Related papers: Ruin probabilities for risk processes in a biparti…
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…
A high order expansion of the renewal function is provided under the assumption that the inter-renewal time distribution is light tailed with finite moment generating function g on a neighborhood of 0. This expansion relies on complex…
We consider a competing risks model, in which system failures are due to one out of two mutually exclusive causes, formulated within the framework of shock models driven by bivariate Poisson process. We obtain the failure densities and the…
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…
We consider a $d-$dimensional insurance network, with initial capital $a\in\R^d_+,$ operating under a risk diversifying treaty; this is described in terms of a regulated random walk $\{Z^{(a)}_n\}$ via Skorokhod problem in $\R^d_+$ with…
Generalizing earlier works of Delbaen & Haezendonck [5] as well as of [18] and [16] for given compound mixed renewal process S under a probability measure P, we characterize all those probability measures Q on the domain of P such that Q…
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…
We model the influence of sharing large exogeneous losses to the reinsurance market by a bipartite graph. Using Pareto-tailed claims and multivariate regular variation we obtain asymptotic results for the Value-at-Risk and the Conditional…
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…
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…
Within the last fifteen years, network theory has been successfully applied both to natural sciences and to socioeconomic disciplines. In particular, bipartite networks have been recognized to provide a particularly insightful…
We consider a model of two interdependent networks, where every node in one network depends on one or more supply nodes in the other network and a node fails if it loses all of its supply nodes. We develop algorithms to compute the failure…
In this paper, we consider the problem of experience rating within the classic Markov chain life insurance framework. We begin by establishing a link between mixed Poisson distributions and the problem of pricing group disability insurance…
In this work, we derive a complete characterization of all ruin-inducing probability measures that preserve the structure of a given compound renewal process in terms of suitable pairs of functions $(\gamma,\delta)$. This result allows us…
We analyze the probability of ruin for the {\it scaled} classical Cram\'er-Lundberg (CL) risk process and the corresponding diffusion approximation. The scaling, introduced by Iglehart \cite{I1969} to the actuarial literature, amounts to…
We consider an insurance company in the case when the premium rate is a bounded non-negative random function $c_\zs{t}$ and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion…
In this paper, we generalise the results presented in the literature for the ruin probability for the insurer--reinsurer model under a pro-rata reinsurance contract. We consider claim amounts that are described by a phase-type distribution…
In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{\'e}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin…
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a new reliability property, Ising…
We consider a surplus process of drifted fractional Brownian motion with the Hurst index $H>1/2$, which appears as a functional limit of drifted compound Poisson risk models with correlated claims, and this is a kind of representation of a…