Related papers: Exit problem of a two-dimensional risk process fro…
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.
We investigate the asymptotic of ruin probabilities when the company invests its reserve in a risky asset with a switching regime price. We assume that the asset price is a conditional geometric Brownian motion with parameters modulated by…
This paper investigates the Parisian ruin probability for processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptotics as the ruin boundary tends to infinity and extend the previous…
Parisian ruin probability in the classical Brownian risk model, unlike the standard ruin probability can not be explicitly calculated even in one-dimensional setup. Resorting on asymptotic theory, we derive in this contribution an…
The field of risk theory has traditionally focused on ruin-related quantities. In particular, the socalled Expected Discounted Penalty Function has been the object of a thorough study over the years. Although interesting in their own right,…
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…
We analyze the asymptotics of crossing a high piecewise linear barriers by a renewal compound process with the subexponential jumps. The study is motivated by ruin probabilities of two insurance companies (or two branches of the same…
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…
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 study the rough asymptotic behaviour of a general economic risk model in a discrete setting. Both financial and insurance risks are taken into account. Loss during the first $n$ years is modelled as a random variable…
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…
In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result,…
We study the problem of optimal risk policies and dividend strategies for an insurance company operating under the constraint that the timing of shareholder payouts is governed by the arrival times of a Poisson process. Concurrently, risk…
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…
The paper investigates a discrete time Binomial risk model with different types of polices and shock events may influence some of the claim sizes. It is shown that this model can be considered as a particular case of the classical compound…
Let $\mathbf{B}(t)=(B_1(t), B_2(t))$, $t\geq 0$ be a two-dimensional Brownian motion with independent components and define the $\mathbf{\gamma}$-reflected process…
The optimal stopping problem for the risk process with interests rates and when claims are covered immediately is considered. An insurance company receives premiums and pays out claims which have occured according to a renewal process and…
We study a ruin problem for an annuity model where a fixed fraction of capital is invested in a risky asset. Under weak assumptions on jumps, the ruin probability solves a second-order integro-differential equation and decays as a power…
For a multivariate L\'evy process satisfying the Cram\'er moment condition and having a drift vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant that is being…
We consider a classical risk process with arrival of claims following a non-stationary Hawkes process. We study the asymptotic regime when the premium rate and the baseline intensity of the claims arrival process are large, and claim size…