Articles Thesis Popular publications Selected technical reports Lecture notes


Articles
  1. Shota Gugushvili, Frank van der Meulen, Moritz Schauer and Peter Spreij (2019), Nonparametric Bayesian estimation of a Hölder continuous diffusion coefficient, Brazilian Journal of Probability and Statistics, accepted for publication.

  2. Peter Spreij and Jaap Storm (2019), Diffusion limits for a markov modulated binomial counting process, Probability in the Engineering and Informational Sciences, online.

  3. Shota Gugushvili, Frank van der Meulen, Moritz Schauer and Peter Spreij (2019), Nonparametric Bayesian volatility estimation, 2017 MATRIX Annals, Editors: David R. Wood, Jan de Gier, Cheryl E. Praeger, Terence Tao. MATRIX Book Series, Volume 2, Springer, 279-302. (pdf)

  4. G.A. Delsing, M.R.H. Mandjes, P.J.C. Spreij, E.M.M. Winands (2019), An optimization approach to adaptive multi-dimensional capital management, Insurance: Mathematics and Economics 84, 87-97.

  5. Shota Gugushvili, Frank van der Meulen and Peter Spreij (2018), A non-parametric Bayesian approach to decompounding from high frequency data, Statistical Inference for Stochastic Processes 21, 53-79.

  6. Michel Mandjes and Peter Spreij (2017), A note on the central limit theorem for the idleness process in a one-sided reflected Ornstein-Uhlenbeck model, Statistica Neerlandica 71(3), 225-235.

  7. Michel Mandjes and Peter Spreij (2016), Explicit computations for some Markov modulated counting processes, Advanced Modelling in Mathematical Finance, In Honour of Ernst Eberlein, Jan Kallsen and Antonis Papapantoleon Eds., Springer Proceedings in Mathematics & Statistics 189, 63-92.

  8. Shota Gugushvili and Peter Spreij (2016), Posterior contraction rate for non-parametric Bayesian estimation of the dispersion coefficient of a stochastic differential equation, ESAIM: Probability and Statistics 20, 143-153.

  9. Gang Huang, Michel Mandjes, Peter Spreij (2016), Large deviations for Markov-modulated diffusion processes with rapid switching, Stochastic Processes and their Applications 126, 1785-1818.

  10. Gang Huang, Marijn Jansen, Michel Mandjes, Peter Spreij, Koen De Turck (2016), Markov-modulated Ornstein-Uhlenbeck processes, Advances in Applied Probability 48(1), 235-254.

  11. Lorenzo Finesso and Peter Spreij (2016), Factor analysis models via I-divergence optimizations, Psychometrika 81, 702-726.

  12. Lorenzo Finesso and Peter Spreij (2015), Approximation of Nonnegative Systems by Finite Impulse Response Convolutions, IEEE Transactions on Information Theory 61(8), 4399-4409.

  13. Shota Gugushvili, Frank van der Meulen, Peter Spreij (2015), Non-parametric Bayesian inference for multi-dimensional compound Poisson processes, Modern Stochastics: Theory and Applications 2, 1-15.

  14. André Klein and Peter Spreij (2014), A block Hankel generalized confluent Vandermonde matrix, Linear Algebra and its Applications 455, 32-72.

  15. M. van Beek, M. Mandjes, P. Spreij, E. Winands (2014), Markov switching affine processes and applications to pricing, Proceedings of the Actuarial and financial mathematics conference, Brussel, February 6-7, 2014, 97-102 (Griselda Deelstra, Ann De Schepper, Jan Dhaene, Wim Schoutens, Steven Vanduffel, Michèle Vanmaele, David Vyncke eds.).

  16. Shota Gugushvili and Peter Spreij (2014), Non-parametric Bayesian drift estimation for stochastic differential equations, Lithuanian Mathematical Journal 54(2) 127-141.

  17. Gang Huang, Michel Mandjes, Peter Spreij (2014), Weak convergence of Markov-modulated diffusion processes with rapid switching, Statistics & Probability Letters 86, 74-79.

  18. Shota Gugushvili and Peter Spreij (2014), Consistent non-parametric Bayesian estimation for a time-inhomogeneous Brownian motion, ESAIM: Probability and Statistics 18, 332-341.

