This paper investigates the problem of optimal reinsurance by evaluating four critical criteria:
ruin probability, variance of retained risk, profit, and expected utility. The study focuses on …

In this note we find a formula for the supremum distribution of spectrally positive or negative
L\'evy processes with a broken linear drift. This gives formulas for ruin probabilities in the …

In this paper, we consider a two-dimensional risk process in which the companies split each
claim and premium in a fixed proportion. It serves as a classical framework of a quota-share …

We introduce here a diffusion-type approximation of the ruin probability both in finite and
infinite time for a two-dimensional risk process, where claims and premiums are shared with …

We deal with a generalization of the risk model with stochastic premiums where dividends
are paid according to a constant dividend strategy and consider heuristic approximations for …

The underwriting operation of insurance firms is to assume the risk of the insured in return of
premium received. In order to shield itself against extreme losses and avoid the risk of …

Artykuł przedstawia podstawy teoretyczne teorii ruiny oraz opis klasycznego modelu
procesu nadwyżki. Przedstawiono analityczne obliczenia prawdopodobieństwa ruiny w …

The Parisian ruin occurs as the capital of the insurance company is negative longer than a
predefined period of time. In this article, we propose a simple and fast technique for …

W tej pracy rozważany jest dwuwymiarowy proces ryzyka, który może służyć do opisu
dynamiki kapitałów firm ubezpieczeniowych, które dla wybranej linii ubezpieczeniowej …