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Optimal reinsurance when Value at Risk and expected surplus is balanced through their ratio is studied, and it is demonstrated how results for risk-adjusted surplus can be utilized. Simplifications for large portfolios are derived, and this…

Applications · Statistics 2019-12-10 Erik Bølviken , Yinzhi Wang

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…

Probability · Mathematics 2024-10-11 Yang Chen , Zhaolei Cui , Yuebao Wang

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

In this paper, we study an optimal reinsurance-investment problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. We assume that the…

Optimization and Control · Mathematics 2020-10-26 Xia Han , Zhibin Liang

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

We consider an optimal control problem of a property insurance company with proportional reinsurance strategy. The insurance business brings in catastrophe risk, such as earthquake and flood. The catastrophe risk could be partly reduced by…

Risk Management · Quantitative Finance 2010-09-08 Zongxia Liang , Lin He , Jiaoling Wu

The aim of this paper is to construct the confidence interval of the ultimate ruin probability under the insurance surplus driven by a L\'evy process. Assuming a parametric family for the L\'evy measures, we estimate the parameter from the…

Probability · Mathematics 2021-12-15 Yasutaka Shimizu

The net-premium principle is considered to be the most genuine and fair premium principle in actuarial applications. However, an insurance company, applying the net-premium principle, goes bankrupt with probability one in the long run, even…

Risk Management · Quantitative Finance 2013-04-03 Alois Pichler

We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an…

General Finance · Quantitative Finance 2015-03-17 Edward Hoyle , Lane P. Hughston , Andrea Macrina

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…

Risk Management · Quantitative Finance 2010-11-08 Serguei Pergamenchtchikov , Zeitouny Omar

In this paper, we study finite-time ruin probabilities for the compound Markov binomial risk model - a discrete-time model where claim sizes are modulated by a finite-state ergodic Markov chain. In the classic (non-modulated) case, the risk…

Probability · Mathematics 2025-07-23 Zbigniew Palmowski , Lewis Ramsden , Apostolos D. Papaioannou

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

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…

Probability · Mathematics 2022-10-12 Pavlina K. Jordanova , Evelina Veleva

The main purpose of the paper is to study ruin probabilities in two discrete time risk models under rates of interest, where the premiums and claims are two independent sequences of m-dependent random variables, and the rate of interest is…

Probability · Mathematics 2025-08-21 Nguyen Huy Hoang , Tran Dinh Phung

A second order linear integro-differential equation with Volterra integral operator and strong singularities at the endpoints (zero and infinity) is considered. Under limit conditions at the singular points, and some natural assumptions,…

Risk Management · Quantitative Finance 2015-11-30 Tatiana Belkina , Nadezhda Konyukhova , Sergey Kurochkin

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…

Probability · Mathematics 2010-04-21 Irmina Czarna , Zbigniew Palmowski

We study an optimal reinsurance problem under a diffusion risk model for an insurer who aims to minimize the probability of lifetime ruin. To rule out moral hazard issues, we only consider moral-hazard-free reinsurance contracts by imposing…

Mathematical Finance · Quantitative Finance 2023-04-19 Zhuo Jin , Zuo Quan Xu , Bin Zou

We formulate a dynamic reinsurance problem in which the insurer seeks to control the terminal distribution of its surplus while minimizing the L2-norm of the ceded risk. Using techniques from martingale optimal transport, we show that,…

Risk Management · Quantitative Finance 2026-01-16 Beatrice Acciaio , Brandon Garcia Flores , Antonio Marini , Gudmund Pammer

We consider the classical Cram\'er-Lundberg risk model with claim sizes that are mixtures of phase-type and subexponential variables. Exploiting a specific geometric compound representation, we propose control variate techniques to…

Probability · Mathematics 2020-06-16 Hansjörg Albrecher , Martin Bladt , Eleni Vatamidou

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