Related papers: Ruin probability for the quota share model with~ph…
In this article we consider the surplus process of an insurance company within the Cramer-Lundberg framework. We study the optimal reinsurance strategy and dividend distribution of an insurance company under proportional reinsurance, in…
We investigate models of the life annuity insurance when the company invests its reserve into a risky asset with price following a geometric Brownian motion. Our main result is an exact asymptotic of the ruin probabilities for the case of…
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…
This paper investigates an insurance model with a finite number of major clients and a large number of small clients, where the dynamics of the latter group are modeled by a spectrally positive L\'evy process. We begin by analyzing this…
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 studies risk balancing features in an insurance market by evaluating ruin probabilities for single and multiple components of a multivariate compound Poisson risk process. The dependence of the components of the process is…
We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains $C_i$ ($i=1,2,\dots$) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model…
Lundberg-type inequalities for ruin probabilities of non-homogeneous risk models are presented in this paper. By employing martingale method, the upper bounds of ruin probabilities are obtained for the general risk models under weak…
In this work, we consider extensions of the dual risk model with proportional gains by introducing a dependence structure between gain sizes and gain interrarrival times. Among others, we further consider the case where the proportional…
In this short note, we derive explicit formulas for the joint densities of the time to ruin and the number of claims until ruin in perturbed classical risk models, by constructing several auxiliary random processes.
In this paper, we study Runge--Kutta methods for the computation of ruin probabilities in the classical risk model through the associated Volterra integro-differential equation. The proposed framework combines fourth-order one-step and…
In this paper, we address the aggregation of dependent stop loss reinsurance risks where the dependence among the ceding insurer(s) risks is governed by the Sarmanov distribution and each individual risk belongs to the class of Erlang…
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…
In actuarial research, a task of particular interest and importance is to predict the loss cost for individual risks so that informative decisions are made in various insurance operations such as underwriting, ratemaking, and capital…
Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem…
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance…
We present a joint copula-based model for insurance claims and sizes. It uses bivariate copulae to accommodate for the dependence between these quantities. We derive the general distribution of the policy loss without the restrictive…
We study solvency of insurers in a comprehensive model where various economic factors affect the capital developments of the companies. The main interest is in the impact of real growth to ruin probabilities. The volume of the business is…
The Gerber-Shiu function provides a way of measuring the risk of an insurance company. It is given by the expected value of a function that depends on the ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation…
Important models in insurance, for example the Carm{\'e}r--Lundberg theory and the Sparre Andersen model, essentially rely on the Poisson process. The process is used to model arrival times of insurance claims. This paper extends the…