  19. Gang Huang, Michel Mandjes, Peter Spreij (2014), Limit theorems for reflected Ornstein-Uhlenbeck processes, Statistica Neerlandica 68(1), 25-42.

  20. André Klein and Peter Spreij (2012). Transformed statistical distance measures and the fisher information matrix, Linear Algebra and its Applications 437(2), 692-712.

  21. Shota Gugushvili and Peter Spreij (2012), Parametric inference for stochastic differential equations: a smooth and match approach, Latin American Journal of Probability and Mathematical Statistics, 9(2), 609-635.

  22. Peter Spreij and Enno Veerman (2012), Affine diffusions with non-canonical state space, Stochastic Analysis and Applications 30, 605-641.

  23. Vincent Leijdekker, Michel Mandjes, Peter Spreij (2011), Sample-path Large Deviations in Credit Risk, Journal of Applied Mathematics, Article ID 354171.

  24. Bert van Es, Shota Gugushvili, Peter Spreij (2011), Deconvolution for an atomic distribution: rates of convergence, Journal of Nonparametric Statistics 23(4), 1003-1029.

  25. Bert van Es, Peter Spreij (2011), Estimation of a multivariate stochastic volatility density by kernel deconvolution, Journal of Multivariate Analysis 102, 683-697.

  26. Vincent Leijdekker and Peter Spreij (2011), Explicit Computations for a Filtering Problem with Point Process Observations with Applications to Credit Risk, Probability in the Engineering and Informational Sciences 25, 393-418.

  27. A.J. van Es, P.J.C. Spreij, J.H. van Zanten (2011), Nonparametric methods for volatility density estimation, Advanced Mathematical Methods for Finance, Chapter 11, 293-312 (Giulia di Nunno, Bernt Øksendal Eds., Springer).

  28. Peter Spreij, Enno Veerman and Peter Vlaar (2011), An affine two-factor heteroskedastic macro-finance term structure model, Applied Mathematical Finance, 18(4), 331-352.

  29. L. Finesso, A. Grassi, and P. Spreij (2010), Two-step nonnegative matrix factorization algorithm for the approximate realization of hidden Markov models, Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems - MTNS 2010, 5-9 July, 2010, Budapest (A. Edelmayer ed.), 369-374.

  30. Lorenzo Finesso, Angela Grassi, Peter Spreij (2010), Approximation of stationary processes by Hidden Markov Models, Mathematics of Control, Signals and Systems 22(1), 1-22.

  31. André Klein and Peter Spreij (2010), Tensor Sylvester matrices and the Fisher information matrix of VARMAX processes, Linear Algebra and its Applications 432(8), 1975-1989.

  32. André Klein and Peter Spreij (2009), Matrix differential calculus applied to multiple stationary time series and an extended Whittle formula for information matrices, Linear Algebra and its Applications 430(2-3), 674-691.

  33. Matthijs van Veelen and Peter Spreij (2009), Evolution in games with a continuous action space, Economic Theory 39, 355-376.

  34. Lorenzo Finesso, Angela Grassi, Peter Spreij (2008), Approximation of the I-divergence between stationary and hidden Markov processes, Proceedings of the 4th International Workshop on Applied Probability, Université de Technologie de Compiègne, France, July 7-10, 2008.

  35. Bert van Es, Shota Gugushvili, Peter Spreij (2008), Deconvolution for an atomic distribution, Electronic Journal of Statistics 2, 265-297.

  36. André Klein and Peter Spreij (2007), Recursive Solution of Certain Structured Linear Systems, SIAM Journal on Matrix Analysis and Applications 29(4), 1191-1217.

  37. Lorenzo Finesso and Peter Spreij (2007), Factor Analysis and Alternating Minimization, in Modeling, Estimation and Control, Festschrift in Honor of Giorgio Picci on the Occasion of his Sixty-Fifth Birthday, Alessandro Chiuso, Stefano Pinzoni and Augusto Ferrante Eds, Springer Lecture Notes in Control and Information Sciences 364, 85-96.

  38. Bert van Es, Shota Gugushvili and Peter Spreij (2007), A kernel type nonparametric density estimator for decompounding, Bernoulli 13(3), 672-694.

