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Corrected normal approximation for the probability of ruin within finite time [PDF]

Scandinavian Actuarial Journal, 1994
Abstract A new second-order approximation for the probability of ruin before time t in the framework of Andersen's risk model is suggested. This approximation is proved to be a refinement of the classical normal-type approximation and is deduced from von Bahr's representation of ruin probability in terms of ladder height distributions.
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The probability of ruin in finite time with discrete claim size distribution

Scandinavian Actuarial Journal, 1997
Abstract The ruin time T is considered as the time of first crossing between a compound Poisson trajectory and an upper increasing boundary. Under the assumption that the claim sizes are integer-valued, we show that the distribution of T can be expressed in terms of generalized Appell polynomials.
Philippe Picard, Claude Lefèvre
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Uniform Asymptotics for Finite-time Ruin Probability in a Dependent Risk Model with General Stochastic Investment Return Process

Acta Mathematicae Applicatae Sinica (English Series), 2021
Yang Yang, K. Yuen, Jun-feng Liu
semanticscholar   +1 more source

A note on the uniform asymptotic behavior of the finite-time ruin probability in a nonstandard renewal risk model

Lithuanian Mathematical Journal, 2020
Yuquan Cang, Yang Yang, Xixi Shi
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A property of the renewal counting process with application to the finite-time ruin probability

Lithuanian Mathematical Journal, 2009
We consider the renewal counting process \( \mathit{\Theta} \left( t \right) = \sup \left\{ {n \geqslant 1:\theta_1 + \cdots + \theta_n \leqslant t} \right\} \), where θ1, θ2,… are nonnegative independent identically distributed nondegenerate random variables with finite mean. The asymptotics for the tail of the exponential moment are derived.
Remigijus Leipus, Jelena Kočetova, Jonas Šiaulys   +2 more
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An improved finite-time ruin probability formula and its Mathematica implementation

Insurance: Mathematics and Economics, 2001
Abstract An improved version of a ruin probability formula due to Ignatov and Kaishev [Scand. Actu. J. 1 (2000) 46], allowing for the exact evaluation of the finite-time survival probability for discrete, dependent, individual claims, Poisson claim arrivals and arbitrary, increasing premium income function is derived.
Zvetan G. Ignatov, Rossen S. Krachunov, Vladimir K. Kaishev, Vladimir K. Kaishev   +3 more
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The finite-time ruin probability of time-dependent risk model with stochastic return and Brownian perturbation

Japan journal of industrial and applied mathematics, 2020
Baoyin Xun, Kaiyong Wang, K. Yuen
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An optimal consumption problem in finite time with a constraint on the ruin probability

Finance and Stochastics, 2015
In this paper, we investigate the following problem: For a given upper bound for the ruin probability, maximize the expected discounted consumption of an investor in finite time. The endowment of the agent is modeled by a Brownian motion with positive drift.
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Finite-time ruin probability for Erlang risk model with exponential claims

The 2nd International Conference on Information Science and Engineering, 2010
In this paper, under the conditions that the claimsize is exponentially distributed, a simple asymptotic of ruin probability for Erlang risk model within finite time is obtained. The result contained the classical Cramer-Lundberg model as special case.
Jiang Tao, Tong Congyan
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Explicit finite-time and infinite-time ruin probabilities in the continuous case

Insurance: Mathematics and Economics, 1999
Abstract In this rather self-contained paper we indicate general explicit analytic expressions for finite-time and infinite-time ruin probabilities in the classical risk model corresponding to initial risk reserves u≥0. We assume that the claimsize distribution has a density on [0,∞).
F. Etienne De Vylder, Marc Goovaerts
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