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Related papers: Fractional Risk Process in Insurance

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This paper establishes the first analytical relationship between predictive model performance and loss ratio in insurance pricing. We derive a closed-form formula connecting the Pearson correlation between predicted and actual losses to…

Risk Management · Quantitative Finance 2025-12-04 C. Evans Hedges

Modeling the dependence between multiple risk types is a central challenge in contemporary insurance risk management. The standard approaches, L\'evy copulas and zero-mixed models, often face practical difficulties in simulation and…

Risk Management · Quantitative Finance 2026-05-26 Roberto Baviera , Pietro Manzoni , Michele Domenico Massaria

A multivariate fractional Poisson process was recently defined in Beghin and Macci (2016) by considering a common independent random time change for a finite dimensional vector of independent (non-fractional) Poisson processes; moreover it…

Probability · Mathematics 2016-09-13 Luisa Beghin , Claudio Macci

Every time drivers take to the road, and with each mile that they drive, exposes themselves and others to the risk of an accident. Insurance premiums are only weakly linked to mileage, however, and have lump-sum characteristics largely. The…

Risk Management · Quantitative Finance 2020-03-11 Safoora Zarei , Ali R. Fallahi

The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…

Methodology · Statistics 2022-09-14 Denis Talbot , Miceline Mésidor , Yohann Chiu , Marc Simard , Caroline Sirois

We deal with a generalization of the classical risk model when an insurance company gets additional funds whenever a claim arrives and consider some practical approaches to the estimation of the ruin probability. In particular, we get an…

Probability · Mathematics 2015-03-19 Yuliya Mishura , Olena Ragulina , Oleksandr Stroyev

We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index $\alpha \in (0,1]$ and the service completions are triggered by an independent fractional Poisson…

Probability · Mathematics 2026-03-20 Nicos Georgiou , Enrico Scalas , Vladislav Vysotsky

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 reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on…

Methodology · Statistics 2024-12-16 Nicolas Baradel

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.

Statistics Theory · Mathematics 2009-01-05 H. Cossette , E. Marceau , V. Maume-Deschamps

This note is a complement to the paper by Eberlein, Kabanov, and Schmidt on the asymptotic of the ruin probability in a Sparre Andersen non-life insurance model with investments a risky asset whose price follows a geometric L\'evy process.…

Probability · Mathematics 2026-04-08 Yuri Kabanov , Platon Promyslov

We review basic modeling approaches for failure and maintenance data from repairable systems. In particular we consider imperfect repair models, defined in terms of virtual age processes, and the trend-renewal process which extends the…

Methodology · Statistics 2007-08-03 Bo Henry Lindqvist

We consider predictions of the random number and the magnitude of each iid component in a random sum based on its distributional structure, where only a total value of the sum is available and where iid random components are non-negative.…

Probability · Mathematics 2015-07-13 Muneya Matsui

The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through…

Risk Management · Quantitative Finance 2020-08-06 Benjamin Avanzi , Greg Taylor , Bernard Wong , Alan Xian

In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractional Poisson process and space-fractional Poisson processes.…

Probability · Mathematics 2018-08-03 Neha Gupta , Arun Kumar , Nikolai Leonenko

We consider in this paper a risk reserve process where the claims and gains arrive according to two independent Poisson processes. While the gain sizes are phase-type distributed, we assume instead that the claim sizes are phase-type…

Probability · Mathematics 2020-06-16 Zbigniew Palmowski , Eleni Vatamidou

This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…

Applications · Statistics 2009-07-29 Marie-Pierre Etienne , Eric Parent , Benoit Hugues , Bernier Jacques

In this manuscript we propose a method for pricing insurance products that cover not only traditional risks, but also unforeseen ones. By considering the Poisson process parameter to be a mixed random variable, we capture the heterogeneity…

General Finance · Quantitative Finance 2020-08-10 Weihong Ni , Corina Constantinescu , Alfredo Egídio dos Reis , Véronique Maume-Deschamps

In this short note, we derive explicit formulas for the joint densities of the time to ruin and the number of claims until ruin in perturbed classical risk models, by constructing several auxiliary random processes.

Probability · Mathematics 2016-08-22 Peng Liu , Chunsheng Zhang , Lanpeng Ji

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…

Risk Management · Quantitative Finance 2021-12-14 Helena Jasiulewicz , Wojciech Kordecki