Related papers: On the ruin problem in the renewal risk processes …
A high order expansion of the renewal function is provided under the assumption that the inter-renewal time distribution is light tailed with finite moment generating function g on a neighborhood of 0. This expansion relies on complex…
We consider the problem of minimizing the probability of ruin by purchasing reinsurance whose premium is computed according to the mean-variance premium principle, a combination of the expected-value and variance premium principles. We…
For two nonstandard renewal risk models, we investigate the precise large deviations of the finite-time ruin probability and a random sum of the net-loss process, and the asymptotics of the random-time ruin probability. Notably, in one of…
In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve…
The paper deals with a generalization of the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. First of all, we derive piecewise integro-differential equations for the Gerber--Shiu…
We apply the theory of linear recurrence sequences to find an expression for the ultimate ruin probability in a discrete-time risk process. We assume the claims follow an arbitrary distribution with support $\{0,1,\ldots,m\}$, for some…
This paper investigates ruin probabilities for a two-dimensional fractional Brownian risk model with a proportional reinsurance scheme. We focus on joint and simultaneous ruin probabilities in a finite-time horizon. The risk processes of…
We consider an insurance company which faces financial risk in the form of insurance claims and market-dependent surplus fluctuations. The company aims to simultaneously control its terminal wealth (e.g. at the end of an accounting period)…
In this manuscript we consider the dual risk model with financial application, where the random gains occur under a renewal process. We particularly work the Erlang(n) case for common distribution of the inter-arrival times, from there it…
In this article, we introduce a new definition of bankruptcy for a spectrally negative L\'evy insurance risk process. More precisely, we study the Gerber-Shiu distribution for a ruin model where at each time the surplus goes negative, an…
In this paper we give few expressions and asymptotics of ruin probabilities for a Markov modulated risk process for various regimes of a time horizon, initial reserves and a claim size distribution. We also consider few versions of the ruin…
The Gerber-Shiu function is a classical research topic in actuarial science.However, exact solutions are only available in the literature for very specific cases where the claim amounts follow distributions such as the exponential…
The discrete time risk model with two seasons and dependent claims is considered. An algorithm is created for computing the values of the ultimate ruin probability. Theoretical results are illustrated with numerical examples.
This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to…
In this paper a quantitative analysis of the ruin probability in finite time of discrete risk process with proportional reinsurance and investment of finance surplus is focused on. It is assumed that the total loss on a unit interval has a…
In this paper, we adapt the classic Cram\'er-Lundberg collective risk theory model to a perturbed model by adding a Wiener process to the compound Poisson process, which can be used to incorporate premium income uncertainty, interest rate…
We study a general perturbed risk process with cumulative claims modelled by a subordinator with finite expectation, with the perturbation being a spectrally negative Levy process with zero expectation. We derive a Pollaczek-Hinchin type…
We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a…
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 case when two insurance companies (or two…
The Cram\'er-Lundberg model with exponential claims and proportional investment is solved exactly: the integro-differential equation for the survival probability reduces to a doubly confluent Heun equation, yielding an explicit solution in…