The Gerber–Shiu Discounted Penalty Function for the Bi-Seasonal Discrete Time Risk Model

Navickienė, Olga; Sprindys, Jonas; Šiaulys, Jonas

doi:10.15388/Informatica.2018.190

Informatica

The Gerber–Shiu Discounted Penalty Function for the Bi-Seasonal Discrete Time Risk Model

Volume 29, Issue 4 (2018), pp. 733–756

Olga Navickienė Jonas Sprindys Jonas Šiaulys

https://doi.org/10.15388/Informatica.2018.190

Pub. online: 1 January 2018 Type: Research Article

Open Access

Received
1 March 2018

Accepted
1 October 2018

Published
1 January 2018

Abstract

In this work, the discrete time risk model with two seasons is considered. In such model, the claims repeat with time periods of two units, i.e. claim distributions coincide at all even instants and at all odd instants. Our purpose is to derive an algorithm for calculating the values of the particular case of the Gerber–Shiu discounted penalty function $\mathbb{E}({\mathrm{e}^{-\delta T}}{\mathbb{1}_{\{T<\infty \}}})$, where T is the time of ruin, and δ is a constant nonnegative force of interest. Theoretical results are illustrated by some numerical examples.

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Biographies

Navickienė Olga

O. Navickienė is a PhD student at Institute of Mathematics of Vilnius University. Her research interests include probability theory, actuarial mathematics and economics.

Sprindys Jonas

J. Sprindys is a PhD student at Institute of Mathematics of Vilnius University. His research interests include probability theory, risk theory and actuarial mathematics.

Šiaulys Jonas

jonas.siaulys@mif.vu.lt

J. Šiaulys is a professor at Institute of Mathematics of Vilnius University. His fields of interest are number theory, probability theory, risk theory and actuarial mathematics. He has authored or co-authored around 80 papers.

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Keywords

bi-seasonal model discrete time risk model Gerber–Shiu function penalty function; time of ruin

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