Related papers: A Note on the Ruin Problem with Risky Investments

We study the discrete time risk process modelled by the skip-free random walk and we derive the results connected to the ruin probability, such as crossing the fixed level, for this kind of process. We use the method relying on the…

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…

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…

Applying excursion theory, we re-express several well studied fluctuation quantities associated to Parisian ruin problem for L\'evy risk processes in terms of integrals with respect to excursion measure for spectrally negative L\'evy…

This note is an addendum to the work initiated by Eberlein, Kabanov, and Schmidt and developed further by Kabanov and Promyslov on the asymptotics of the ruin probabilities in the Sparre Andersen model with investments in a risky asset.…

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.

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 investigate Parisian ruin for a L\'evy surplus process with an adaptive premium rate, namely a refracted L\'evy process. More general Parisian boundary-crossing problems with a deterministic implementation delay are also…

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…

In ruin theory, the net profit condition intuitively means that the incurred random claims on average do not occur more often than premiums are gained. The breach of the net profit condition causes guaranteed ruin in few but simple cases…

We deal with a generalization of the classical risk model when an insurance company gets additional funds whenever a claim arrives and consider some practical approaches to the estimation of the ruin probability. In particular, we get an…

We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival time distributions depending on the claims that arrived within a fixed (past) time window. This dependence could be explained through a regenerative…

In this paper we consider the Parisian ruin probabilities for the dual risk model in a discrete-time setting. By exploiting the strong Markov property of the risk process we derive a recursive expression for the fnite-time Parisian ruin…

This note explores the mathematical theory to solve modern gamblers ruin problems. We establish a ruin framework and solve for the probability of bankruptcy. We also show how this relates to the expected time to bankruptcy and review the…

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…

We study a risk sensitive control version of the lifetime ruin probability problem. We consider a sequence of investments problems in Black-Scholes market that includes a risky asset and a riskless asset. We present a differential game that…

We consider an interesting natural extension to the Parisian ruin problem under the assumption that the risk reserve dynamics are given by a spectrally negative L\'evy process. The distinctive feature of this extension is that the…

In this paper, we unify two popular approaches for the definition of actuarial ruin with implementation delays, also known as Parisian ruin. Our new definition of ruin includes both deterministic delays and exponentially distributed delays:…

We consider the dividend maximization problem including a ruin penalty in a diffusion environment. The additional penalty term is motivated by a constraint on dividend strategies. Intentionally, we use different discount rates for the…

The study deals with the ruin problem when an insurance company having two business branches, life insurance and non-life insurance, invests its reserve into a risky asset with the price dynamics given by a geometric Brownian motion. We…