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Ruin Probabilities in Perturbed Risk Process with Stochastic Investment and Force of interest
- Source :
- Afr. Stat. 13, no. 2 (2018), 1593-1608, Afrika Statistika; Vol 13, No 2 (2018); 1593-1608
- Publication Year :
- 2018
- Publisher :
- The Statistics and Probability African Society, 2018.
-
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 integrodifferential 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. Keywords: Risk Reserve; Ruin Probability; Interest; Stochastic Investment; Exponential distribution; Kummer hyper-geometric equation AMS 2010 Mathematics Subject Classification : 60J25; 60J60
- Subjects :
- Exponential distribution
Stochastic Investment
Mathematics::Optimization and Control
Ruin Probability
Kummer hypergeometric equation
Investment (macroeconomics)
Hypergeometric distribution
Actuarial notation
Mathematics Subject Classification
Risk process
60J25
Risk Reserve
General Earth and Planetary Sciences
Applied mathematics
Interest
Fraction (mathematics)
Constant (mathematics)
General Environmental Science
Mathematics
60J60
Subjects
Details
- Language :
- English
- ISSN :
- 2316090X
- Database :
- OpenAIRE
- Journal :
- Afr. Stat. 13, no. 2 (2018), 1593-1608, Afrika Statistika; Vol 13, No 2 (2018); 1593-1608
- Accession number :
- edsair.doi.dedup.....c00545ba4dcab8be7f95848f8b08bdbd