Linear Generalized Stochastic Systems for Insurance Portfolios

References

• Balzer , L.A. , and Benjamin , S. 1980 . Dynamic response of insurance systems with delayed profit/loss sharing feedback to isolated unpredicted claims . Journal of the Institute of Actuaries 1007 : 513 – 528 .
   Google Scholar
• Balzer , L.A. 1988 . A model of the underwriting cycle in property/liability insurance industry . Journal of Risk and Insurance 55 : 298 – 306 .
   Google Scholar
• Barth , J.R. , and Bennett , J.T. 1974 . The role of money in the Canadian economy: An empirical test . Canadian Journal of Economics 7 : 306 – 311 .
   Web of Science ®Google Scholar
• Bellmann , R. , and Cooke , K.L. 1963 . Differential-Difference Equations . Academic Press , New York .
   Google Scholar
• Benjamin , S. 1984 . An actuarial layman looks at control theory . Transactions of the 2nd International Congress of Actuaries 4 : 295 – 310 .
   Google Scholar
• Campbell , S.L. 1980/1982. Singular Systems of Differential Equations . Vols. 1 and 2. Pitman , San Francisco.
   Google Scholar
• Ciccolo , J.H. , Jr. 1978 . Money, equity values and income: Tests for exogeneity . Journal of Money, Credit and Banking 10 : 46 – 64 .
   Google Scholar
• Dai , L. 1989 . Singular Control Systems . Springer-Verlag , Berlin .
   Google Scholar
• Feige , E.L. , and Pearce , D.K. 1979 . The casual causal relationship between money and income: Some caveats for time series analysis . Review of Economics and Statistics 61 : 521 – 533 .
   Web of Science ®Google Scholar
• Gantmacher , R.F. 1977 . The Theory of Matrices . Vol. I and II . Chelsea , New York .
   Google Scholar
• Granger , C.W.J. 1969 . Investigating causal relations by econometric models and cross-spectral methods . Econometrica 37 : 424 – 438 .
   Web of Science ®Google Scholar
• Grispos , E. , and Kalogeropoulos , G.I. 1998 . The causality for generalized linear discrete-time dynamical systems . Journal of Institute of Mathematics and Computer Science (Mathematical Series) 11 ( 3 ): 145 – 154 .
   Google Scholar
• Holly , S. , and Hallett , H.A. 1989 . Optimal Control, Expectations and Uncertainty . Cambridge , U.K. .
   Google Scholar
• Hsiao , C. 1979 . Autoregressive modelling of Canadian money and income data . Journal of the American Statistical Association 74 : 553 – 560 .
   Web of Science ®Google Scholar
• Hsiao , C. 1981 . Autoregressive modelling and money-income causality detection . Journal of Monetary Economics 7 : 85 – 106 .
   Web of Science ®Google Scholar
• Kalogeropoulos , G.I. 1985 . Matrix Pencils and Linear Systems . PhD Thesis , City University , London .
   Google Scholar
• Karcanias , N. 1979 . Matrix pencil approach to geometric systems theory . Proc. IEE 126 : 585 – 590 .
   Google Scholar
• Karcanias , N. , and Hayton , G.E. 1981 . Generalized autonomous differential systems, algebraic duality, and geometric theory . Proceedings, IFAC VIII , Triennial World Congress , Kyoto , Japan .
   Google Scholar
• Kendrick , D.A. 1972 . On the Leontief dynamic inverse . Quarterly Journal of Economics 86 : 693 – 696 .
   Web of Science ®Google Scholar
• Kendrick , D.A. 2005 . Stochastic control for economic models: past, present and the paths ahead . Journal of Economic Dynamics and Control 29 : 3 – 30 .
   Google Scholar
• King , R.G. , and Watson , M.W. 1998 . The solution of singular linear difference systems under rational expectations . International Economic Review 39 ( 4 ): 1015 – 1026 .
   Web of Science ®Google Scholar
• Kreijger , R.G. , and Neudecker , H. 1976 . Kendrick's forward integration method and the dynamic Leontief multisectoral model . Quarterly Journal of Economics 90 : 505 – 507 .
   Google Scholar
• Leontief , W. 1954 . Mathematics in economics . Bulletin of the American Mathematical Society 60 : 215 – 233 .
   Google Scholar
• Leontief , W. 1977 . Essays in Economics . M. E. Sharpe , New York .
   Google Scholar
• Leontief , W. 1986 . Input-Output Economics. , 2nd ed. Oxford University Press , New York .
   Google Scholar
• Livesey , D.A. 1973 . The singularity problem in the dynamic input-output model . International Journal of System Science 4 : 437 – 440 .
   Web of Science ®Google Scholar
• Luenberger , D.G. , Arbel , A. 1977 . Singular dynamic Leontief systems . Economitrica 45 : 991 – 995 .
   Web of Science ®Google Scholar
• Lütkepohl , H. 1982 . Non-causality due to omitted variables . Journal of Econometrics 19 : 367 – 378 .
   Web of Science ®Google Scholar
• Sims , C.A. 1972 . Money, income and causality . American Economic Review 62 : 540 – 552 .
   Web of Science ®Google Scholar
• Tustin , A. 1953 . The Mechanism of Economic Systems: An Approach to the Problem of Economic Stabilisation from the Point of View of Control-System Engineering . Harvard University Press , Cambridge , MA .
   Google Scholar
• Williams , D. , Goodhart , C.A.E. , and Gowland , D.H. 1976 . Money, income and causality: The U.K. experience . American Economic Review 66 : 417 – 423 .
   Web of Science ®Google Scholar
• Zimbidis , A.A. , and Haberman , S. 2001. Controlling the solvency interaction among group of insurance companies. Journal of Actuarial Practice 9:151–187.
   Google Scholar
• Zimbidis , A.A. , and Haberman , S. 2001 . The combined effect of delay and feedback in the insurance pricing process . Insurance Mathematics and Economics 28 : 263 – 280 .
   Google Scholar
• Zimbidis , A.A. , Pantelous , A.A. , and Kalogeropoulos , G.I. 2008 . A generalized linear discrete time model for managing the solvency interaction and singularities arising from potential regulatory constraints imposed within a portfolio of different insurance products . Proceedings of the 38th ASTIN Colloquium , July , Manchester UK .
   Google Scholar