相关论文: Uniform bounds for ruin probability in Multidimens…
This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the…
In this work, we consider extensions of the dual risk model with proportional gains by introducing a dependence structure between gain sizes and gain interrarrival times. Among others, we further consider the case where the proportional…
We study the closure properties of the class of Bivariate Regular Variation, symbolically BRV , in standard and nonstandard cases, with respect to the randomly weighted sums. However, we take into consideration a weak dependence structure…
In this paper we revisited the classical problem of max-sum equivalence of randomly weighted sums in two dimensions. In opposite to the most papers in literature, we consider that there exists some interdependence between the primary random…
In this note, we study the ultimate ruin probabilities of a real-valued L{\'e}vy process X with light-tailed negative jumps. It is well-known that, for such L{\'e}vy processes, the probability of ruin decreases as an exponential function…
Using a capacity approach, and the theory of measure's perturbation of Dirichlet forms, we give the probabilistic representation of the General Robin boundary value problems on an arbitrary domain $\Omega$, involving smooth measures, which…
We investigate the asymptotic risk of a general class of overparameterized likelihood models, including deep models. The recent empirical success of large-scale models has motivated several theoretical studies to investigate a scenario…
We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin…
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…
In this paper we determine bounds and exact asymptotics of the ruin probability for risk process with arrivals given by a linear marked Hawkes process. We consider the light-tailed and heavy-tailed case of the claim sizes. Main technique is…
We introduce the concept of cumulative Parisian ruin, which is based on the time spent in the red by the underlying surplus process. Our main result is an explicit representation for the distribution of the occupation time, over a…
We consider the simple random walk on the $N$-dimensional integer lattice from the perspective of evaluating asymptotically the duration of play in the multidimensional gambler\apost s ruin problem. We show that, under suitable rescalings,…
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 adapt the classic Cram\'er-Lundberg collective risk theory model to a perturbed model by adding a Wiener process to the compound Poisson process, which can be used to incorporate premium income uncertainty, interest rate…
Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this…
We explicitly find the rate of exponential long-term convergence for the ruin probability in a level-dependent L\'evy-driven risk model, as time goes to infinity. Siegmund duality allows to reduce the pro blem to long-term convergence of a…
We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our…
We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of…
This paper investigates the second order asymptotic expansion for tail probabilities of discounted aggregate claims in continuous-time renewal risk models with constant interest force. Concretely, two types of continuous-time renewal risk…
In this paper, we consider a classical risk model refracted at given level. We give an explicit expression for the joint density of the ruin time and the cumulative number of claims counted up to ruin time. The proof is based on solving…