相关论文: Absolute ruin in the Ornstein-Uhlenbeck type risk …
This survey treats the problem of ruin in a risk model when assets earn investment income. In addition to a general presentation of the problem, topics covered are a presentation of the relevant integro-differential equations, exact and…
We reprove a result concerning certain ruin in the classical problem of the probability of ruin with risky investments and several of it's generalisations. We also provide the combined transition density of the risk and investment processes…
For a bivariate L\'evy process $(\xi_t,\eta_t)_{t\geq 0}$ the generalised Ornstein-Uhlenbeck (GOU) process is defined as V_t:=e^{\xi_t}(z+\int_0^t e^{-\xi_{s-}}d\eta_s), t\ge0, where $z\in\mathbb{R}.$ We define necessary and sufficient…
We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events,…
We derive the Markov-modulated generalized Ornstein-Uhlenbeck process by embedding a Markov-modulated random recurrence equation in continuous time. The obtained process turns out to be the unique solution of a certain stochastic…
In this paper we evaluate the probability of the discrete time Parisian ruin that occurs when surplus process stays below or at zero at least for some fixed duration of time $d>0$. We identify expressions for the ruin probabilities within…
This article studies in detail the solution of an integral equation due to Rongming et al. [13]. The methods involve complex analysis. As an application, we find the ruin probability of a given Bonus-Malus system in a steady state. We…
In this text, we establish the risk model based on AR(1) series and propose the basic model which has a dependent structure under intensity of claim number. Considering some properties of the risk model, we take advantage of newton…
Using the results of precise large deviation and renewal theory for widely dependent random variables, this paper obtains the asymptotic estimation of the random-time ruin probability and the uniform asymptotic estimation of finite-time…
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 investigate continuity properties for ruin probability in the classical risk model. Properties of contractive integral operators are used to derive continuity estimates for the deficit at ruin. These results are also…
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…
We consider the classical Cram\'er-Lundberg risk model with claim sizes that are mixtures of phase-type and subexponential variables. Exploiting a specific geometric compound representation, we propose control variate techniques to…
We study a Sparre Andersen model in which the business activity of the company is described by a compound renewal process with drift assuming that the capital reserves are invested in a risky asset. The price of the latter is assumed to…
We introduce the hybrid risk process, constructed via a time-change transformation applied to the solution of a hybrid stochastic differential equation. The framework covers several modern ruin settings, incorporating features like…
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 examine hitting probability problems for Ornstein-Uhlenbeck (OU) processes and Geometric Brownian motions (GBM) with respect to exponential boundaries related to problems arising in risk theory and asset and liability models in pension…
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…
Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting…
In this paper we analyze so-called Parisian ruin probability that happens when surplus process stays below zero longer than fixed amount of time $\zeta>0$. We focus on general spectrally negative L\'{e}vy insurance risk process. For this…