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Using the results of precise large deviation and renewal theory for widely dependent random variables, this paper obtains the asymptotic estimation of the random-time ruin probability and the uniform asymptotic estimation of finite-time…

Probability · Mathematics 2025-06-24 Yang Chen , Zhaolei Cui , Yuebao Wang

The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions.} Under the condition that the two Brownian motions $\{B_1(t), t\ge 0\}$ and…

Probability · Mathematics 2023-06-29 Dan Zhu , Ming Zhou , Chuancun Yin

In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve…

Risk Management · Quantitative Finance 2008-12-02 Henrik Hult , Filip Lindskog

This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common Markovian environmental process. We subsequently…

Probability · Mathematics 2018-12-24 G. A. Delsing , M. R. H. Mandjes , P. J. C. Spreij , E. M. M. Winands

We formulate the insurance risk process in a general Levy process setting, and give general theorems for the ruin probability and the asymptotic distribution of the overshoot of the process above a high level, when the process drifts to…

Probability · Mathematics 2007-05-23 Claudia Kluppelberg , Andreas E. Kyprianou , Ross A. Maller

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

The ruin probability in the classical Brownian risk model can be explicitly calculated for both finite and infinite-time horizon. This is not the case for the simultaneous ruin probability in two-dimensional Brownian risk model. Resorting…

Probability · Mathematics 2018-11-13 Krzysztof Dȩbicki , Enkelejd Hashorva , Zbigniew Michna

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

We analyze the distance $\mathcal{R}_T(u)$ between the first and the last passage time of $\{X(t)-ct:t\in [0,T]\}$ at level $u$ in time horizon $T\in(0,\infty]$, where $X$ is a centered Gaussian process with stationary increments and…

Probability · Mathematics 2018-01-09 Krzysztof Debicki , Peng Liu

We study the discrete time risk process modelled by the skip-free random walk and we derive the results connected to the ruin probability, such as crossing the fixed level, for this kind of process. We use the method relying on the…

Probability · Mathematics 2017-09-08 Ivana Geček Tuđen

This paper studies the tail probability of weighted sums of the form $\sum_{i=1}^n c_i X_i$, where random variables $X_i$'s are either independent or pairwise quasi-asymptotical independent with heavy tails. Using $h$-insensitive function,…

Probability · Mathematics 2014-04-01 Chenhua Zhang

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

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 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

For a given centered Gaussian process with stationary increments $\{X(t), t\geq 0\}$ and $c>0$, let $$ W_\gamma(t)=X(t)-ct-\gamma\inf_{0\leq s\leq t}\left(X(s)-cs\right), \quad t\geq 0$$ denote the $\gamma$-reflected process, where…

Probability · Mathematics 2017-11-08 Krzysztof Debicki , Enkelejd Hashorva , Peng Liu

Let $\chi_n(t) = (\sum_{i=1}^n X_i^2(t))^{1/2},t\ge0$ be a chi-process with $n$ degrees of freedom where $X_i$'s are independent copies of some generic centered Gaussian process $X$. This paper derives the exact asymptotic behavior of…

Probability · Mathematics 2013-09-03 Enkelejd Hashorva , Lanpeng Ji

Consider a multi-dimensional Brownian motion which models the surplus processes of multiple lines of business of an insurance company. Our main result gives exact asymptotics for the cumulative Parisian ruin probability as the initial…

Probability · Mathematics 2020-04-28 Lanpeng Ji

We apply the theory of linear recurrence sequences to find an expression for the ultimate ruin probability in a discrete-time risk process. We assume the claims follow an arbitrary distribution with support $\{0,1,\ldots,m\}$, for some…

Probability · Mathematics 2023-02-14 David J. Santana , Luis Rincón

In this paper we consider some generalizations of the classical d-dimensional Brownian risk model. This contribution derives some non-asymptotic bounds for simultaneous ruin probabilities of interest. In addition, we obtain non-asymptotic…

Probability · Mathematics 2022-05-17 Nikolai Kriukov

In this paper we consider a compound Poisson risk model with regularly varying claim sizes. For this model in [1] an asymptotic formula for the finite time ruin probability is provided when the time is scaled by the mean excess function. In…

Probability · Mathematics 2011-12-13 Søren Asmussen , Dominik Kortschak