correspondence between their sub-populations and the elements of one of them can go to another, if and only if the same occurs with elements from the...

New statistical procedures for a change in means problem within a very general panel data structure are proposed. Unlike classical inference tools used for the changepoint problem in the panel data framework, we allow for mutually dependent panels, unequal variances across the panels, and possibly an extremely short follow up period. Two competitive ratio type test statistics are introduced and their asymptotic properties are derived for a large number of available panels. The proposed tests are...