Loss Models

Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.

doi:10.1002/9781118787106

Cited by 171 publications

(67 citation statements)

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“…Despite the algorithm used to generate a pair of observations from a specified BLT procedure is already given as above but when apply the procedures here we encounter the difficulty on how to simulate from distributions with LTs given by There is a vast literature on survival or distribution copula, we just mention a few here. For a good general review on distribution or survival copula models with emphasis on goodness-of-fit test statistics, see Genest et al [25] and for a good review of inference methods based on survival copulas used in actuarial science, see Klugman et al [17] (pp. 187-213), Frees and Valdez [26].…”

Section: Lt Copulasmentioning

confidence: 99%

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Maximum Entropy Empirical Likelihood Methods Based on Bivariate Laplace Transforms and Moment Generating Functions

Luong¹

2018

OJS

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Maximum Entropy Empirical Likelihood (MEEL) methods are extended to bivariate distributions with closed form expressions for their bivariate Laplace transforms (BLT) or moment generating functions (BMGF) without closed form expressions for their bivariate density functions which make the implementation of the likelihood methods difficult. These distributions are often encountered in joint modeling in actuarial science and finance. Moment conditions to implement MEEL methods are given and a bivariate Laplace transform power mixture (BLTPM) is also introduced, the new operator generalizes the existing univariate one in the literature. Many new bivariate distributions including infinitely divisible(ID) distributions with closed form expressions for their BLT can be created using this operator and MEEL methods can also be applied to these bivariate distributions.

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Section: Lt Copulasmentioning

confidence: 99%

“…One can recognize that this is a LT of a negative binomial distribution and for this distribtion, the corresponding probability generating function (PGF) et al[17] (p. 83)…”

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confidence: 99%

Maximum Entropy Empirical Likelihood Methods Based on Bivariate Laplace Transforms and Moment Generating Functions

Luong¹

2018

OJS

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“…For a finite n , IRS thus can serve as a natural index to measure the impact of non‐diversifiable interest risk in the given portfolio. Interestingly, the IRS is the same form as the credibility factor of Bühlman, under a different setup and context; see, for example, Klugman et al . One may consider an alternative index to measure the mortality risk within the portfolio by switching the condition in the IRS formula to the lifetimes of individuals from δ , that is, by replacing the numerator of the IRS with

V a r [E_{δ} (_{t} \overset{L}{true} | T_{1}, T_{2}, \dots, T_{n})]

.…”

Section: Portfolio Risk Analysismentioning

confidence: 99%

Application of the phase‐type mortality law to life contingencies and risk management

Kim

Bae

Kim

2017

Appl Stoch Models Bus & Ind

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The class of phase‐type distributions has recently gained much popularity in insurance applications due to its mathematical tractability and denseness in the class of distributions defined on positive real line. In this paper, we show how to use the phase‐type mortality law as an efficient risk management tool for various life insurance applications. In particular, pure premiums, benefit reserves, and risk‐loaded premiums using CTE for standard life insurance products are shown to be available in analytic forms, leading to efficient computation and straightforward implementation. A way to explicitly determine provisions for adverse deviation for interest rate and mortality is also proposed. Furthermore, we show how the interest rate risk embedded in life insurance portfolios can be analyzed via interest rate sensitivity index and diversification index which are constructed based on the decomposition of portfolio variance. We also consider the applicability of phase‐type mortality law under a few non‐flat term structures of interest rate. Lastly, we explore how other properties of phase‐type distributions may be applied to joint‐life products as well as subgroup risk ordering and pricing within a given pool of insureds. Copyright © 2017 John Wiley & Sons, Ltd.

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“…This leads to a composite null hypothesis and ideally we would like to use goodness-of-fit test statistics which follow a unique asymptotic distribution ∈ Ω θ , Ω assumed to be compact. The multidimensional model testing often poses difficulties as often goodness-of-fit test statistics used either have very complicated distributions such as the case of statistics which make use of multivariate empirical characteristic functions, see Csörgö [1] or for the classical chi-square tests where the asymptotic distributions for simple and composite hypotheses are simple but observations must be grouped into cells and there is some arbitrariness on choosing cells, see Moore [2], Klugman et al [3] (pages 208-209) on extending chi-square tests for continuous multidimensional models. Goodness of fit test statistics using multivariate sample distribution function often has a very complicated null distribution, see Babu and Rao [4] and extensive simulations are needed to obtain the p values of the tests.…”

Section: Introductionmentioning

confidence: 99%

“…procedures on the use of the maximum value of the log likelihood function for assessing goodness-of-fit of the model, see Klugman et al[15] but note that the condition of no tied observation is needed for the use of test based on the log of likelihood function as given by exand the log of these values are undefined meanwhile test based on is well defined even with the presence of tied obsevations and in general we should fix a value for α near 0 for balancing efficiency and robustness for the estimation procedures.…”

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confidence: 99%

Pseudodistance Methods Using Simultaneously Sample Observations and Nearest Neighbour Distance Observations for Continuous Multivariate Models

Luong¹

2019

OJS

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Using the fact that a multivariate random sample of n observations also generates n nearest neighbour distance (NND) univariate observations and from these NND observations, a set of n auxiliary observations can be obtained and with these auxiliary observations when combined with the original multivariate observations of the random sample, a class of pseudodistance h D is allowed to be used and inference methods can be developed using this class of pseudodistances. The h D estimators obtained from this class can achieve high efficiencies and have robustness properties. Model testing also can be handled in a unified way by means of goodness-of-fit tests statistics derived from this class which have an asymptotic normal distribution. These properties make the developed inference methods relatively simple to implement and appear to be suitable for analyzing multivariate data which are often encountered in applications.

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Loss Models

Cited by 171 publications

References 0 publications

Maximum Entropy Empirical Likelihood Methods Based on Bivariate Laplace Transforms and Moment Generating Functions

Maximum Entropy Empirical Likelihood Methods Based on Bivariate Laplace Transforms and Moment Generating Functions

Application of the phase‐type mortality law to life contingencies and risk management

Pseudodistance Methods Using Simultaneously Sample Observations and Nearest Neighbour Distance Observations for Continuous Multivariate Models

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