Modern Actuarial Risk Theory

Kaas, Rob; Goovaerts, Marc; Dhaene, Jan; Denuit, Michel

doi:10.1007/978-3-540-70998-5

Cited by 471 publications

(412 citation statements)

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“…GARNADI, E. SYAHRIL ipar (9) : = 0 jika tidak tersedia tebakan awal bagi solusi. = 1 jika tebakan awal tersedia pada fungsiguess.…”

Section: Zetaunclassified

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Pengantar Kontrol Optimum dan Metode Numeriknya dalam SCILAB

Garnadi¹,

Syahril²

2018

Preprint

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Buku ini terdiri dari 2 bagian utama.Pada bagian pertama, merupakan catatan perkuliahan Kontrol Optimum yang diampu selama beberapa tahun oleh para penulisnya. Bagian pertama ini terdiri dari 3 bab,membahas kontrol optimum dan teknik kalkulus variasi.Pada bagian kedua, terdiri atas babyang memberi pengetahuan bagaimana menyelesaikan masalah kontrol optimum menggunakan metode numerik.Perangkat lunak yang digunakan adalah SCILAB, sehingga disertakan sebuah bab khusus mengenaibagaimana melakukan/menulis program dalam SCILAB. Selain itu, diberikan perluasan salah satuprinsip Maksimum di dalam Kontrol Optimun ke masalah yang merupakan kajian terkini, yaituKontrol Optimum Stokastik. Selain itu, diberikan sebuah daftar kepustakaandimana Kontrol Optimum klasik dan stokastik diaplikasikan dalam bidang ekonomi dan asuransi.

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“…GARNADI, E. SYAHRIL ipar (9) : = 0 jika tidak tersedia tebakan awal bagi solusi. = 1 jika tebakan awal tersedia pada fungsiguess.…”

Section: Zetaunclassified

“…Pada contoh berikut diberikan sebuah MSB yang berasal dari formula kredibilitas yang memungkinkan aktuaris untuk menyeimbangkan dua hal, yaitu keakuratan dan kelinearan [9]. Berikut merupakan MSB untuk kasus di mana sebaran marginal ( ) dari besarnya klaim( ) ialah tak nol pada suatu interval terbatas , lihat Young [10].…”

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Pengantar Kontrol Optimum dan Metode Numeriknya dalam SCILAB

Garnadi¹,

Syahril²

2018

Preprint

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“…BBOP appears in reinsurance field, and specifically in the analysis of the the effect of reinsurance contracts on the solvency of the two agents that participate in the contract (insurer and reinsurer) [13,19,5,4]. One of the main measures used to control solvency is the ruin probability.…”

Section: Black-box Optimization Problems In Reinsurancementioning

confidence: 99%

An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

et al. 2013

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Black-box optimization problems (BBOP) are defined as those optimization problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program). This paper is focussed on BBOPs that arise in the field of insurance, and more specifically in reinsurance problems. In this area, the complexity of the models and assumptions considered to define the reinsurance rules and conditions produces hard black-box optimization problems, that must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in BBOP, so new computational paradigms must be applied to solve these problems. In this paper we show the performance of two evolutionary-based techniques (Evolutionary Programming and Particle Swarm Optimization). We provide an analysis in three BBOP in reinsurance, where the evolutionary-based approaches exhibit an excellent behaviour, finding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.

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“…This model plays a prominent role in risk theory and a considerable literature is devoted to its study. The reader is referred to the books by Gerber [12], Grandell [15], Panjer and Willmot [23], Asmussen [2] and Kaas et al [19]); see also, e.g., Gerber and Shiu [16], Albrecher et al [1] and Cardoso and Waters [3] for recent results on the ruin problem.…”

Section: Compound Poisson Risk Modelmentioning

confidence: 99%

On finite-time ruin probabilities for classical risk models

Lefèvre

Loisel

2008

Scandinavian Actuarial Journal

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This paper is concerned with the problem of ruin in the classical compound binomial and compound Poisson risk models. Our primary purpose is to extend to those models an exact formula derived by Picard and Lefèvre [24] for the probability of (non-)ruin within finite time. First, a standard method based on the ballot theorem and an argument of Seal-type provides an initial (known) formula for that probability. Then, a concept of pseudo-distributions for the cumulated claim amounts, combined with some simple implications of the ballot theorem, leads to the desired formula. Two expressions for the (non-)ruin probability over an infinite horizon are also deduced as corollaries. Finally, an illustration within the framework of Solvency II is briefly presented.Keywords: ruin probability, finite and infinite horizon, compound binomial model, compound Poisson model, ballot theorem, pseudo-distributions, Solvency II, Value-at-Risk. IntroductionThe two classical models in risk theory are the compound binomial model, which is a discrete-time process where the claim amounts are usually assumed to be integer-valued random variables, and the compound Poisson model, which is a continuous-time analogue of this process where the claim amounts are generally assumed to have an absolutely continuous distribution. Although the continuous-time version is quite popular, a discretetime version can be appropriate for some applications and provides a better intuitive understanding.The present paper deals with the problem of evaluating, for both risk models, the probability of (non-)ruin within finite time. This problem has received much attention in the literature, and different algorithms have been proposed, with their own advantages and drawbacks; see, e.g., the analysis by Dickson [11] and the references therein.Recently, Picard and Lefèvre [24] derived an elegant explicit formula, called P.L. formula below, for the finite-time non-ruin probability in a compound Poisson model where the claim amounts are integer-valued. Such a case is important because in practice a et al. [17]. A refined discussion of its merits in comparison with other available formulas is given in Rullière and Loisel [28]. Besides, De Vylder and Goovaerts [10] proved that a similar formula holds too for a compound Poisson model with continuous claim amounts; see also Ignatov and Kaishev [18].1 discretization of the claim amounts is often required for numerical calculations (e.g., de Vylder and Goovaerts [9]). The importance of the P.L. formula has been pointed out by De Vylder [6], [7] and IgnatovSeveral methods are possible to establish the P.L. formula. In Picard and Lefèvre [24] and De Vylder and Goovaerts [10], the first step consists in stipulating for a total claim amount until some time t and conditioning on the last claim instant and amount before t. This yields an integral equation which is then solved by the former authors using the generalized Appell polynomials (in an extended framework), and by the latter authors using the convolution products and th...

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Modern Actuarial Risk Theory

Cited by 471 publications

References 0 publications

Pengantar Kontrol Optimum dan Metode Numeriknya dalam SCILAB

Pengantar Kontrol Optimum dan Metode Numeriknya dalam SCILAB

An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

On finite-time ruin probabilities for classical risk models

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