Related papers: Duality for multidimensional ruin problem
Downtime of industrial assets such as wind turbines and medical imaging devices is costly. To avoid such downtime costs, companies seek to initiate maintenance just before failure, which is challenging because: (i) Asset failures are…
The robustness of fault detection algorithms against uncertainty is crucial in the real-world industrial environment. Recently, a new probabilistic design scheme called distributionally robust fault detection (DRFD) has emerged and received…
We consider a reflected process in the positive orthant driven by an exogenous jump process. For a given input process, we show that there exists a unique minimal strong solution to the given particle system up until a certain maximal…
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…
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 propose an SIR spread model in a population network coupled with an infrastructure network that has a pathogen spreading in it. We develop a threshold condition to characterize the monotonicity and peak time of a weighted…
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…
For two nonstandard renewal risk models, we investigate the precise large deviations of the finite-time ruin probability and a random sum of the net-loss process, and the asymptotics of the random-time ruin probability. Notably, in one 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…
Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…
Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate the ultimate ruin probability in the Gerber-Dickson risk model is provided when claims follow a negative binomial mixture distribution. The…
In this paper we consider dividend problem for an insurance company whose risk evolves as a spectrally negative L\'{e}vy process (in the absence of dividend payments) when Parisian delay is applied. The objective function is given by the…
We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model…
We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics,…
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…
Given a set S of n \geq d points in general position in R^d, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree…
We study the asymptotic of the ruin probability for a process which is the solution of linear SDE defined by a pair of independent L\'evy processes. Our main interest is the model describing the evolution of the capital reserve of an…
Networked-guarantee loans may cause the systemic risk related concern of the government and banks in China. The prediction of default of enterprise loans is a typical extremely imbalanced prediction problem, and the networked-guarantee make…
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…
We investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin…