Tomasz R. Bielecki   
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. . . . . . . . . . . . . . . . . . . . . .       Publications . . . . . . . . . . . . . . . . . . . . . .
Selected Publications
  1. Generalized Hawkes Processes, Generalized Multivariate Hawkes Processes and Some of Their Properties and Applications (with J. Jakubowski and Mariusz Niewęgłowski), submitted, 2021,
  2. Time-inconsistent Markovian control problems under model uncertainty with application to the mean-variance portfolio selection (with I. Cialenco and T. Chen), forthcoming, International Journal of Theoretical and Applied Finance, 2021,
  3. Wiener-Hopf Factorization Technique for Time-Inhomogeneous Finite Markov Chains (with I. Cialenco, Z. Cheng and R. Gong), Stochastics: An International Journal of Probability and Stochastic Processes, Volume 93, Issue 1, pp. 130-166, 2021,
  4. Semimartingales and Shrinkage of Filtration (with J. Jakubowski, M. Jeanblanc and Mariusz Niewęgłowski), forthcoming, Annals of Applied Probability, 2021,
  5. Wiener-Hopf Factorization for Arithmetic Brownian Motion with Time-Dependent Drift and Volatility (with Z. Cheng and R. Gong), submitted, 2020,
  6. Fair Estimation of Capital Risk Allocation (with I. Cialenco, M. Pitera and T. Schmidt), Statistics & Risk Modeling, Volume 37, Issue 1-2, pp. 1-24, 2020,
  7. Wiener-Hopf Factorization for Time-Inhomogeneous Markov Chains and Its Application (with I. Cialenco, R. Gong and Y. Huang), Probability and Mathematical Statistics, 40(2), 225 – 244, 2020,
  8. Adaptive Robust Control Under Model Uncertainty (with I. Cialenco, T. Chen, A. Cousin and M. Jeanblanc), SIAM J. Control Optim (SICON) 57(2), pp. 925–946, 2019,
  9. A Dynamic Model of Central Counterparty Risk (with I. Cialenco and S. Feng), International Journal of Theoretical and Applied Finance, Vol. 21, No. 08, 1850050 (32 pages), 2018,
    10. (with Tomasz R. Bielecki, )
  10. Arbitrage-Free Pricing of Derivatives in Nonlinear Market Models (with I. Cialenco adn M. Rutkowski), Probability, Uncertainty and Quantitative Risk 3:2, (56 pages), 2018,
  11. Recursive Construction of Confidence Regions (with T. Chen and I. Cialenco), Electronic J. Statistics, 11(2), pp. 4674-4700, 2017,
  12. A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective (with M. Pitera and I. Cialenco), Probability, Uncertainty and Quantitative Risk, 2:3, pp.1-52, 2017,
  13. Conditional Markov Chains: Properties, Construction and Structured Dependence (with J. Jakubowski and M. Nieweglowski), Stochastic Processes and their Applications, Volume 127, Issue 4, Pages 1125-1170, 2017,
  14. Dynamic Conic Finance via Backward Stochastic Difference Equations (with T. Chen and I. Cialenco), SIAM J. Financial Math., vol. 6, pp. 1068-1122, 2015,
  15. Conditional Markov Chains Part II: Consistency and Copulae (with J. Jakubowski and M. Nieweglowski), 2015,
  16. Conditional Markov Chains Revisited Part I: Construction and properties (with J. Jakubowski and M. Nieweglowski), 2015,
  17. Valuation and hedging of contracts with funding costs and collateralization (with M. Rutkowski), SIAM J. Finan. Math., 6(1), 594–655, 2015
  18. Joint Hitting-Time Densities for Finite State Markov Processes (with M. Jeanblanc and D. A. Sezer), Turk. J. Math. vol. 42, pp. 586 – 608, 2018 2014,
  19. On time consistency of dynamic risk and performance measures in discrete time (with I. Cialenco and Marcin Pitera) 2014, < arXiv, PDF
  20. Dynamic Limit Growth Indices in Discrete Time (with I. Cialenco and Marcin Pitera) 2013, arXiv, PDF
  21. Dynamic Assessment Indices, (with I. Cialenco, Samuel Drapeau and Martin Karliczek) 2013, arXiv.
  22. Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices, (with I. Cialenco, I. Iyigunler and R. Rodriguez), International Journal of Theoretical and Applied Finance, vol. 16, No 1, 2013. DOI:10.1142/S0219024913500027, arXiv.
  23. Collateralized CVA Valuation with Rating Triggers and Credit Migrations, (with I. Cialenco and I. Iyigunler), International Journal of Theoretical and Applied Finance, vol. 16, No 2, 2013. DOI:10.1142/S021902491350009X, arXiv.
  24. Intricacies of Dependence between Components of Multivariate Markov Chains: Weak Markov Consistency and Markov Copulae, (with J. Jakubowski and M. Nieweglowski), , 2011.
  25. Dynamic Modeling of Portfolio Credit Risk with Common Shocks, (with A. Cousin, S. Crepey and A. Herbertsson), , 2011.
  26. Counterparty Risk and the Impact of Collateralization in CDS Contracts, (with I. Cialenco and I. Iyigunler), in Stochastic Processes, Finance and Control: A Festschrift in Honor of Robert J. Elliott (Vol. 1, Advances in Statistics, Probability and Actuarial Sciences), Editors Samuel N. Cohen, Dilip Madan, Tak Kuen Siu, World Scientific, 2012 arXiv.
  27. Dynamic Coherent Acceptability Indices and their Applications to Finance, (with I. Cialenco and Z. Zhang), Forthcoming in Mathematical Finance, 2011, arXiv.
  28. Dynamic Hedging of Counterparty Exposure, (with S. Crepey), Forthcoming in The Musiela Festschrift, Zariphopoulou, T., Rutkowski, M. and Kabanov, Y., eds, Springer, 2011.
  29. Valuation and Hedging of CDS Counterparty Exposure in a Markov Copula Model, (with S. Crepey, M. Jeanblanc and B. Zargari), Forthcoming in International Journal of Theoretical and Applied Finance, 2011.
  30. Dynamic Modeling of Dependence in Finance via Copulae Between Stochastic Processes, (with J. Jakubowski and M. Nieweglowski), to appear in the special invited Copula Theory and Its Applications: Proceedings of the Workshop Held in Warsaw, 25 - 26 September 2009.
  31. CVA computation for counterparty risk assessment in credit portfolios, (with S. Assefa, S. Crepey and M. Jeanblanc), to appear in the special invited Volume "Credit Risk Frontiers: Subprime crisis, Pricing and Hedging, CVA, MBS, Ratings and Liquidity," Wiley, 2011.
  32. Study of Dependence for Some Stochastic Processes; Part II: Symbolic Markov Copulae, (with J. Jakubowski and M. Nieweglowski), Stochastic Processes and Applications, in revision, 2011.
  33. Hedging of Credit Default Swaptions in a Hazard Process Model, (with M. Jeanblanc and M, Rutkowski), Forthcoming in Finance and Stochastics, 2010.
  34. Convertible Bonds in a Defaultable Diffusion Model, (with S. Crepey, M. Jeanblanc and M. Rutkowski), Stochastic Analysis with Financial Applications, A. Kohatsu - Higa, N. Privault, S.J. Sheu, eds, Birkhauser Verlag, 2010.
  35. Markov Chain Models of Portfolio Credit Risk, (with S. Crepey and A. Herbertsson), Oxford Handbook of Credit Derivatives edited by A. Rennie and A. Lipton, Oxford University Press, 2011.
  36. Up and down credit risk, (with S. Crepey and M. Jeanblanc), Quantitative Finance, Vol. 10, No. 10, PP. 1137 - 1151, 2010.
  37. Defaultable Game Options in a Hazard Process Model, (with S. Crepey, M. Jeanblanc and M. Rutkowski), Journal of Applied Mathematics and Stochastic Analysis , Article ID 695798, 2009.
  38. Pricing and Trading Credit Default Swaps in a Hazard Process Model, (with M. Jeanblanc, M. Rutkowski), Annals of Applied Probability, Vol. 18, No. 6, pp. 2495 - 2529, 2008.
  39. Study of Dependence for Some Stochastic Processes, (with J. Jakubowski, A. Vidozzi, L. Vidozzi), Stochastic Analysis and Applications, vol. 26, Issue 4, pp. 903 - 924, 2008.
  40. Mathematical Models of Credit Risk, (with Monique Jeanblanc), Encyclopedia of Quantitative Risk Assessment, Editors - in - Chiefs Brian Everitt and Ed Melnick, John Wiley & Sons, 2008.
  41. Defaultable Options in a Markovian Intensity Model of Credit Risk, (with S. Crepey, M. Jeanblanc and M. Rutkowski), Mathematical Finance, Vol. 18, Issue 4, pp. 493 - 518, October 2008.
  42. Completeness of a general semimartingale market under constrained trading, (with M. Jeanblanc and M. Rutkowski), Stochastic finance, 83 - 106, Springer, New York, 2006.
  43. Hedging of Credit Derivatives in Models with Totally Unexpected Default, (with M. Jeanblanc and M. Rutkowski), Stochastic processes and applications to mathematical finance, 35 - 100, World Sci. Publ., Hackensack, NJ, 2006.
  44. PDE Approach to Valuation and Hedging of Credit Derivatives, (with M. Jeanblanc and M. Rutkowski), Quantitative Finance, Vol. 5, No. 3, pp. 257 - 270, 2005.
  45. Markov Copulae Approach to Pricing and Hedging of Credit Index Derivatives and Ratings Triggered Step - Up Bonds, (with A. Vidozzi and L. Vidozzi), Journal of Credit Risk, Vol. 4, No. 1, pp. 47 - 76, 2008.
  46. An Efficient Approach to Valuation of Credit Basket Products and Ratings Triggered Step - up Bonds, (with A. Vidozzi and L. Vidozzi), Preprint, 2006.
  47. Valuation of Basket Credit Derivatives in the Credit Migrations Environment, (with S. Crepey, M. Jeanblanc and M. Rutkowski), Chapter 11 in Handbook on Financial Engineering, J. Birge and V. Linetsky eds., Elsevier, 2007.
  48. Hedging of Basket Credit Derivatives in Credit Default Swap Market, (with M. Jeanblanc and M. Rutkowski), Journal of Credit Risk, Vol. 3, No. 1, pp. 91 - 132, 2007.
  49. Dependent Defaults and Credit Migrations, (with M. Rutkowski), Appl. Math., Vol. 30, No. 2, pp. 121 - 145, 2003.
  50. Portfolio Optimization with a Defaultable Security, (with I. Jang), Asia - Pacific Financial Markets, Vol. 13, No. 2, 2006.
  51. Arbitrage Pricing of Defaultable Game Options with Applications to Convertible Bonds, (with S. Crepey, M. Jeanblanc and M. Rutkowski), Quantitative Finance, Vol. 8, No. 8, pp. 795 - 810, 2008.
  52. Hedging of defaultable claims, (with M. Jeanblanc and M. Rutkowski), Carmona, R. A. (ed.) et al., Paris - Princeton lectures on mathematical finance. Berlin: Springer, Lecture Notes in Mathematics 1847, 1 - 132, 2004.
  53. Multiple ratings model of defaultable term structure, (with M. Rutkowski), Mathematical Finance, Vol. 10, pp. 125 - 139, 2000.
  54. Modeling of the defaultable term structure: conditionally Markov approach, (with M. Rutkowski), IEEE Trans. Automat. Control, Vol. 49, No. 3, pp. 361 - 373, 2004.
  55. Risk sensitive portfolio management with Cox - Ingersoll - Ross interest rates: the HJB equation, (with S.R. Pliska and S.J. Sheu), SIAM J. Control Optim., Vol. 44, No. 5, pp. 1811 - 1843, 2006.
  56. Optimal investment decisions for a portfolio with a rolling horizon bond and a discount bond, (with S.R. Pliska and J. Yong), Int. J. Theor. Appl. Finance, Vol. 8, No. 7, pp. 871 - 913, 2005.
  57. Continuous - time mean - variance portfolio selection with bankruptcy prohibition, (with S.R. Pliska H. Jin and X.Y. Zhou,), Mathematical Finance, Vol. 15, No. 2, pp. 213 - 244, 2005.
  58. Economic Properties of the Risk Sensitive Criterion for Portfolio Management, (with S.R. Pliska), Review of Accounting and Finance, Vol. 2, pp. 3 - 17, 2003.
  59. Identification and control in the partially known Merton portfolio selection model, (with M. Frei), J. Optim. Theory Appl., Vol. 77, No. 2, pp. 399 - 420, 1993.
  60. Risk sensitive asset management with transaction costs, (with S.R. Pliska), Finance and Stochastics, Vol. 4, pp. 1 - 33, 2000.
  61. Risk - sensitive ICAPM with application to fixed - income management, (with S.R. Pliska), IEEE Trans. Automat. Control, Vol. 49, No. 3, pp. 420 - 432, 2004.
  62. HJM with Multiples, (with M. Rutkowski), RISK Magazine, April 2000.
  63. Risk sensitive asset allocation, (with S.R. Pliska and M. Sherris), J. Econ. Dyn. Control, Vol. 24, No.8, pp. 1145 - 1177, 2000.
  64. Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management, (with S.R. Pliska and D. Hernandez - Hernandez), Math. Methods Oper. Res., Vol. 50, pp. 167 - 188, 1999.
  65. Risk - sensitive dynamic asset management, (with S.R. Pliska), Appl. Math. Optimization, Vol. 39, No.3, pp. 337 - 360, 1999.
  66. Risk sensitive dynamic asset allocation, (with S.R. Pliska), Asset & Liability Management: A Synthesis of New Methodologies, RISK Publications, Dec 1998.
  67. Ergodic control of a singularly perturbed Markov process in discrete time with general state and compact action spaces, (with L. Stettner), Appl. Math. Optimization, Vol. 38, No.3, pp. 261 - 281, 1998.
  68. Approximations of dynamic Nash games with general state and action spaces and ergodic costs for the players, Appl. Math., Vol. 24, No. 2, pp. 195 - 202, 1996.
  69. Wavelet representations of general signals, (with J. Chen, E.B. Lin and S. Yau), Nonlinear Anal., Vol. 35, No. 1, Ser. B: Real World Appl., pp. 125 - 141, 1999.
  70. The linear - quadratic control problem revisited, SIAM J. Control & Optim., Vol. 33, pp. 1425 - 1442, 1995.
  71. Algorithms for singularly perturbed limiting average Markov control problems, (with A.J. Filar and M. Abbad), IEEE Trans. Autom. Control, Vol. 37, No.9, pp. 1421 - 1425, 1992.
  72. Singulary perturbed Markov control problem: Limiting average cost, (with A.J. Filar), Ann. Oper. Res., Vol. 28, No. 1 - 4, pp. 153 - 168, 1991.
  73. On ergodic control problems for singularly perturbed Markov processes, (with L. Stettner), Appl. Math. Optimization, Vol. 20, No.2, pp. 131 - 161, 1989.
  74. On some problems arising in asymptotic analysis of Markov processes with singularly perturbed generators, (with L. Stettner), Stochastic Anal. Appl., Vol. 6, No.2, pp. 129 - 168, 1988.
  75. On Limit Control Principle for Singularly Perturbed Markov Processes, (with L. Stettner), Stochastic Systems and Optimization, Lecture Notes in Control and Information Sciences, Volume 136/1989, pp. 274 - 283, 1989.
  76. Optimality of zero - inventory policies for unreliable manufacturing systems, (with P.R. Kumar), Oper. Res., Vol. 36, No.4, pp. 532 - 541, 1988.
  77. Adaptive control of a Markov chain over a finite parameter set without continuity assumptions on the control laws, IEEE Trans. Autom. Control, Vol. 31, pp. 985 - 987, 1986.