  39. André Klein and Peter Spreij (2006), An explicit expression for the Fisher information matrix of a multiple time series process, Linear Algebra and its Applications 417, 140-149.

  40. Lorenzo Finesso and Peter Spreij (2006), Nonnegative Matrix Factorization and I-Divergence Alternating Minimization, Linear Algebra and its Applications 416, 270-287.

  41. André Klein and Peter Spreij (2006), The Bezoutian and Fisher's information matrix of an ARMA process, Linear Algebra and its Applications 416, 160-174.

  42. André Klein, Guy Mélard and Peter Spreij (2005), On the resultant property of the Fischer information matrix of a vector ARMA process, Linear Algebra and its Applications 403, 291-313.

  43. André Klein and Peter Spreij (2005), On the solution of Stein's equation and Fishers information matrix of an ARMAX process, Linear Algebra and its Applications 396, 1-34.

  44. A.J. van Es, P.J.C. Spreij, J.H. van Zanten (2005), Nonparametric volatility density estimation for discrete time models, Journal of Nonparametric Statistics 17 (2), 237-249.

  45. Lorenzo Finesso and Peter Spreij (2004), Approximate Nonnegative Matrix Factorization via Alternating Minimization, Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems, Leuven, July 5-9, 2004.

  46. A. Lucas, P. Klaassen, P.J.C. Spreij and S. Straetmans (2003), Tail behaviour of credit loss distributions for general latent factor models, Applied Mathematical Finance 10 (4), 337-357.

  47. Peter Spreij (2003), On hidden Markov chains and finite stochastic systems, Statistics and Probability Letters 62, 189-201.

  48. A. Klein and P.J.C. Spreij (2003), Some results on Vandermonde matrices with an application to time series analysis, SIAM Journal on Matrix Analysis, 25 (1), 213-223.

  49. A.J. van Es, P.J.C. Spreij, J.H. van Zanten (2003), Nonparametric Volatility Density Estimation, Bernoulli 9 (3), 451-645.

  50. K. Dzhaparidze, P.J.C. Spreij and E. Valkeila (2003), Information processes for semimartingale experiments, Annals of Probability 31, 216-243.

  51. K. Dzhaparidze, P.J.C. Spreij and E. Valkeila (2003), Information concepts for filtered experiments, Theory of Probability and Mathematical Statistics 67, 38-56.

  52. L. Finesso and P.J.C. Spreij (2002), Stochastic Realization of Hidden Markov Chains, Proceedings of the IEEE Information Theory Workshop, Bangalore, October 20-25, 2002, 90-93.

  53. A. Lucas, P. Klaassen, P.J.C. Spreij, S. Straetmans (2002), Extreme Tails for Linear Portfolio Credit Risk Models, Proceedings of the Third Joint Central Bank Research Conference, Basle, 271-283.

  54. P.J.C. Spreij (2001), On the Markov property of a finite hidden Markov chain, Statistics and Probability Letters, Vol 52/3, 279-288.

  55. A. Klein and P.J.C. Spreij (2001), On Stein's equation, Vandermonde matrices and Fisher's information matrix of time series processes. Part I: The autoregressive moving average process, Linear Algebra and its Applications 329(1-3), 9-47.

  56. A. Lucas, P. Klaassen, P.J.C. Spreij and S. Straetmans (2001), An analytic approach to credit risk of large corporate bond and loan portfolios, Journal of Banking and Finance 25 (9), 1635-1664; Erratum, Journal of Banking and Finance, 26 (1), 201-202.

  57. K. Dzhaparidze. P.J.C. Spreij and J.H. van Zanten (2000), Some aspects of modeling and statistical inference for financial models, Statistica Neerlandica 54, 265-292.

  58. P. Klaassen, A. Lucas, P. Spreij, S. Straetmans. (1999): On the Distribution of Credit Losses of Corporate Bond and Loan Portfolios, in: Financiering en Belegging 1999 (deel 22), Rotterdam, Erasmus Universiteit, 172-188.

  59. P.J.C. Spreij (1998), A representation result for finite Markov chains, Statistics and Probability Letters 38, 183-186.

