In this paper, we study the generalized expected discounted penalty (Gerber–Shiu) function in a risk process with credit and debit interests. We define Tu,z to be the first time that the surplus process drops below a certain level z from the initial surplus u(z). The time of ruin and the time...

In this paper, we consider the dual of the compound Poisson risk model with exponentially distributed observation time and constant dividend barrier strategy. We derive and solve the integro-differential equations satisfied by the expected total discounted dividend payments until ruin and ruin...

Consider a discrete time risk model under random interest based on the compound Pascal model. The insurer pays a dividend of 1 with a probability q0 when the surplus is greater than or equal to a non-negative b. In addition, the effect of interest is considered in our model. We derive recursion...

In this note we provide an operational interpretation of the economic index of riskiness of Aumann and Serrano (2008) and discuss its existence in the case of non-finite gambles.

In this paper, we consider a risk process with the arrival of claims modelled by a dynamic contagion process, a generalisation of the Cox process and Hawkes process introduced by Dassios and Zhao (2011). We derive results for the infinite horizon model that are generalisations of the...

We prove some heavy-traffic limit theorems for processes which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution.

We consider a renewal jump–diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for...

Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative errors. Motivated by statistical analysis, we assume...

Assume that an insurer has two dependent lines of business. The reserves of the two lines of business are modeled by a two-dimensional compound Poisson risk process or a common shock model. To protect from large losses and to reduce the ruin probability of the insurer, the insurer applies a...

In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a...