3 edition of Upper bounds on stop-loss premiums under constraints on claim size distribution found in the catalog.
Upper bounds on stop-loss premiums under constraints on claim size distribution
Taylor, G. C.
by Macquarie University, School of Economics & Financial Studies in [Sydney]
Written in English
Bibliography: p. 19.
|Statement||G. C. Taylor.|
|Series||Research paper - Macquarie University, School of Economic & Financial Studies ; no. 104, Research paper (Macquarie University. School of Economic and Financial Studies) ;, no. 104.|
|LC Classifications||HG8782 .T353|
|The Physical Object|
|Pagination||19 p. ;|
|Number of Pages||19|
|LC Control Number||78320758|
Journal of Actuarial Practice, Vol. 72, Table 1 Parameters A ()(A B Large Claims Small Claims 20 necessarily hit the working layer. To use the multivariate extension of the Panjer's algorithm, we discretize the claims size distributions, thusAuthor: Jean-François Walhin, Michel Denuit. For example: the various articles    investigated the effect of the reinsurance contract on the upper bound of the cedent’s ruin probability. The upper bounds of ruin probabilities of the cedent and the reinsurer were estimated in   where Dam and Chung considered the risk model under quota share : Nguyen Quang Chung.
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K.C. Cheung, S. Vanduffel (). Bounds for sums of random variables when the marginal distributions and the variance of the sum are given. Scandinavian Actuarial Journal, vol. , K.C. Cheung, F. Liu, S.C.P. Yam (). Average Value-at-Risk minimizing reinsurance under Wang's premium principle with constraints. For a certain health insurance policy, losses are uniformly distributed on the interval [0, b]. The policy has a deductible of and the expected value of .
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Upper bounds on stop-loss premiums under constraints on claim size distribution as derived tram representation theorems for distribution functions. Scandinavian Actuarial Journal. Goovaerts, M., by: BOUNDS ON STOP-LOSS PREMIUMS TABLE 3 BOUNDS FOR STOP-LOSS PREMIUMS WITH CLAIM RANGE [0,3], MEAN 2, VARIANCE 31 AND CLAIM NUMBER POISSON (10) 17 Stop-Loss Gerber's Upper Upper Lower Lower Point t Exact Value Bound (4) Bound (15) Bound (15) Bound (4) 15 5 4% 0% 99 0% 99 0%.
TAYLOR, G C () Upper Bounds on Stop-Loss Premiums under Constraints on Claim Size Distributions S A J, DE VVLDER, F and GOOVAERTS. M (b) Analytical best upper bounds for stop-loss premtums Insurance Mathematm~ and Economw3 I, 3 P.
BROCKETT, M. GOOVAERTS, G. TAYLOR. Because the larger claims were given exactly, the minimal and maximal moments do not differ much, especially the higher ones.
The bounds for stop-loss premiums differed by only about 1%o under each assumption. As an upper bound we took b =but any value larger than would have given the same by: Recently a lot of results have been obtained for determining bounds on integrals with integral constraints.
As a consequence best bounds on excess of loss and stop loss premiums are determined under various practical by: 3.
A note on the sampling distribution of the maximum likelihood estimators in a competing exponential risks model. Upper bounds on stop-loss premiums under constraints on claim size distribution.
Taylor. book review Nonlife actuarial models, theory, methods and evaluation by Yiu-Kuen Tse. Summary. A class of optimization problems is introduced which contains the stop-loss problem from risk theory as a special case. Two abstract optimization models, viz. linear programming in normed vector spaces, and Tchebycheff systems, are presented, and it is shown how to solve the initial problems by methods derived from the general by: 5.
On the use of bounds on stop-loss premium for an inventory management decision problem. A specific integral, which is used in insurance mathematics for the determination of a stop-loss premium, corresponds to the definition of a performance characteristic of an inventory management decision problem.
estimate the upper tail of claim size distribution to compute reinsurance premiums) (Hossack, Pollard and Zehnwirth ).
The number of claims incurred by an insurance company is always a discrete random variable. This means they can be counted on a state space with non- negative integer values 0,1,2,3,4 and so on.
A random coefficients approach to claims reserving / by Piet de Jong and Benjamin Zehnwirth; Claims reserving, state-space models and the Kalman filter / Piet de Jong, Ben Zehnwirth; Upper bounds on stop-loss premiums under constraints on claim size distribution / G.
Taylor. suitable probability distribution for the claims data and testing for the goodness of fit of the supposed distribution .
A good introduction to the subject of fitting distributions to losses is given by Hogg and Klugman. Emphasis is on the  distribution of single losses related to claims made against various types of insurance Size: KB. For bounds under more restrictive hypotheses on the claim size distribution (e.g., additional moment conditions, nite range, unimodality, etc.), see De Vylder and Goovaerts (), Jansen et al.
() and Hurlimann (), among others.D The purpose ofthis paper is to examine strategies for nding upper bounds on (X;d) when. A constraint that can be imposed naturally in most insurance applications is that F must be unimodal with fixed mode M.
We will show that the problem to find an extremal stop-loss premium under this extra constraint can be reduced to another instance of problem (1) and (2). Atkinson, M. & Dickson, D.An introduction to actuarial studies / M.E. Atkinson, D.C.M. Dickson Edward Elgar Pub Cheltenham Wikipedia Citation Please see Wikipedia's template documentation for further citation fields that may be required.
An upper bound is obtained for the tail of the total claims distribution in terms of a ‘new worse than used’ distribution. A simple bound exists when the claim size distribution is also new.
STATISTICAL MODELS OF CLAIM DISTRIBUTIONS 3 homogeneous classes, especially with respect to size, the description by number of claims and mean claim will suffice for our purpose. For a thorough survey of these questions we refer to the lecture by G.
Benktander at the congress of actuaries EReI. 3].File Size: 1MB. This paper presents explicit formulae giving tight upper and lower bounds on the expectations of alpha-unimodal random variables having a known range and given set of moments. Such bounds can be useful in ordering of random variables in terms of risk and in PERT analysis where there is only incomplete stochastic information concerning the variables under : Patrick L.
Brockett, SamuelRichard D. MacMinn, Bo Shi. bounds on the expectation of the convex function of the variable under investigation where the supremum and infimum are taken over all random variables satisfying the given information constraints. This, then, produces a partial ordering on the space of probability distributions satisfying the informational constraints.
A B S T R A C T Inventory systems with uncertainty go hand in hand with the determination of a safety stock level. The decision on the safety stock level is based on a performance measure, for example the expected shortage per replenishment period or the probability of a stock-out per replenishment period.
The performance measure assumes. 1 Answer 1. The lower and upper bounds specify the range over which the probability is uniform. For example, imagine you go to a bus stop where the bus arrives once every five minutes.
If you walk to the bus stop at random times, your wait at the stop will have a lower bound of 0 minutes and an upper bound of 5 minutes. (i) Ground-up losses follow an exponential distribution with mean θ.
(ii) Losses under 50 are not reported to the insurer. (iii) For each loss o there is a deductible of 50 and a policy limit of (iv) A random sample of five claim payments for this policy is: 50 + +File Size: KB.For the Asian case the approach generally taken has been to approximate the distribution of the arithmetic average price, while for the portfolio option case, attempts have focused on discretizing the joint distribution of the terminal prices of the assets comprising the portfolio and approximating the expected risk-neutral option payoff with a Cited by: exponential distribution with mean 1.
if reinsurance = "none", a numeric value of the premium rate; otherwise, an expression written as a function of y, or alternatively the name of a function, giving the premium rate function. numeric; an upper bound for the coefﬁcient, usually the upper bound of theFile Size: KB.