  60. K. Dzhaparidze, P.J.C. Spreij and E. Valkeila (1997), On Hellinger Processes for Parametric Families of Experiments, Statistics and control of stochastic processes, the Liptser Festschrift, Yu.M. Kabanov, B.L. Rozovskii, A.N. Shiryaev Eds., 41-61, World Scientific.

  61. A. Klein and P.J.C. Spreij (1997), On Fisher's information matrix of an ARMA process, Stochastic differential and difference equations, I. Csiszar and Gy. Michaletzky eds., 273-284, Birkhäuser.

  62. P.J.C. Spreij (1996), A crash course in stochastic calculus with applications to mathematical finance, CWI Quarterly 9, 357-388.

  63. P.J.C. Spreij (1996), On Markov chains and filtrations (no wine nor bottles), in `Frontiers in pure and applied probability II', A.N. Shiryaev et al. eds, TVP Science Publishers, Moscow, 187-194.

  64. A. Klein and P.J.C. Spreij (1996), On Fisher's information matrix of an ARMAX process and Sylvester's resultant matrices, Linear Algebra and its Applications 237/238, 579-590.

  65. K. Dzhaparidze and P.J.C. Spreij (1996), On optimality for regular projective estimators for semimartingale models, part III: One step improvements, Stochastics and Stochastics Reports 56, 63-74.

  66. P.J.C. Spreij (1994), On Markov chains and point processes, in: "Information theory, statistical decision functions, random processes", P. Lachout, J.A. Vísek eds., Academy of Sciences of the Czech Republic.

  67. K. Dzhaparidze and P.J.C. Spreij (1994), Spectral characterization of the optional quadratic variation process, Stoch. Proc. Applic. 54, 165-174.

  68. K. Dzhaparidze and P.J.C. Spreij (1994), On optimality of regular projective estimators for semimartingale models, part II: asymptotically linear estimators, Stochastics and Stochastics Reports 47, 247-268.

  69. K. Dzhaparidze and P.J.C. Spreij (1993), On optimality of regular projective estimators, Stochastics and Stochastics Reports 43, 161-178.

  70. K. Dzhaparidze and P.J.C. Spreij (1993), The strong law of large numbers for martingales with deterministic quadratic variation, Stochastics and Stochastics Reports 42, 53-65.

  71. K. Dzhaparidze and P.J.C. Spreij (1993), On correlation calculus for multivariate martingales, Stoch. Proc. Appl. 46, 283-299.

  72. P.J.C. Spreij (1991), Recursive approximate ML estimation for a class of counting process models, Journal of Multivariate Analysis 39, 236-245.

  73. P.J.C. Spreij (1990), Minimality and reducibility of conditionally Poisson systems with finite state space, Stochastics 31, 55-77.

  74. P.J.C. Spreij (1990), Selfexciting counting process systems with finite state space, Stoch. Proc. Appl. 34, 275-295.

  75. P.J.C. Spreij (1986), Recursive parameter estimation for counting processes with linear intensity, Stochastics 18, 277-312.

  76. P.J.C. Spreij (1986), An on-line parameter estimation algorithm for counting process systems, IEEE Tr. Inf. Th. 32, 300-303.

  77. P.J.C. Spreij (1985), Parameter estimation for a specific software reliability model, IEEE Tr. Rel. 34, 323-329.

  78. G. Koch and P.J.C. Spreij (1983), Software reliability as an application of martingale and filtering theory, IEEE Tr. Rel. 32, 342-345.

Thesis Popular publications
  1. Peter Spreij (2013), Open brief aan Louise Gunning.

  2. Peter Spreij (2011), Het woord aan .... Peter Spreij, Scoop (September 2011), volledige tekst (June 2011).

  3. Peter Spreij (2003), Webklassen, Nieuwe Wiskrant 22(4), 26-27 .

  4. Peter Spreij (2002), De Itô-formule zonder stochastische integralen, Nieuw Archief voor Wiskunde, vijfde serie, deel 3, nummer 1, 21-22.

  5. Frans Boshuizen, Peter Spreij (2002), Rekenen aan hypotheken, Nieuw Archief voor Wiskunde, vijfde serie, deel 3, nummer 1, 42-48.

  6. Bert van Es en Peter Spreij (2001), Zucht, nee hè ... niet nog een paradox!, Nieuwsbrief van het KdV Insituut, september 2001, 17-20.

