A numerical method to find the probability of ultimate ruin in the classical risk model with stochastic return on investments

Paulsen, Jostein; Kasozi, Juma; Steigen, Andreas

doi:10.1016/j.insmatheco.2005.02.008

Cited by 17 publications

(31 citation statements)

References 28 publications

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“…provided g is four times continuously differentiable as is the case here by Theorem 2.1 in Paulsen et al [23] . On the other hand, ( ) With this value of…”

Section: Methodsmentioning

confidence: 80%

“…Note that the stepsize in Table 4 is 10 times that in Table 1-3. For a detailed description of such a model, see e.g Paulsen et al [23] . The same method is likely to work once the corresponding Volterra equation is obtained.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In the event that the distribution is difficult to achieve analytically, Simpson's rule can be employed. Such an approach was used in Paulsen et al [23] .…”

Section: Numerical Resultsmentioning

confidence: 99%

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Numerical Ultimate Ruin Probabilities under Interest Force

Kasozi¹,

Paulsen²

2005

J. of Mathematics and Statistics

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This work addresses the issue of ruin of an insurer whose portfolio is exposed to insurance risk arising from the classical surplus process. Availability of a positive interest rate in the financial world forces the insurer to invest into a risk free asset. We derive a linear Volterra integral equation of the second kind and apply an order four Block-by-block method in conjuction with the Simpson rule to solve the Volterra equation for ultimate ruin. This probability is arrived at by taking a linear combination of some two solutions to the Volterra integral equation. The several numerical examples given show that our results are excellent and reliable.

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“…provided g is four times continuously differentiable as is the case here by Theorem 2.1 in Paulsen et al [23] . On the other hand, ( ) With this value of…”

Section: Methodsmentioning

confidence: 80%

Section: Numerical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Ultimate Ruin Probabilities under Interest Force

Kasozi¹,

Paulsen²

2005

J. of Mathematics and Statistics

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“…In [51], following an idea from [63], but allowing σ 2 P > 0, using integration by parts the equation (2.2) was turned into a Volterra integral equation and methods from numerical analysis was used to solve this numerically. In the finite time case several methods have been proposed when σ P = σ R = 0, see e.g.…”

Section: Analytical and Numerical Solutionsmentioning

confidence: 99%

Ruin Models with Investment Income

Paulsen

2010

Encyclopedia of Quantitative Finance

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This survey treats the problem of ruin in a risk model when assets earn investment income. In addition to a general presentation of the problem, topics covered are a presentation of the relevant integrodifferential equations, exact and numerical solutions, asymptotic results, bounds on the ruin probability and also the possibility of minimizing the ruin probability by investment and possibly reinsurance control. The main emphasis is on continuous time models, but discrete time models are also covered. A fairly extensive list of references is provided, particularly of papers published after 1998. For more references to papers published before that, the reader can consult [47].

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“…To enhance his financial base, the insurer invests in a risk free asset whose price dynamics are governed by a constant force of interest. We derive a linear Volterra integral equation of the second kind and apply an order four Block-byblock method of Paulsen et al [1] in conjunction with the Simpson rule to solve the Volterra integral equations for each chosen barrier thus generating corresponding dividend value functions. We have obtained the optimal barrier that maximizes the dividends.…”

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confidence: 99%

Flow of Dividends under a Constant Force of Interest

Kasozi¹,

Paulsen²

2005

American J. of Applied Sciences

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This study addresses the issue of maximization of dividends of an insurer whose portfolio is exposed to insurance risk. The insurance risk arises from the classical surplus process commonly known as the Cramér-Lundberg model in the insurance literature. To enhance his financial base, the insurer invests in a risk free asset whose price dynamics are governed by a constant force of interest. We derive a linear Volterra integral equation of the second kind and apply an order four Block-byblock method of Paulsen et al. [1] in conjunction with the Simpson rule to solve the Volterra integral equations for each chosen barrier thus generating corresponding dividend value functions. We have obtained the optimal barrier that maximizes the dividends. In the absence of the financial world, the analytical solution has been used to assess the accuracy of our results.

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A numerical method to find the probability of ultimate ruin in the classical risk model with stochastic return on investments

Cited by 17 publications

References 28 publications

Numerical Ultimate Ruin Probabilities under Interest Force

Numerical Ultimate Ruin Probabilities under Interest Force

Ruin Models with Investment Income

Flow of Dividends under a Constant Force of Interest

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