On a renewal risk process with dependence under a Farlie - Gumbel - Morgenstern copula

Chadjiconstantinidis, S. and Vrontos, S. 2014. On a renewal risk process with dependence under a Farlie - Gumbel - Morgenstern copula. Scandinavian Actuarial Journal. 2014 (2), pp. 125-158.

TitleOn a renewal risk process with dependence under a Farlie - Gumbel - Morgenstern copula
AuthorsChadjiconstantinidis, S. and Vrontos, S.
Abstract

In this article, we consider an extension to the renewal or Sparre Andersen risk process by introducing a dependence structure between the claim sizes and the interclaim times through a Farlie–Gumbel–Morgenstern copula proposed by Cossette et al. (2010) for the classical compound Poisson risk model. We consider that the inter-arrival times follow the Erlang(n) distribution. By studying the roots of the generalised Lundberg equation, the Laplace transform (LT) of the expected discounted penalty function is derived and a detailed analysis of the Gerber–Shiu function is given when the initial surplus is zero. It is proved that this function satisfies a defective renewal equation and its solution is given through the compound geometric tail representation of the LT of the time to ruin. Explicit expressions for the discounted joint and marginal distribution functions of the surplus prior to the time of ruin and the deficit at the time of ruin are derived. Finally, for exponential claim sizes explicit expressions and numerical examples for the ruin probability and the LT of the time to ruin are given.

JournalScandinavian Actuarial Journal
Journal citation2014 (2), pp. 125-158
ISSN0346-1238
Year2014
PublisherTaylor & Francis
Digital Object Identifier (DOI)doi:10.1080/03461238.2012.663730
Publication dates
Published2014

Related outputs

A quantile regression approach to equity premium prediction
Meligkotsidou, L., Panopoulou, E., Vrontos, I.D. and Vrontos, S. 2014. A quantile regression approach to equity premium prediction. Journal of Forecasting. 33 (7), pp. 558-576.

Performance evaluation of mutual fund investments: the impact of non-normality and time-varying volatility
Vrontos, I.D., Meligkotsidou, L. and Vrontos, S. 2011. Performance evaluation of mutual fund investments: the impact of non-normality and time-varying volatility. Journal of Asset Management. 12 (4), pp. 292-307.

Quantile regression analysis of hedge fund strategies
Meligkotsidou, L., Vrontos, I.D. and Vrontos, S. 2009. Quantile regression analysis of hedge fund strategies. Journal of Empirical Finance. 16 (2), pp. 264-279.

Hedge fund pricing and model uncertainty
Vrontos, S., Vrontos, I.D. and Giamouridis, D. 2008. Hedge fund pricing and model uncertainty. Journal of Banking and Finance. 32 (5), pp. 741-753.

Permalink - https://westminsterresearch.westminster.ac.uk/item/8yq31/on-a-renewal-risk-process-with-dependence-under-a-farlie-gumbel-morgenstern-copula


Share this
Tweet
Email