Related papers: Ruin probability for the quota share model with~ph…
We study the asymptotics of the ruin probability in the Cram\'er-Lundberg model with a modified notion of ruin. The modification is as follows. If the portfolio becomes negative, the asset is not immediately declared ruined but may survive…
In this note we consider the two-dimensional risk model introduced in Avram et al. \cite{APP08} with constant interest rate. We derive the integral-differential equations of the Laplace transforms, and asymptotic expressions for the finite…
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…
The ruin probability in the classical Brownian risk model can be explicitly calculated for both finite and infinite-time horizon. This is not the case for the simultaneous ruin probability in two-dimensional Brownian risk model. Resorting…
We propose a stochastic model allowing property and casualty insurers with multiple business lines to measure their liabilities for incurred claims risk and calculate associated capital requirements. Our model includes many desirable…
The collective risk model differentiates usually between claims frequencies (and their distribution) and claim sizes (and their distribution). For the claims frequencies typically classical discrete distributions are considered, such as…
Our paper explores a discrete-time risk model with time-varying premiums, investigating two types of correlated claims: main claims and by-claims. Settlement of the by-claims can be delayed for one time period, representing real-world…
We consider two insurance companies with endowment processes given by Brownian motions with drift. The firms can collaborate by transfer payments in order to maximize the probability that none of them goes bankrupt. We show that pushing…
The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by…
In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as…
Modeling insurance claim amounts and classifying claims into different risk levels are critical yet challenging tasks. Traditional predictive models for insurance claims often overlook the valuable information embedded in claim…
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…
We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our…
We propose a model in which, in exchange to the payment of a fixed transaction cost, an insurance company can choose the retention level as well as the time at which subscribing a perpetual reinsurance contract. The surplus process of the…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
The aim of this paper is to construct the confidence interval of the ultimate ruin probability under the insurance surplus driven by a L\'evy process. Assuming a parametric family for the L\'evy measures, we estimate the parameter from the…
Following an article by Muller and Pflug, we study the adjustment coefficient of ruin theory in a context of temporal dependency. We provide a consistent estimator of this coefficient, and perform some simulations.
We consider a diffusion approximation to an insurance risk model where an external driver models a stochastic environment. The insurer can buy reinsurance. Moreover, investment in a financial market is possible. The financial market is also…
Due to its practical use, De Vylder's approximation of the ruin probability has been one of the most popular approximations in ruin theory and its application to insurance. Surprisingly, only heuristic and numerical evidence has supported…
If a given aggregate process $S$ is a compound mixed renewal process under a probability measure $P$, we provide a characterization of all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and…