English
Related papers

Related papers: Approximations to ultimate ruin probabilities with…

200 papers

In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown for the scaled Cram\'er-Lundberg risk model when the reinsurance premium is computed according to the mean-variance premium principle. We…

Optimization and Control · Mathematics 2022-01-04 Pablo Azcue , Xiaoqing Liang , Nora Muler , Virginia R. Young

Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior.…

Machine Learning · Statistics 2020-01-29 Robert Bamler , Cheng Zhang , Manfred Opper , Stephan Mandt

In this paper, we study Runge--Kutta methods for the computation of ruin probabilities in the classical risk model through the associated Volterra integro-differential equation. The proposed framework combines fourth-order one-step and…

Numerical Analysis · Mathematics 2026-05-26 George Kanakoudis , Lazaros Kanellopoulos

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…

Probability · Mathematics 2026-04-28 Spyridon M. Tzaninis , Apostolos Bozikas

Let $\left\{\sum_{i=1}^n \lambda_i X_i(t), t\in [0,T]\right\}$ be an aggregate Gaussian risk process with $X_i, i\leq n$ independent Gaussian processes satisfying Piterbarg conditions and $\lambda_i$'s given positive weights. In this paper…

Probability · Mathematics 2014-04-24 Krzysztof Debicki , Enkelejd Hashorva , Lanpeng Ji , Zhongquan Tan

The classical Cram\'er-Lundberg risk process models the ruin probability of an insurance company experiencing an incoming cash flow - the premium income, and an outgoing cash flow - the claims. From a system's viewpoint, the web of…

Probability · Mathematics 2021-04-13 Rukuang Huang

We consider a spectrally-negative Markov additive process as a model of a risk process in random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees…

Probability · Mathematics 2013-10-14 Hansjoerg Albrecher , Jevgenijs Ivanovs

Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…

Probability · Mathematics 2011-02-22 Aihua Xia , Fuxi Zhang

In this paper we consider the Parisian ruin probabilities for the dual risk model in a discrete-time setting. By exploiting the strong Markov property of the risk process we derive a recursive expression for the fnite-time Parisian ruin…

Probability · Mathematics 2017-08-24 Zbigniew Palmowski , Lewis Ramsden , Apostolos D. Papaioannou

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…

Probability · Mathematics 2023-11-07 Denis Denisov , Niklas Gotthardt , Dmitry Korshunov , Vitali Wachtel

This paper is a continuation of work arXiv:2006.09583 devoted to establishment of the convergence rate in the strong invariance principle for cumulative processes. We establish optimal rate of convergence for the case when regeneration…

Probability · Mathematics 2020-07-31 Elena Bashtova , Alexey Shashkin

We study the asymptotic behavior of ruin probabilities, as the initial reserve goes to infinity, for a reserve process model where claims arrive according to a renewal process, while between the claim times the process has the dynamics of…

Probability · Mathematics 2023-02-24 Ying He , Konstantin Borovkov

We study the problem of minimizing the discounted probability of exponential Parisian ruin, that is, the discounted probability that an insurer's surplus exhibits an excursion below zero in excess of an exponentially distributed clock. The…

Optimization and Control · Mathematics 2020-07-07 Xiaoqing Liang , Virginia R. Young

This paper presents a numerical model to solve the problem of cash accumulation strategies for products with an unknown future price, like assets. Stock prices are modeled by a discretized Wiener Process, and by the means of ordinary…

Mathematical Finance · Quantitative Finance 2017-11-07 Renko Siebols

This paper studies proportional risk sharing at claim occurrence time in community-based insurance. Each participant is modeled by an individual Cram\'er-Lundberg surplus process, and, whenever a claim is reported within the pool, its cost…

Probability · Mathematics 2026-04-01 Michel Denuit , José Miguel Flores-Contró , Christian Y. Robert

We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this…

Probability · Mathematics 2020-07-16 Yuchao Dong , Jérôme Spielmann

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…

Probability · Mathematics 2012-07-17 Ze-Chun Hu , Bin Jiang

This paper obtains an asymptotic formula for the finite-time ruin probability of the compound nonhomogeneous Poisson risk model with a constant interest force, in which the claims are conditionally independent random variables with a common…

Probability · Mathematics 2017-05-30 Hui Xu , Fengyang Cheng

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…

Probability · Mathematics 2020-01-28 Nikolai Kriukov

In this paper, we propose the discrete time Compound Beta-Binomial Risk Model with by-claims, delayed by-claims and randomized dividends. We then analyze the Gerber-Shiu function for the cases where the dividend threshold $d=0$ and $d>0$…

Statistical Finance · Quantitative Finance 2019-08-12 Aparna B. S , Neelesh S Upadhye