Publications

Prof. Dr. Christian Bender

Articles

  • C. Bender, S. Meyer (2024+)
    A Segment-Wise Dynamic Programming Algorithm for BSDEs.  Probab. Uncertain. Quant. Risk, forthcoming.
     (online supplement)
  • C. Bender, S. Ferrando, A. Gonzalez (2024+)
    Conditional Non-Lattice Integration, Pricing and Superhedging. Rev. Un. Mat. Argentina, forthcoming.
  • C. Bender, J. Lebovits, J. Levy Vehel (2024)
    General Transfer Formula for Stochastic Integrals with respect to Multifractional Brownian Motion. J. Theor. Probab, 37(1), 905-932.
  • D. Belomestny, C. Bender, J. Schoenmakers (2023)
    Solving Optimal Stopping Problems via Randomization and Empirical Dual Optimization. Math. Oper. Res. 48(3), 1454-1480.
  • C. Bender, M. Bormann, Y. Butko (2022)
    Subordination Principle and Feynman-Kac Formulae for Generalized Time-Fractional Evolution Equations. Fract. Calc. Appl. Anal. 25(5), 1818-1836.
  • C. Bender, Y. Butko (2022)
    Stochastic Solutions of Generalized Time-Fractional Evolution Equations. Fract. Calc. Appl. Anal. 25(2), 488-519.
  • C. Bender, N. Schweizer (2021)
    'Regression Anytime' with Brute-Force SVD Truncation. Ann. Appl. Probab. 31(3), 1140-1179.
  • C. Bender, M. Thiel (2020)
    Arbitrage-Free Interpolation of Call Option Prices. Stat. Risk Model. 37(1-2), 55-78.
  • C. Bender (2020)
    Ito's Formula for Gaussian Processes with Stochastic Discontinuities. Ann. Probab. 48(1), 458-492.
  • C. Bender, P. Parczewski (2018)
    Discretizing Malliavin calculus. Stochastic Processes Appl., 128(8), 2489-2537.
  • C. Bender, C. Gaertner, N. Schweizer (2018)
    Pathwise Dynamic Programming. Math. Oper. Res., 43(3), 965-995.
  • C. Bender, C. Gaertner, N. Schweizer (2017)
    Iterative Improvement of Lower and Upper Bounds for Backward SDEs. SIAM J. Sci. Comput., 39(2), B442-B466.
  • C. Bender, L. Viitasaari (2017)
    A General Non-Existence Result for Linear BSDEs Driven by Gaussian Processes. Stochastic Processes Appl., 127(4), 1204-1233.
  • C. Bender, N. Schweizer, J. Zhuo (2017)
    A Primal-Dual Algorithm for BSDEs. Math. Finance, 27(3), 866-901.
  • C. Bender, N. Dokuchaev (2017)
    A First Order BSPDE for Swing Option Pricing: Classical Solutions, Math. Finance, 27(3), 902-925.
  • C. Bender, L. Viitasaari (2016)
    Fractional Brownian Motion in Financial Modeling. Wiley StatsRef.
  • C. Bender, N. Dokuchaev (2016)
    A First Order BSPDE for Swing Option Pricing. Math. Finance, 26(3), 461-491.
  • C. Bender, R. Knobloch, P. Oberacker (2015)
    Maximal Inequalities for Fractional Levy and Related Processes. Stochastic Anal. Appl., 33(4), 701-714.
  • C. Bender, R. Knobloch, P. Oberacker (2015)
    A Generalised Ito Formula for Levy-Driven Volterra Processes. Stochastic Processes Appl., 125(8), 2989-3022 .
  • C. Bender, M. S. Pakkanen, H. Sayit (2015)
    Sticky Continuous Processes Have Consistent Price Systems. J. Appl. Probab., 52(2).
  • C. Bender, J. Schoenmakers, J. Zhang (2015)
    Dual Representations for General Multiple Stopping Problems. Math. Finance, 25(2), 339-370.
  • D. Belomestny, C. Bender, F. Dickmann, N. Schweizer (2014)
    Solving Stochastic Dynamic Programs by Convex Optimization and Simulation. In: Dahlke et al. (Eds.), Extraction of Quantifiable Information from Complex Systems. Springer, 1-23.
  • C. Bender (2014)
    Backward SDEs Driven by Gaussian Processes. Stochastic Processes Appl., 124, 2892-2916.
  • C. Bender, J. Steiner (2013)
