TY  - JOUR
A1  - Gaigall, Daniel
ED  - AitSahlia, Farid
T1  - Allocating and forecasting changes in risk
JF  - Journal of risk
N2  - We consider time-dependent portfolios and discuss the allocation of changes in the risk of a portfolio to changes in the portfolio’s components. For this purpose we adopt established allocation principles. We also use our approach to obtain forecasts for changes in the risk of the portfolio’s components. To put the approach into practice we present an implementation based on the output of a simulation. Allocation is illustrated with an example portfolio in the context of Solvency II. The quality of the forecasts is investigated with an empirical study.
KW  - portfolio risk
KW  - allocation
KW  - forecast
KW  - covariance principle
KW  - conditional expectation principle
Y1  - 2023
U6  - https://doi.org/10.21314/JOR.2022.048
SN  - 1755-2842
SN  - 1465-1211
VL  - 25
IS  - 3
SP  - 1
EP  - 24
PB  - Infopro Digital Risk
CY  - London
ER  - 
TY  - JOUR
A1  - Baringhaus, Ludwig
A1  - Gaigall, Daniel
T1  - A goodness-of-fit test for the compound Poisson exponential model
JF  - Journal of Multivariate Analysis
N2  - On the basis of bivariate data, assumed to be observations of independent copies of a random vector (S,N), we consider testing the hypothesis that the distribution of (S,N) belongs to the parametric class of distributions that arise with the compound Poisson exponential model. Typically, this model is used in stochastic hydrology, with N as the number of raindays, and S as total rainfall amount during a certain time period, or in actuarial science, with N as the number of losses, and S as total loss expenditure during a certain time period. The compound Poisson exponential model is characterized in the way that a specific transform associated with the distribution of (S,N) satisfies a certain differential equation. Mimicking the function part of this equation by substituting the empirical counterparts of the transform we obtain an expression the weighted integral of the square of which is used as test statistic. We deal with two variants of the latter, one of which being invariant under scale transformations of the S-part by fixed positive constants. Critical values are obtained by using a parametric bootstrap procedure. The asymptotic behavior of the tests is discussed. A simulation study demonstrates the performance of the tests in the finite sample case. The procedure is applied to rainfall data and to an actuarial dataset. A multivariate extension is also discussed.
KW  - Bootstrapping
KW  - Collective risk model
Y1  - 2022
U6  - https://doi.org/10.1016/j.jmva.2022.105154
SN  - 0047-259X
SN  - 1095-7243
VL  - 195
IS  - Article 105154
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Ditzhaus, Marc
A1  - Gaigall, Daniel
T1  - A consistent goodness-of-fit test for huge dimensional and functional data
JF  - Journal of Nonparametric Statistics
N2  - A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is investigated. To verify the null hypothesis that the data come from a specific distribution, an integral type test based on a Cramér-von-Mises statistic is suggested. The convergence in distribution of the test statistic under the null hypothesis is proved and the test's consistency is concluded. Moreover, properties under local alternatives are discussed. Applications are given for data of huge but finite dimension and for functional data in infinite dimensional spaces. A general approach enables the treatment of incomplete data. In simulation studies the test competes with alternative proposals.
KW  - Cramér-von-Mises statistic
KW  - separable Hilbert space
KW  - huge dimensional data
KW  - functional data
Y1  - 2018
U6  - https://doi.org/10.1080/10485252.2018.1486402
SN  - 1029-0311
VL  - 30
IS  - 4
SP  - 834
EP  - 859
PB  - Taylor & Francis
CY  - Abingdon
ER  -