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We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the…

Probability · Mathematics 2018-02-14 Frank Aurzada , Micha Buck

We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains $C_i$ ($i=1,2,\dots$) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model…

Probability · Mathematics 2020-12-02 Onno Boxma , Esther Frostig , Zbigniew Palmowski

This paper studies risk balancing features in an insurance market by evaluating ruin probabilities for single and multiple components of a multivariate compound Poisson risk process. The dependence of the components of the process is…

Probability · Mathematics 2020-02-04 Anita Behme , Claudia Klüppelberg , Gesine Reinert

In this paper, we study a continuous time structural asset value model for two correlated firms using a two-dimensional Brownian motion. We consider the situation of incomplete information, where the information set available to the market…

Mathematical Finance · Quantitative Finance 2016-01-28 Wai-Ki Ching , Jia-Wen Gu , Harry Zheng

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…

Probability · Mathematics 2015-11-25 Jaakko Lehtomaa

In this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin.…

Optimization and Control · Mathematics 2011-12-20 Shangzhen Luo , Michael Taksar

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…

Probability · Mathematics 2025-04-23 Ioannis Dimitriou

Given a Gaussian risk process $R(t)=u+c(t)-X(t),t\ge 0$, the cumulative Parisian ruin probability on a finite time interval $[0,T]$ with respect to $L \geq 0$ is defined as the probability that the sojourn time that the risk process $R$…

Probability · Mathematics 2024-02-06 Svyatoslav M. Novikov

Recent studies have identified long-range dependence as a key feature in the dynamics of both mortality and interest rates. Building on this insight, we develop a novel bi-variate stochastic framework based on mixed fractional Brownian…

Risk Management · Quantitative Finance 2025-08-26 Kenneth Q. Zhou , Hongjuan Zhou

We construct a binomial tree model fitting all moments to the approximated geometric Brownian motion. Our construction generalizes the classical Cox-Ross-Rubinstein, the Jarrow-Rudd, and the Tian binomial tree models. The new binomial model…

Pricing of Securities · Quantitative Finance 2016-12-07 Y. S. Kim , S. Stoyanov , S. Rachev , F. Fabozzi

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…

Probability · Mathematics 2020-06-03 David J. Santana , Luis Rincon

Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different…

Statistical Mechanics · Physics 2025-03-10 Michał Balcerek , Adrian Pacheco-Pozo , Agnieszka Wyłomanska , Krzysztof Burnecki , Diego Krapf

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

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…

Probability · Mathematics 2015-09-24 Hélène Guérin , Jean-François Renaud

Let B_1,B_2, ... be independent one-dimensional Brownian motions defined over the whole real line such that B_i(0)=0. We consider the nth iterated Brownian motion W_n(t)= B_n(B_{n-1}(...(B_2(B_1(t)))...)). Although the sequences of…

Probability · Mathematics 2011-12-19 Nicolas Curien , Takis Konstantopoulos

In this paper, we develop a theory of common decomposition for two correlated Brownian motions, in which, by using change of time method, the correlated Brownian motions are represented by a triplet of processes, $(X,Y,T)$, where $X$ and…

Mathematical Finance · Quantitative Finance 2020-11-10 Tianyao Chen , Xue Cheng , Jingping Yang

In ruin theory, the net profit condition intuitively means that the incurred random claims on average do not occur more often than premiums are gained. The breach of the net profit condition causes guaranteed ruin in few but simple cases…

Probability · Mathematics 2024-01-08 Andrius Grigutis , Arvydas Karbonskis , Jonas Šiaulys

This paper focuses on a discrete-time risk model in which both insurance risk and financial risk are taken into account. We study the asymptotic behaviour of the ruin probability and the tail probability of the aggregate risk amount.…

Probability · Mathematics 2019-02-20 Enkelejd Hashorva , Jinzhu Li

In this text, we establish the risk model based on AR(1) series and propose the basic model which has a dependent structure under intensity of claim number. Considering some properties of the risk model, we take advantage of newton…

Risk Management · Quantitative Finance 2017-10-31 Wenhao Li , Bolong Wang , Tianxiang Shen , Ronghua Zhu , Dehui Wang

We study solvency of insurers in a comprehensive model where various economic factors affect the capital developments of the companies. The main interest is in the impact of real growth to ruin probabilities. The volume of the business is…

Probability · Mathematics 2015-11-06 Harri Nyrhinen