In this paper, we consider a nonstandard multidimensional risk model, in which the claim sizes $\{\vec{X}_k, k\ge 1\}$ form an independent and identically distributed random vector sequence with dependent components. By assuming that there exists the regression dependence structure between inter-arrival time and the claim-size vectors, we extend the regression dependence to a more practical multidimensional risk model. For the univariate marginal distributions of claim vectors with consistently varying tails, we obtain the precise large deviation formulas for the multidimensional risk model with the regression size-dependent structure.

Mortality at older ages varies by season, increasing the uncertainty associated with modelling and projecting mortality at older ages and ultimately contributing to pension providers’ overall risk. As the population ages, it becomes more important to understand variations in seasonal mortality between pensioners and to identify those most vulnerable to seasonal mortality differences. Using data from the Self-Administered Pension Schemes mortality investigation of the Continuous Mortality Investigation of the Institute and Faculty of Actuaries, UK, this paper investigates variations in seasonal mortality amongst members of UK occupational pension schemes over the period 2000–2016. Results are also compared with the corresponding population of England and Wales. For the oldest age groups (80+), which are most affected by seasonality, females are more vulnerable to seasonal differences in mortality for each pensioner group relative to males. Following a long-term decline in the winter-summer mortality gap the gap increased over the period, particularly for female pensioners and dependants. Seasonality remains a feature of UK mortality at older ages and risk management for pension schemes should consider seasonality when analysing overall mortality experience.

We consider the minimum spanning tree problem on a weighted complete bipartite graph $K_{n_R, n_B}$ whose $n=n_R+n_B$ vertices are random, i.i.d. uniformly distributed points in the unit cube in $d$ dimensions and edge weights are the $p$-th power of their Euclidean distance, with $p\gt 0$. In the large $n$ limit with $n_R/n \to \alpha _R$ and $0\lt \alpha _R\lt 1$, we show that the maximum vertex degree of the tree grows logarithmically, in contrast with the classical, non-bipartite, case, where a uniform bound holds depending on $d$ only. Despite this difference, for $p\lt d$, we are able to prove that the total edge costs normalized by the rate $n^{1-p/d}$ converge to a limiting constant that can be represented as a series of integrals, thus extending a classical result of Avram and Bertsimas to the bipartite case and confirming a conjecture of Riva, Caracciolo and Malatesta.