Risk models with premiums adjusted to claims number

Li, Bo; Ni, Wenda; Constantinescu, Corina

doi:10.1016/j.insmatheco.2015.09.001

Cited by 12 publications

(34 citation statements)

References 6 publications

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“…In this subsection, we introduce main definitions and quantities from the classical BMS as known from the literature. Following Lemaire (1995), see also Denuit et al (2007), for a BMS with transition rules based only on claim frequency, we consider that the level/class, for each policyholder, in a given annual period is determined uniquely by the class of the preceding year and by the number of claims reported during that time period. The classical model for BMS is defined by the triplet = (T, b, i 0 ), where b = (b 1 , .…”

Section: Bms For Homogeneous Markov Chainsmentioning

confidence: 99%

“…We consider that assumption in our developments. For a more detailed view over BMS, please consider Lemaire (1995) or Denuit et al (2007). In our application quantities, E [S(1)] and π (i ) ( j ) have to be estimated with historical data, annual number of claims in class j will be considered Poisson distributed with mean λ j , j = 1, 2, .…”

Section: Bms For Homogeneous Markov Chainsmentioning

confidence: 99%

“…Technically, in the classical models, the dynamics are estimated through Markov chain procedures. This procedure brings a higher variation in the premia during the lifetime of the portfolio [see e.g., Lemaire (1995)], when compared to a standard procedure. The model in Afonso et al (2009), that we retrieve, is built under the assumption of an homogeneous classical compound Poisson process, with Afonso et al (2010), we bring some sort of heterogeneity to the portfolio.…”

Section: Introductionmentioning

confidence: 99%

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MEASURING THE IMPACT OF A BONUS-MALUS SYSTEM IN FINITE AND CONTINUOUS TIME RUIN PROBABILITIES FOR LARGE PORTFOLIOS IN MOTOR INSURANCE

Afonso¹,

Cardoso²,

Reis

et al. 2017

ASTIN Bull.

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Motor insurance is a very competitive business where insurers operate with quite large portfolios, often decisions must be taken under short horizons and therefore ruin probabilities should be calculated in finite time. The probability of ruin, in continuous and finite time, is numerically evaluated under the classical Cramér–Lundberg risk process framework for a large motor insurance portfolio, where we allow for a posteriori premium adjustments, according to the claim record of each individual policyholder. Focusing on the classical model for bonus-malus systems, we propose that the probability of ruin can be interpreted as a measure to decide between different bonus-malus scales or even between different bonus-malus rules. In our work, the required initial surplus can also be evaluated. We consider an application of a bonus-malus system for motor insurance to study the impact of experience rating in ruin probabilities. For that, we used a real commercial scale of an insurer operating in the Portuguese market, and we also work on various well-known optimal bonus-malus scales estimated with real data from that insurer. Results involving these scales are discussed.

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Section: Bms For Homogeneous Markov Chainsmentioning

confidence: 99%

Section: Bms For Homogeneous Markov Chainsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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MEASURING THE IMPACT OF A BONUS-MALUS SYSTEM IN FINITE AND CONTINUOUS TIME RUIN PROBABILITIES FOR LARGE PORTFOLIOS IN MOTOR INSURANCE

Afonso¹,

Cardoso²,

Reis

et al. 2017

ASTIN Bull.

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“…We discuss now when conditions (12)-(16) are satisfied. Assume that (12), (13) and (14). Then by representation (4) we can easily check that X 1 also satisfies…”

Section: The Intermediate Casementioning

confidence: 99%

Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window

Constantinescu

Dai

et al. 2016

Risks

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Abstract:We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival times depending on the claims that arrive within a fixed (past) time window. This dependence could be explained through a regenerative structure. The main inspiration of the model comes from the bonus-malus (BM) feature of pricing car insurance. We discuss first the asymptotic results of ruin probabilities for different regimes of claim distributions. For numerical results, we recognise an embedded Markov additive process, and via an appropriate change of measure, ruin probabilities could be computed to a closed-form formulae. Additionally, we employ the importance sampling simulations to derive ruin probabilities, which further permit an in-depth analysis of a few concrete cases.

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“…On the other hand, dependence between the claim arrival process and the premium rate has been studied by Dubey (1977), Li et al . (2015). In this paper, we would like to generalise and combine the mentioned dependence and extend to a broader dependence framework.…”

Section: Introductionmentioning

confidence: 99%

Ruin probabilities in a Sparre Andersen model with dependency structure based on a threshold window

Cheung

Dai

2017

Ann. actuar. sci.

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We analyse ruin probabilities for an insurance risk process with a more generalised dependence structure compared to the one introduced in Constantinescu et al. (2016). In this paper, we assume that a random threshold window is generated every time after a claim occurs. By comparing the previous inter-claim time with the threshold window, the distributions of the current threshold window and the inter-arrival time are determined. Furthermore, the statuses for the previous and current inter-arrival times give rise to the current claim size distribution as well. Like Constantinescu et al. (2016), we first identify the embedded Markov additive process where all the randomness takes a general form. Inspired by the Erlangisation technique, the key message of this paper is to analyse such risk process using a Markov fluid flow model where the underlying random variables follow phase-type distributions. This would further allow us to approximate the fixed observation windows by Erlang random variables. Then ruin probabilities under the process with Erlang(n) observation windows are proved to be Erlangian approximations for those related to the process with fixed threshold windows at the limit. An exact form of the limit can be obtained whose application will be illustrated further by a numerical example.

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Risk models with premiums adjusted to claims number

Cited by 12 publications

References 6 publications

MEASURING THE IMPACT OF A BONUS-MALUS SYSTEM IN FINITE AND CONTINUOUS TIME RUIN PROBABILITIES FOR LARGE PORTFOLIOS IN MOTOR INSURANCE

MEASURING THE IMPACT OF A BONUS-MALUS SYSTEM IN FINITE AND CONTINUOUS TIME RUIN PROBABILITIES FOR LARGE PORTFOLIOS IN MOTOR INSURANCE

Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window

Ruin probabilities in a Sparre Andersen model with dependency structure based on a threshold window

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