On ruin probabilities in risk models with interest rate

Nino Kordzakhia; Alexander Novikov; Gurami Tsitsiashvili

doi:10.1007/978-88-470-2342-0_29

On ruin probabilities in risk models with interest rate

Nino Kordzakhia^*, Alexander Novikov, Gurami Tsitsiashvili

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

1 Citation (Scopus)

Abstract

An explicit formula for the finite-time ruin probability in a discrete-time collective ruin model with constant interest rate is found under the assumption that claims follow a generalised hyperexponential distribution. The formula can be used for finding approximations for finite-time ruin probabilities in the case when claim sizes follow a heavy-tailed distribution e.g. Pareto. We also provide theoretical bounds for the accuracy of approximations of the finite-time ruin probabilities in terms of a distance between the distribution of claims and its approximation. Results of numerical comparisons with asymptotic formulas and simulations are presented.

Original language	English
Title of host publication	Mathematical and Statistical Methods for Actuarial Sciences and Finance
Editors	Cira Perna, Marilena Sibillo
Place of Publication	Milan, Italy
Publisher	Springer, Springer Nature
Pages	245-253
Number of pages	9
ISBN (Print)	9788847023413
DOIs	https://doi.org/10.1007/978-88-470-2342-0_29
Publication status	Published - 2012
Event	5th International Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2012 - Venice, Italy Duration: 10 Apr 2012 → 12 Apr 2012

Other

Other	5th International Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2012
Country/Territory	Italy
City	Venice
Period	10/04/12 → 12/04/12

Access to Document

10.1007/978-88-470-2342-0_29

Cite this

@inproceedings{2e41dcdae6c848688e6777720915ac62,

title = "On ruin probabilities in risk models with interest rate",

abstract = "An explicit formula for the finite-time ruin probability in a discrete-time collective ruin model with constant interest rate is found under the assumption that claims follow a generalised hyperexponential distribution. The formula can be used for finding approximations for finite-time ruin probabilities in the case when claim sizes follow a heavy-tailed distribution e.g. Pareto. We also provide theoretical bounds for the accuracy of approximations of the finite-time ruin probabilities in terms of a distance between the distribution of claims and its approximation. Results of numerical comparisons with asymptotic formulas and simulations are presented.",

author = "Nino Kordzakhia and Alexander Novikov and Gurami Tsitsiashvili",

year = "2012",

doi = "10.1007/978-88-470-2342-0_29",

language = "English",

isbn = "9788847023413",

pages = "245--253",

editor = "Cira Perna and Marilena Sibillo",

booktitle = "Mathematical and Statistical Methods for Actuarial Sciences and Finance",

publisher = "Springer, Springer Nature",

address = "United States",

note = "5th International Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2012 ; Conference date: 10-04-2012 Through 12-04-2012",

}

Kordzakhia, N, Novikov, A & Tsitsiashvili, G 2012, On ruin probabilities in risk models with interest rate. in C Perna & M Sibillo (eds), Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Springer Nature, Milan, Italy, pp. 245-253, 5th International Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2012, Venice, Italy, 10/04/12. https://doi.org/10.1007/978-88-470-2342-0_29

On ruin probabilities in risk models with interest rate. / Kordzakhia, Nino; Novikov, Alexander; Tsitsiashvili, Gurami.
Mathematical and Statistical Methods for Actuarial Sciences and Finance. ed. / Cira Perna; Marilena Sibillo. Milan, Italy: Springer, Springer Nature, 2012. p. 245-253.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

TY - GEN

T1 - On ruin probabilities in risk models with interest rate

AU - Kordzakhia, Nino

AU - Novikov, Alexander

AU - Tsitsiashvili, Gurami

PY - 2012

Y1 - 2012

N2 - An explicit formula for the finite-time ruin probability in a discrete-time collective ruin model with constant interest rate is found under the assumption that claims follow a generalised hyperexponential distribution. The formula can be used for finding approximations for finite-time ruin probabilities in the case when claim sizes follow a heavy-tailed distribution e.g. Pareto. We also provide theoretical bounds for the accuracy of approximations of the finite-time ruin probabilities in terms of a distance between the distribution of claims and its approximation. Results of numerical comparisons with asymptotic formulas and simulations are presented.

AB - An explicit formula for the finite-time ruin probability in a discrete-time collective ruin model with constant interest rate is found under the assumption that claims follow a generalised hyperexponential distribution. The formula can be used for finding approximations for finite-time ruin probabilities in the case when claim sizes follow a heavy-tailed distribution e.g. Pareto. We also provide theoretical bounds for the accuracy of approximations of the finite-time ruin probabilities in terms of a distance between the distribution of claims and its approximation. Results of numerical comparisons with asymptotic formulas and simulations are presented.

UR - http://www.scopus.com/inward/record.url?scp=84900654351&partnerID=8YFLogxK

U2 - 10.1007/978-88-470-2342-0_29

DO - 10.1007/978-88-470-2342-0_29

M3 - Conference proceeding contribution

AN - SCOPUS:84900654351

SN - 9788847023413

SP - 245

EP - 253

BT - Mathematical and Statistical Methods for Actuarial Sciences and Finance

A2 - Perna, Cira

A2 - Sibillo, Marilena

PB - Springer, Springer Nature

CY - Milan, Italy

T2 - 5th International Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2012

Y2 - 10 April 2012 through 12 April 2012

ER -

On ruin probabilities in risk models with interest rate

Abstract

Other

Access to Document

Other files and links

Fingerprint

Cite this