For a random walk with negative mean and heavy-tailed increment distribution F, it is well known that under suitable subexponential assumptions, the distribution [pi] of the maximum has a tail [pi](x,[infinity]) which is asymptotically proportional to . We supplement here this by a local result...

In this article, we propose a class of convex risk measures defined on appropriate wedges of a space of financial positions which denote the cumulative surplus variables created by undertaking risks by either an insurance or a reinsurance company. The form of the wedge which is the domain of...

The present paper addresses the situation where the reserve of an insurance business is currently invested in an asset that may yield negative interest. Upper and lower bounds for the probability of ruin are obtained in the case where the cash flow of premiums less claims and the logarithm of...

The paper is devoted to analysis of geometric convolutions emerging in various fields of applied probability and, in particular, in reliability. The problem of bounding the distribution of such sums has been the subject of numerous works for last 20 years. Various bounds were proposed but their...