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Forecasting compositional risk allocations. (English) Zbl 1419.91350
Summary: We analyse models for panel data that arise in risk allocation problems, when a given set of sources are the cause of an aggregate risk value. We focus on the modelling and forecasting of proportional contributions to risk over time. Compositional data methods are proposed and the time-series regression is flexible to incorporate external information from other variables. We guarantee that projected proportional contributions add up to 100%, and we introduce a method to generate confidence regions with the same restriction. An illustration is provided for risk capital allocations.
##### MSC:
 91B30 Risk theory, insurance (MSC2010)
##### Software:
compositions; robCompositions; vars
Full Text:
##### References:
 [1] Aitchison, J., The Statistical Analysis of Compositional Data, (1986), Chapman and Hall · Zbl 0688.62004 [2] Aitchison, J.; Egozcue, J., Compositional data analysis: Where are we and where should we be heading?, Math. Geol., 37, 7, 829-850, (2005) · Zbl 1177.86017 [3] Akaike, H., Information theory and an extension of the maximum likelihood principle, (Second International Symposium on Information Theory, (1973), Akademiai Kiado: Akademiai Kiado Budapest), 267-281 · Zbl 0283.62006 [4] Asimit, A. V.; Furman, E.; Tang, Q.; Vernic, R., Asymptotics for risk capital allocations based on Conditional Tail Expectation, Insurance Math. Econom., 49, 3, 310-324, (2011) · Zbl 1228.91029 [5] Bauer, D.; Reuss, A.; Singer, D., On the calculation of the solvency capital requirement based on nested simulations, Astin Bull., 42, 2, 453-499, (2012) · Zbl 1277.91074 [6] Belles-Sampera, J.; Guillen, M.; Santolino, M., Compositional methods applied to capital allocation problems, J. Risk, 19, 1, 1-15, (2016) [7] van den Boogaart, K.G., Tolosana, R., Bren, M., 2015. compositions: Compositional Data Analysis. R package version 1.40-1. [8] van den Boogaart, K. G.; Tolosana-Delgado, R., Analyzing Compositional Data with R, (2013), Springer-Verlag Berlin Heidelberg · Zbl 1276.62011 [9] Boonen, T. J.; Tsanakas, A.; Wthrich, M. V., Capital allocation for portfolios with non-linear risk aggregation, Insurance Math. Econom., 72, 95-106, (2017) · Zbl 1394.91191 [10] Buch, A.; Dorfleitner, G.; Wimmer, M., Risk capital allocation for RORAC optimization, J. Bank. Finance, 35, 11, 3001-3009, (2011) [11] Cossette, H.; Mailhot, M.; Marceau, E., TVaR-based capital allocation for multivariate compound distributions with positive continuous claim amounts, Insurance Math. Econom., 50, 247-256, (2012) · Zbl 1235.91086 [12] Denault, M., Coherent allocation of risk capital, J. Risk, 4, 1-34, (2001) [13] Dhaene, J.; Tsanakas, A.; Valdez, E. A.; Vanduffel, S., Optimal capital allocation principles, J. Risk Insurance, 79, 1, 1-28, (2012) [14] Egozcue, J. J.; Pawlowsky-Glahn, V.; Mateu-Figueras, G.; Barcelo-Vidal, C., Isometric logratio transformations for compositional data analysis, Math. Geol., 35, 3, 279-300, (2003) · Zbl 1302.86024 [15] Furman, E.; Zitikis, R., Weighted risk capital allocations, Insurance Math. Econom., 43, 2, 263-269, (2008) · Zbl 1189.62163 [16] Gan, G.; Lin, X. S., Valuation of large variable annuity portfolios under nested simulation: A functional data approach, Insurance Math. Econom., 62, 138-150, (2015) · Zbl 1318.91112 [17] Glassman, D.; Riddik, L., Why empirical international portfolio models fail: evidence that model misspecification creates home asset bias, J. Int. Money Finance, 15, 2, 275-312, (1996) [18] Kalkbrener, M., An axiomatic approach to capital allocation, Math. Finance, 15, 3, 425-437, (2005) · Zbl 1102.91049 [19] Kynclová, P.; Filzmoser, P.; Hron, K., Modeling compositional time series with vector autoregressive models, J. Forecast., 34, 4, 303-314, (2015), for.2336 · Zbl 1376.62105 [20] Panjer, H., Jing, J., 2001. Solvency and Capital allocation. Technical report, Institute of Insurance and Pension Research Research Report 01-14, Univerisity of Waterloo. [21] Pawlowsky-Glahn, V.; Egozcue, J.; Tolosana-Delgado, R., Lecture Notes on Compositional Data Analysis, (2011), Univeristy of Girona [22] Perez-Foguet, A.; Gine-Garriga, R.; Ortego, M., Compositional data for global monitoring: The case of drinking water and sanitation, Sci. Total Environ., 590, Supplement C, 554-565, (2017) [23] Pfaff, B., Stigler, M., 2013. vars: VAR Modelling. R package version 1.52. [24] Schwarz, G., Estimating the dimension of a model, Ann. Statist., 6, 2, 461-464, (1978) · Zbl 0379.62005 [25] Snyder, R. D.; Ord, J. K.; Koehler, A. B.; McLaren, K. R.; Beaumont, A. N., Forecasting compositional time series: A state space approach, Int. J. Forecast., 33, 2, 502-512, (2017) [26] Tasche, D., 1999. Risk contributions and performance measurement. Preprint, TU Munich. [27] Templ, M., Hron, K., Filzmoser, P., 2017. robComposition: Robust Estimation for Compositional Data. R package version 2.0.6. · Zbl 1304.65033 [28] Tsanakas, A., Dynamic capital allocation with distortion risk measures, Insurance Math. Econom., 35, 2, 223-243, (2004) · Zbl 1103.91316 [29] Tsanakas, A., To split or not to split: Capital allocation with convex risk measures, Insurance Math. Econom., 44, 2, 268-277, (2009) · Zbl 1165.91423 [30] Urbina, J.; Guillen, M., An application of capital allocation principles to operational risk and the cost of fraud, Expert Syst. Appl., 41, 16, 7023-7031, (2014) [31] Verbelen, R.; Antonio, K.; Claeskens, G., Unravelling the predictive power of telematics data in car insurance pricing, J. Roy. Statist. Soc. Ser. C, 67, 5, 1275-1304, (2018) [32] Yang, Y., Can the strengths of aic and bic be shared? a conflict between model indentification and regression estimation, Biometrika, 92, 4, 937-950, (2005) · Zbl 1151.62301 [33] Zaks, Y.; Tsanakas, A., Optimal capital allocation in a hierarchical corporate structure, Insurance Math. Econom., 56, 48-55, (2014) · Zbl 1304.91239
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