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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…

Probability · Mathematics 2018-07-02 Pierre-Olivier Goffard , Andrey Sarantsev

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

We study a Sparre Andersen model in which the business activity of the company is described by a compound renewal process with drift assuming that the capital reserves are invested in a risky asset. The price of the latter is assumed to…

Probability · Mathematics 2020-12-15 Ernst Eberlain , Yuri Kabanov , Thorsten Schmidt

This paper considers the ruin problem with random premiums, whose densities have rational Laplace transforms, and investments in a risky asset whose price follows a geometric Brownian motion. The asymptotic behavior of the ruin probability…

Probability · Mathematics 2025-08-12 Viktor Antipov

In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{\'e}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin…

Probability · Mathematics 2018-07-02 Lioudmila Vostrikova , Jérôme Spielmann

Let $(Z_n)_{n\geqslant 0}$ be a branching process in a random environment defined by a Markov chain $(X_n)_{n\geqslant 0}$ with values in a finite state space $\mathbb X$ starting at $X_0=i \in\mathbb X$. We extend from the i.i.d.…

Probability · Mathematics 2017-08-02 Ion Grama , Ronan Lauvergnat , Emile Le Page

Whereas classical Markov decision processes maximize the expected reward, we consider minimizing the risk. We propose to evaluate the risk associated to a given policy over a long-enough time horizon with the help of a central limit…

Optimization and Control · Mathematics 2015-12-03 Pengqian Yu , Jia Yuan Yu , Huan Xu

In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance…

Computational Finance · Quantitative Finance 2013-08-15 Hansjörg Albrecher , Corina Constantinescu , Zbigniew Palmowski , Georg Regensburger , Markus Rosenkranz

We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival time distributions depending on the claims that arrived within a fixed (past) time window. This dependence could be explained through a regenerative…

Probability · Mathematics 2016-04-22 Corina Constantinescu , Suhang Dai , Weihong Ni , Zbigniew Palmowski

The risk premium of a policy is the sum of the pure premium and the risk loading. In the classification ratemaking process, generalized linear models are usually used to calculate pure premiums, and various premium principles are applied to…

Applications · Statistics 2022-01-07 Liang Yang , Zhengxiao Li , Shengwang Meng

We consider a risk model with a counting process whose intensity is a Markovian shot-noise process, to resolve one of the disadvantages of the Cram\'er-Lundberg model, namely the constant jump intensity of the Poisson process. Due to this…

Probability · Mathematics 2022-05-11 Simon Pojer , Stefan Thonhauser

We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state…

Optimization and Control · Mathematics 2017-11-22 Xin Guo , Yi Zhang

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

The paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing a…

Probability · Mathematics 2023-11-21 Viktor Antipov , Yuri Kabanov

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

Lundberg-type inequalities for ruin probabilities of non-homogeneous risk models are presented in this paper. By employing martingale method, the upper bounds of ruin probabilities are obtained for the general risk models under weak…

Probability · Mathematics 2020-06-05 Qianqian Zhou , Alexander Sakhanenko , Junyi Guo

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…

Probability · Mathematics 2018-02-26 Jérôme Spielmann

We analyze the limiting behavior of the risk premium associated with the Pareto optimal risk sharing contract in an infinitely expanding pool of risks under a general class of law-invariant risk measures encompassing rank-dependent utility…

Risk Management · Quantitative Finance 2021-07-06 Thomas Knispel , Roger J. A. Laeven , Gregor Svindland

We investigate models of the life annuity insurance when the company invests its reserve into a risky asset with price following a geometric Brownian motion. Our main result is an exact asymptotic of the ruin probabilities for the case of…

Probability · Mathematics 2015-05-19 Yuri Kabanov , Serguei Pergamenshchikov

In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as…

Probability · Mathematics 2013-06-21 Jean-François Renaud