Computation and Modelling in Insurance and Finance

Bølviken, Erik

doi:10.1017/cbo9781139020251

Cited by 15 publications

(18 citation statements)

References 285 publications

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“…sd(X i ) follow. The skewness γ i on the right in (6) is the formula for the skewness of log-normal variables, see Bølviken (2014), p 319, and it determines τ i from γ i though a cubic equation for e τ 2 i . There is a unique real solution which is (7).…”

Section: A Log-normal Solutionmentioning

confidence: 99%

“…where V 1 and V 2 are independent and uniform and Z Gamma-distributed with mean 1 and shape 1/θ; consult Chapter 6 in Bølviken (2014) for the construction. Correlation between Premium/Reserve and Cat remains at 0.25 approximately if θ = 0.326 which was used for the experiments.…”

Section: Dependence Through the Clayton Copulamentioning

confidence: 99%

“…where V is uniform and independent of U 1 ; consult Chapter 6 in Bølviken (2014). In a chain of applications where the aim is to capture correlations between groups of variables it does matter which version is used.…”

Section: Referencesmentioning

confidence: 99%

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Risk aggregation in Solvency II through recursive log-normals

Bølviken

Guillén

2017

Insurance: Mathematics and Economics

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It is argued that the accuracy of risk aggregation in Solvency II can be improved by updating skewness recursively. A simple scheme based on the log-normal distribution is developed and shown to be superior to the standard formula and to adjustments of the Cornish-Fisher type. The method handles tail-dependence if a simple Monte Carlo step is included. A hierarchical Clayton copula is constructed and used to confirm the accuracy of the log-normal approximation and to demonstrate the importance of including tail-dependence. Arguably a log-normal scheme makes the logic in Solvency II consistent, but many other distributions might be used as vehicle, a topic that may deserve further study.JEL codes: G22, G28.

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Section: A Log-normal Solutionmentioning

confidence: 99%

Section: Dependence Through the Clayton Copulamentioning

confidence: 99%

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Risk aggregation in Solvency II through recursive log-normals

Bølviken

Guillén

2017

Insurance: Mathematics and Economics

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“…Proses Poisson adalah proses menghitung (counting process) untuk kejadian yang terjadi hingga suatu waktu. Proses Poisson sering disebut juga dengan proses lompatan (jump process) karena keadaan akan berpindah ke yang lebih tinggi setiap kali kejadian terjadi [3][4][5].…”

Section: Distribusi Poissonunclassified

Pemodelan dan Simulasi Peluang Kebangkrutan Perusahaan Asuransi dengan Analisis Nilai Premi dan Ukuran Klaim Diasumsikan Berdistribusi Eksponensial

Diba

2017

IndoJC

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This study is about modelling and simulation probability of bankruptcy in the insurance company at the time of receiving claims by costumers. The company has the funds to pay claims that derived from accumulated initial reserve and income of insurance from premiums that have payed. If the company's funds at time t is smaller than 0 then the insurance company will going bankruptcy. Therefore will be analyzed the premiums that must be payed by insurance costumers. If the premiums that payed by costumer is greater, so the funds of insurance company will greater too at the time-to cover the next claims. Probability of bankcruptcy in the insurance company can be predected from the simulation model n-times with claims frequency which happened at the time between 0 dan is assumed distribution Poisson and claim sizes is distribution Exponential. Keywords: bankruptcy probability, Exponential distribution, Poisson distribution, premiums AbstrakJurnal ini berisi tentang pemodelan dan simulasi peluang kebangkrutan perusahaan asuransi saat menanggung klaim dari pelanggan. Perusahaan mempunyai dana untuk membayar klaim yang diperoleh dari akumulasi cadangan dana awal dan pendapatan perusahaan dari pembayaran premi. Jika dana perusahaan pada waktu ke-lebih kecil sama dengan 0 maka perusahaan asuransi mengalami kebangkrutan. Oleh karena itu dianalisis premi yang harus dibayar oleh pelanggan asuransi. Semakin besar jumlah premi yang dibayar, maka semakin besar dana perusahaan asuransi pada waktu ke-untuk menanggung klaim berikutnya. Sehingga dapat diestimasi peluang kebangrutan dengan simulasi model n-kali jika diasumsikan banyaknya klaim yang terjadi pada selang waktu antara 0 dan berdistribusi Poisson dan ukuran klaim berdistribusi Eksponensial.

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“…An important application of the collective risk model is the estimation of the claim reserve, or solvency capital (Bølviken, 2014), which is a quantile far out in the tail of the distribution of X , given by…”

Section: Introductionmentioning

confidence: 99%

Modelling extreme claims via composite models and threshold selection methods

Wang

Haff

Huseby

2020

Insurance: Mathematics and Economics

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The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of insurance claim data. This paper discusses several composite models with commonly used bulk distributions, combined with a 2-parameter Pareto distribution above the threshold. We have explored how several threshold selection methods perform when estimating the reserve as well as the effect of the choice of bulk distribution, with varying sample size and tail properties. To investigate this, a simulation study has been performed. Our study shows that when data are sufficient, the square root rule has the overall best performance in term of the quality of the reserve estimate. The second best is the exponentiality test, especially when the right tail of the data is extreme. As the sample size becomes small, the simultaneous estimation has the best performance. Further, the influence of the choice of bulk distribution seems to be rather large, especially when the distribution is heavy-tailed. Moreover, it shows that the empirical estimate of p ≤b , the probability that a claim is below the threshold, is more robust than the theoretical one.

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Computation and Modelling in Insurance and Finance

Cited by 15 publications

References 285 publications

Risk aggregation in Solvency II through recursive log-normals

Risk aggregation in Solvency II through recursive log-normals

Pemodelan dan Simulasi Peluang Kebangkrutan Perusahaan Asuransi dengan Analisis Nilai Premi dan Ukuran Klaim Diasumsikan Berdistribusi Eksponensial

Modelling extreme claims via composite models and threshold selection methods

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