Related papers: A note on ruin problems in perturbed classical ris…
Let $\textbf{Z}(t)=(Z_1(t) ,\ldots, Z_d(t))^\top , t \in \mathbb{R}$ where $Z_i(t), t\in \mathbb{R}$, $i=1,...,d$ are mutually independent centered Gaussian processes with continuous sample paths a.s. and stationary increments. For…
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…
The main purpose of the paper is to study ruin probabilities in two discrete time risk models under rates of interest, where the premiums and claims are two independent sequences of m-dependent random variables, and the rate of interest is…
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…
In this paper a quantitative analysis of the ruin probability in finite time of discrete risk process with proportional reinsurance and investment of finance surplus is focused on. It is assumed that the total loss on a unit interval has a…
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…
In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve…
The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions.} Under the condition that the two Brownian motions $\{B_1(t), t\ge 0\}$ and…
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…
In this paper, we build on the techniques developed in Albrecher et al. (2013), to generate initial-boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim…
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 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…
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…
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…
This paper presents a novel model for bivariate stochastic fluid processes that incorporate a ruin-dependent behavioral switch. Unlike typical models that assume a shared underlying process, our model allows each process to operate…
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…
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…
We present here a new extended model of the gambler's ruin problem by incorporating delays in receiving of rewards and paying of penalties. When there is a difference between two delays, an exact analysis of the ruin probability is…
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…
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…