  7. Frans Boshuizen en Peter Spreij (2001), Risicomanagement in financiële instellingen, StatOR 2(2), 22-25.

  8. K. Dzhaparidze and P.J.C. Spreij (1999), Statistical Methods for Financial and other Dynamical Stochastic Models, ERCIM News 38, 9-10.

  9. Peter Spreij en Robin de Vilder (1999), AEX en DAX, Pythagoras 38 (april 1999), 13-17.

  10. Peter Spreij en Robin de Vilder (1999), Beurskoersen en toeval, Pythagoras 38 (februari 1999), 9-14.

Selected technical reports
  1. G.A. Delsing, M.R.H. Mandjes, P.J.C. Spreij, E.M.M. Winands (2018), Asymptotics and approximations of ruin probabilities for multivariate risk processes in a Markovian environment, arXiv:1812.09069.

  2. Lorenzo Finesso, Peter Spreij (2018), Approximation of nonnegative systems by moving averages of fixed order, arXiv:1810.10135.

  3. Shota Gugushvili, Frank van der Meulen, Moritz Schauer, Peter Spreij (2018), Bayesian wavelet de-noising with the caravan prior, arXiv:1810.07668.

  4. Shota Gugushvili, Frank van der Meulen, Moritz Schauer, Peter Spreij (2018), Nonparametric Bayesian volatility learning under microstructure noise, arXiv:1805.05606.

  5. Denis Belomestny, Shota Gugushvili, Moritz Schauer, Peter Spreij (2018), Nonparametric Bayesian inference for Lévy subordinators, arXiv:1804.11267.

  6. Mike Derksen, Peter Spreij, Sweder van Wijnbergen (2018), Accounting Noise and the Pricing of CoCos, arXiv:1804.06890.

  7. Shota Gugushvili, Frank van der Meulen, Moritz Schauer, Peter Spreij (2018), Fast and scalable non-parametric Bayesian inference for Poisson point processes, arXiv:1804.03616.

  8. Shota Gugushvili, Frank van der Meulen, Moritz Schauer, Peter Spreij (2018), Nonparametric Bayesian volatility estimation, arXiv:1801.09956 [math.ST].

  9. Peter Spreij, Jaap Storm (2018), Diffusion limits for a Markov modulated counting process, arXiv:1801.03682 [math.ST].

  10. Shota Gugushvili, Frank van der Meulen, Moritz Schauer, Peter Spreij (2017), Nonparametric Bayesian estimation of a Hölder continuous diffusion coefficient, arXiv:1706.07449 [math.ST].

  11. M. Mandjes, N.J. Starreveld, R. Bekker, P. Spreij (2017), Dynamic Erdös-Rényi graphs, arXiv:1703.05505 [math.PR].

  12. Shota Gugushvili, Peter Spreij (2013), A note on non-parametric Bayesian estimation for Poisson point processes, Mathematics arXiv 1304.7353.

  13. Lorenzo Finesso, Angela Grassi, Peter Spreij (2010), Two-step Nonnegative Matrix Factorization Algorithm for the Approximate Realization of Hidden Markov Models, Mathematics arXiv 0812.1804.

  14. Peter Spreij, Enno Veerman (2010), The affine transform formula for affine diffusions with convex state space, Mathematics arXiv 1005.1099.

  15. Peter Spreij, Enno Veerman (2008), Negative volatility for a 2-dimensional square root SDE, Mathematics arXiv 0807.1224.

  16. A. Lucas, P. Klaassen, P.J.C. Spreij and S. Straetmans (1999), Tail Behavior of Credit Loss Distributions, Vrije Universiteit research memorandum 1999-60.

  17. K. Dzhaparidze, P.J.C. Spreij and E. Valkeila (1998), On a posterior information process for parametric families of experiments, CWI report PNA-R9818.

  18. P.J.C. Spreij (1997), On Markov chains and filtrations, Tinbergen Institute, discussion paper, TI 97-029/4, also on IDEAS.

Lecture notes
  1. Measure theoretic probability

  2. Stochastic integration

  3. Portfolio theory

  4. Introduction to stochastic finance in continuous time



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