The Management of Solvency

Taylor, Greg; Buchanan, Robert J.

doi:10.1007/978-94-009-2677-6_2

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S ( T ) Is a Compound Poisson Process With Poisson Parameter1

Introduction1

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1988

2019

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Cited by 9 publications

(2 citation statements)

References 19 publications

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“…These methods were originally introduced by Goovaerts and De Vylder' for the infinite-time ruin probability (cf. Cases (3) and (4)). Their method will be discussed in the third section.…”

Section: S ( T ) Is a Compound Poisson Process With Poisson Parametermentioning

confidence: 95%

A review of the numerical calculation of ruin probabilities by means of recursions

Steenackers

Goovaerts

1991

Appl. Stochastic Models Data Anal.

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“…These methods were originally introduced by Goovaerts and De Vylder' for the infinite-time ruin probability (cf. Cases (3) and (4)). Their method will be discussed in the third section.…”

Section: S ( T ) Is a Compound Poisson Process With Poisson Parametermentioning

confidence: 95%

A review of the numerical calculation of ruin probabilities by means of recursions

Steenackers

Goovaerts

1991

Appl. Stochastic Models Data Anal.

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“…It has been argued in the literature that the Cramér-Lundberg model is somewhat inadequate for modelling real-world insurance processes (see, e.g., [20,21]). The limitations of this model quickly led to its generalizations (e.g., in [22][23][24]), even at the cost of tractability.…”

Section: Introductionmentioning

confidence: 99%

Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments

Kasumo

2019

MCA

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In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard a Black–Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton–Jacobi–Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed individual claim amount distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

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Solvabilitätskontrolle in der Schadenversicherung

Schradin¹,

Telschow²

1995

Zeitschr. f. d. ges. Versicherungsw.

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The Management of Solvency

Cited by 9 publications

References 19 publications

A review of the numerical calculation of ruin probabilities by means of recursions

A review of the numerical calculation of ruin probabilities by means of recursions

Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments

Solvabilitätskontrolle in der Schadenversicherung

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