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Original Articles

Approximation of insurance liability contracts using radial basis functions

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Pages 2245-2271 | Received 18 Oct 2017, Accepted 10 Aug 2018, Published online: 27 Feb 2019

References

  • D. Bauer, D. Bergmann, and A. Reuss, Solvency II and nested simulations – a least-squares Monte Carlo approach, Proceedings of the 2010 ICA Congress, 2010.
  • M. Benzi, G.H. Golub, and J. Liesen, Numerical solution of saddle point problems, Acta Numer. 14 (2005), pp. 1–137.
  • F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973), pp. 637–654.
  • J.P. Boyd, Six strategies for defeating the Runge phenomenon in Gaussian radial basis functions on a finite interval, Comput. Math. Appl. 60(12) (2010), pp. 3108–3122.
  • D. Brigo and F. Mercurio, Interest Rate Models-Theory and Practice: With Smile, Inflation and Credit, Springer, 2007.
  • M. Buhmann, Radial Basis Functions: Theory and Implementations, volume 12 of Cambridge Monographs on Applied and Computational Mathematics, 2003.
  • J.R. Bunch and J.E. Hopcroft, Triangular factorization and inversion by fast matrix multiplication, Math. Comput. 28(125) (1974), pp. 231–236.
  • J.C. Carr, R.K. Beatson, B.C. McCallum, W.R. Fright, T.J. McLennan, and T.J. Mitchell, Smooth surface reconstruction from noisy range data, Proceedings of the 1st International Conference on Computer Graphics and Interactive Techniques in Australasia and South East Asia, ACM, 2003, p. 119.
  • J. Cramwinckel, S. Singor and A.L. Varbanescu, FiNS: A framework for accelerating nested simulations on heterogeneous platforms, in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 9523, 2015, pp. 246–257.
  • S. De Marchi, On optimal center locations for radial basis function interpolation: Computational aspects, Rend. Sem. Mat. Univ. Pol. Torino (Splines Radial Basis Functions and Applications) 61(3) (2003), pp. 343–358.
  • G.E. Fasshauer, Meshfree Approximation Methods with MATLAB, Vol. 6, World Scientific, 2007.
  • G.E. Fasshauer, Positive definite kernels: Past, present and future, Dolomite Res. Notes Approx. 4 (2011), pp. 21–63.
  • G.E. Fasshauer and M.J. McCourt, Stable evaluation of Gaussian radial basis function interpolants, SIAM J. Sci. Comput. 34(2) (2012), pp. A737–A762.
  • N. Flyer and E. Lehto, Rotational transport on a sphere: Local node refinement with radial basis functions, J. Comput. Phys. 229(6) (2010), pp. 1954–1969.
  • B. Fornberg, T. Driscoll, G. Wright, and R. Charles, Observations on the behavior of radial basis function approximations near boundaries, Comput. Math. Appl. 43(3) (2002), pp. 473–490.
  • B. Fornberg and N. Flyer, A Primer on Radial Basis Functions with Applications to the Geosciences Vol. 87, SIAM, Philadelphia, 2015.
  • B. Fornberg, E. Larsson, and N. Flyer, Stable computations with Gaussian radial basis functions, SIAM J. Sci. Comput. 33(2) (2011), pp. 869–892.
  • B. Fornberg and C. Piret, A stable algorithm for flat radial basis functions on a sphere, SIAM J. Sci. Comput. 30(1) (2007), pp. 60–80.
  • P. Glasserman, Monte Carlo Methods in Financial Engineering, Vol. 53, Springer, New York, 2004.
  • N.A. Gumerov and R. Duraiswami, Fast radial basis function interpolation via preconditioned krylov iteration, SIAM. J. Sci. Comput. 29(5) (2007), pp. 1876–1899.
  • A. Heryudono, E. Larsson, A. Ramage, and L. von Sydow, Preconditioning for radial basis function partition of unity methods, J. Sci. Comput. 67(3) (2016), pp. 1089–1109.
  • Y.-C. Hon and X.-Z. Mao, A radial basis function method for solving options pricing models, J. Financ. Eng. 8 (1999), pp. 31–50.
  • A. Iske, Scattered data modelling using radial basis functions, in Tutorials on Multiresolution in Geometric Modelling, Springer, 2002, pp. 205–242.
  • A. Iske, Multiresolution Methods in Scattered Data Modelling, Vol. 37, Springer Science & Business Media, 2004.
  • J. Lewis, F. Pighin, and K. Anjyo, Scattered data interpolation and approximation for computer graphics, in ACM SIGGRAPH ASIA 2010 Courses, ACM, 2010, p. 2.
  • L. Ling and E.J. Kansa, A least-squares preconditioner for radial basis functions collocation methods, Adv. Comput. Math. 23(1) (2005), pp. 31–54.
  • N. Mai-Duy and T. Tran-Cong, Approximation of function and its derivatives using radial basis function networks, Appl. Math. Model. 27(3) (2003), pp. 197–220.
  • C.A. Micchelli, Interpolation of scattered data: Distance matrices and conditionally positive definite functions, Constr. Approx. 2(1) (1986), pp. 11–22.
  • H. Niederreiter, Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Am. Math. Soc. 84(6) (1978), pp. 957–1042.
  • W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, Vol. 2, Citeseer, 1996.
  • S. Rippa, An algorithm for selecting a good value for the parameter c in radial basis function interpolation, Adv. Comput. Math. 11(23) (1999), pp. 193–210.
  • C. Runge, ‘Uber empirische Funktionen und die Interpolation zwischen 'aquidistanten Ordinaten, Zeitschrift f”ur Mathematik und Physik 46(224–243) (1901), p. 20.
  • Y. Sanyasiraju and C. Satyanarayana, On optimization of the RBF shape parameter in a grid-free local scheme for convection dominated problems over non-uniform centers, Appl. Math. Model. 37(12) (2013), pp. 7245–7272.
  • R. Schaback, Error estimates and condition numbers for radial basis function interpolation, Adv. Comput. Math. 3(3) (1995), pp. 251–264.
  • M. Scheuerer, An alternative procedure for selecting a good value for the parameter c in RBF-interpolation, Adv. Comput. Math. 34(1) (2011), pp. 105–126.
  • I.J. Schoenberg, Metric spaces and completely monotone functions, Ann. Math. 39(4) (1938), pp. 811–841.
  • G. Wahba, Spline Models for Observational Data, SIAM, Philadelphia, 1990.
  • H. Wendland, Scattered Data Approximation, Vol. 17, Cambridge University Press, 2004.
  • Z.-M. Wu and R. Schaback, Local error estimates for radial basis function interpolation of scattered data, IMA J. Numer. Anal. 13(1) (1993), pp. 13–27.

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