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

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

Pub. online: 1 January 2018
Type: Research Article
Open Access

Received

1 March 2018

1 March 2018

Accepted

1 October 2018

1 October 2018

Published

1 January 2018

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.#### 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

**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.