Afrika Statistika

Ruin Probabilities in Perturbed Risk Process with Stochastic Investment and Force of interest

Bamidele Mustapha Oseni and Emmanuel Teju Jolayemi

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Abstract

This work considers a perturbed risk process with investment, where the investments are either into invested in risky and risk-less assets. A third order differential equation for the ruin probability is derived from the resulting integro-differential equation. This equation is further decomposed into two equations describing the contributions of the claim and oscillation to the ruin probability. These two equations are solved separately using suitable transformations as well as theory of Kummer confluence hypergeometric equations. We further investigated these solutions and were able to conclude that the higher the fraction of investment into risky assets, the lower the ruin probability, provided all other parameters are kept constant.

Résumé

Ce travail considère un processus de risque perturbé avec investissement, où les investissements sont investis dans des actifs risqués et sans risque. Une équation différentielle de troisième ordre pour la probabilité de ruine est dérivée de l'équation intégro-différentielle résultante. Cette équation est décomposée en deux équations décrivant les contributions de la revendication et de l'oscillation à la probabilité de ruine. Ces deux équations sont résolues séparément en utilisant des transformations appropriées ainsi que la théorie des équations hypergéométriques de confluence de Kummer. Nous avons étudié ces solutions et avons pu conclure que plus la fraction de l'investissement dans les actifs risqués est élevée, plus la probabilité de ruine est faible, à condition que tous les autres paramètres restent constants.

Article information

Source
Afr. Stat., Volume 13, Number 2 (2018), 1593-1608.

Dates
First available in Project Euclid: 7 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.as/1528336822

Digital Object Identifier
doi:10.16929/as/1593.123

Mathematical Reviews number (MathSciNet)
MR3811759

Zentralblatt MATH identifier
06885662

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces 60J60: Diffusion processes [See also 58J65]

Keywords
Risk Reserve Ruin Probability Interest Stochastic Investment Exponential distribution Kummer hypergeometric equation

Citation

Oseni, Bamidele Mustapha; Jolayemi, Emmanuel Teju. Ruin Probabilities in Perturbed Risk Process with Stochastic Investment and Force of interest. Afr. Stat. 13 (2018), no. 2, 1593--1608. doi:10.16929/as/1593.123. https://projecteuclid.org/euclid.as/1528336822


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