A link between wave governed random motions and ruin processes

Mazza, Christian; Rullière, Didier

doi:10.1016/j.insmatheco.2004.07.014

Cited by 50 publications

(31 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As in the insurance risk model, ruin probability under the dual risk model has also attracted considerable attention. Mazza and Rullière (2004) consider ruin in both the classical insurance and dual risk models and establish a link between them based on wave governed random motion. Dong and Wang (2008) are concerned with the ultimate ruin probability in a dual risk model with generalized assumptions on the capital gain arrival process.…”

Section: S(t)mentioning

confidence: 99%

“…It is worth mentioning that in Mazza and Rullière (2004), both the classical insurance risk model and its corresponding dual risk model are studied and a link between these two models is given based on a wave governed random motion. Our demonstration of the connection is different, more straightforward and applies under more general assumptions.…”

Section: S(t)mentioning

confidence: 99%

“…The assumptions made on the dual risk model are significantly more general than the classical ones (see e.g., Mazza and Rullière (2004) Under this general dual risk model, we consider the probability of non-ruin within a finite time interval [0, x], denoted by P (T dual > x). In order to obtain an explicit formula for P (T dual > x), we note that the definition of the ruin time T dual can be re-written as…”

Section: S(t)mentioning

confidence: 99%

See 2 more Smart Citations

On finite-time ruin probabilities in a generalized dual risk model with dependence

Dimitrova

Kaishev

Zhao

2015

European Journal of Operational Research

View full text Add to dashboard Cite

Citation: Dimitrova, D. S., Kaishev, V. K. and Zhao, S. (2015). On finite-time ruin probabilities in a generalized dual risk model with dependence. European Journal of Operational Research, 242(1), pp. 134-148. doi: 10.1016Research, 242(1), pp. 134-148. doi: 10. /j.ejor.2014 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractIn this paper, we study the finite-time ruin probability in a reasonably generalized dual risk model, where we assume any non-negative non-decreasing cumulative operational cost function and arbitrary capital gains arrival process. Establishing an enlightening link between this dual risk model and its corresponding insurance risk model, explicit expressions for the finite-time survival probability in the dual risk model are obtained under various general assumptions for the distribution of the capital gains. In order to make the model more realistic and general, different dependence structures among capital gains and inter-arrival times and between both are also introduced and corresponding ruin probability expressions are also given. The concept of alarm time, as introduced in Das and Kratz (2012), is applied to the dual risk model within the context of risk capital allocation. Extensive numerical illustrations are provided.

show abstract

Section: S(t)mentioning

confidence: 99%

Section: S(t)mentioning

confidence: 99%

Section: S(t)mentioning

confidence: 99%

See 1 more Smart Citation

On finite-time ruin probabilities in a generalized dual risk model with dependence

Dimitrova

Kaishev

Zhao

2015

European Journal of Operational Research

View full text Add to dashboard Cite

show abstract

“…We can also link the involved ruin probability with the probability that a classical process reaches an upper barrier. For more details, see Mazza and Rullière (2004).…”

Section: Discrete Claim Amount Distributionmentioning

confidence: 99%

Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin

Loisel

Mazza

Rullière

2008

Insurance: Mathematics and Economics

Self Cite

View full text Add to dashboard Cite

We consider the classical risk model and carry out a sensitivity and robustness analysis of finite-time ruin probabilities. We provide algorithms to compute the related influence functions. We also prove the weak convergence of a sequence of empirical finite-time ruin probabilities starting from zero initial reserve toward a Gaussian random variable. We define the concepts of reliable finite-time ruin probability as a Value-at-Risk of the estimator of the finite-time ruin probability. To control this robust risk measure, an additional initial reserve is needed and called Estimation Risk Solvency Margin (ERSM). We apply our results to show how portfolio experience could be rewarded by cut-offs in solvency capital requirements. An application to catastrophe contamination and numerical examples are also developed.JEL classification: G22; C60

show abstract

“…This seems a realistic way to model paths of assets in the financial markets. Mazza and Rullière [14] linked the process (1) and the ruin processes in the context of risk theory. Di Masi, Y. Kabanov, and W. Runggaldier [5] proposed to model the volatility of financial markets in terms of the telegraph process.…”

Section: Introductionmentioning

confidence: 99%

Estimation for the discretely observed telegraph process

Iacus

Yoshida

2009

Theor. Probability and Math. Statist.

View full text Add to dashboard Cite

Abstract. The telegraph process {X(t), t > 0} is supposed to be observed at n + 1 equidistant time points t i = i∆ n , i = 0, 1, . . . , n. The unknown value of λ, the underlying rate of the Poisson process, is a parameter to be estimated. The asymptotic framework considered is the following: ∆ n → 0, n∆ n = T → ∞ as n → ∞. We show that previously proposed moment type estimators are consistent and asymptotically normal but not efficient. We study further an approximated moment type estimator which is still not efficient but comes in explicit form. For this estimator the additional assumption n∆ 3 n → 0 is required in order to obtain asymptotic normality. Finally, we propose a new estimator which is consistent, asymptotically normal and asymptotically efficient under no additional hypotheses.

show abstract

A link between wave governed random motions and ruin processes

Cited by 50 publications

References 14 publications

On finite-time ruin probabilities in a generalized dual risk model with dependence

On finite-time ruin probabilities in a generalized dual risk model with dependence

Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin

Estimation for the discretely observed telegraph process

Contact Info

Product

Resources

About