    A-Posteriori Estimates for Backward SDEs. SIAM/ASA J. Uncertainty Quantification, 1, 139-163. [Addendum]
  • C. Bender, S. Pokalyuk (2013)
    Discretization of Backward Stochastic Volterra Integral Equations. In: Gerstner, Kloeden (Eds.), Recent Developments in Computational Finance. World Scientific, 245-278.
  • C. Bender (2012)
    Simple Arbitrage. Ann. Appl. Probab., 22(5), 2067-2085.
  • C. Bender, P. Parczewski (2012)
    On the Connection between Discrete and Continuous Wick Calculus with an Application to the Fractional Black-Scholes Model. In: Cohen et al. (Eds.), Stochastic Processes, Filtering, Control and Their Applications, World Scientific, 3-40.
  • C. Bender, J. Steiner (2012)
    Least-Squares Monte Carlo for BSDEs. In: Carmona et al. (Eds.), Numerical Methods in Finance, Springer, 257-289.
  • C. Bender, A. Lindner, M. Schicks (2012)
    Finite Variation of Fractional Levy Processes. J. Theor. Probab., 25(2), 595-612.
  • C. Bender (2011)
    Primal and Dual Pricing of Multiple Exercise Options in Continuous Time. SIAM J. Finan. Math., 2, 562-586.
  • C. Bender, T. Sottinen, E. Valkeila (2011)
    Fractional Processes as Models in Stochastic Finance. In: Di Nunno, Oksendal (Eds.), AMaMeF: Advanced Mathematical Methods for Finance, Springer, 75-103.
  • C. Bender (2011)
    Dual Pricing of Multi-Exercise Options under Volume Constraints. Finance Stoch., 15(1), 1-26.
  • C. Bender, P. Parczewski (2010)
    Approximating a Geometric Fractional Brownian Motion and Related Processes via Discrete Wick Calculus. Bernoulli,16(2), 389-417.
  • C. Bender, T. Moseler (2010)
    Importance Sampling for Backward SDEs. Stochastic Analysis Appl., 28(2), 226-253.
  • C. Bender, T. Marquardt (2009)
    Integrating Volatility Clustering into Exponential Levy Models. J. Appl. Probab., 46(3), 609-628.
  • D. Belomestny, C. Bender, J. Schoenmakers (2009)
    True Upper Bounds for Bermudan Products via Non- Nested Monte Carlo. Math. Finance, 19(1), 53-71.
  • C. Bender, T. Sottinen, E. Valkeila (2008)
    Pricing by Hedging and No-Arbitrage beyond Semimartingales. Finance Stoch., 12(4), 441-468.
  • C. Bender, C. R. Niethammer (2008)
    On q-Optimal Martingale Measures in Exponential Levy Models, Finance Stoch., 12(3), 381-410.
  • C. Bender, M. Kohlmann (2008)
    Optimal Superhedging under Nonconvex Constraints: a BSDE approach. Int. J. Theor. Appl. Finance, 11(4), 363-380.
  • C. Bender, T. Marquardt (2008)
    Stochastic Calculus for Convoluted Levy Processes. Bernoulli, 14(2), 499-518.
  • C. Bender, J. Zhang (2008)
    Time Discretization and Markovian Iteration for Coupled FBSDEs. Ann. Appl. Probab., 18(1), 143-177 .
  • C. Bender, A. Kolodko, J. Schoenmakers (2008)
    Enhanced Policy Iteration for American Options via Scenario Selection. Quant. Finance, 8(2), 135-146.
  • C. Bender, R. Denk (2007)
    A Forward Scheme for Backward SDEs. Stochastic Processes Appl., 117(12), 1793-1812.
  • C. Bender, T. Sottinen, E. Valkeila (2007)
    Arbitrage with Fractional Brownian Motion? Theory Stoch. Process., 13(1-2), 23-34 (Special Issue: Kiev Conference on Modern Stochastics).
  • C. Bender, A. Kolodko, J. Schoenmakers (2006)
    Policy Iteration for American Options: Overview. Monte Carlo Methods Appl., 12(5-6), 347-362.
  • C. Bender, A. Kolodko, J. Schoenmakers (2006)
    Iterating Cancellable Snowballs and Related Exotics. Risk September, 126-130.
  • C. Bender, J. Schoenmakers (2006)
    An Iterative Method for Multiple Stopping: Convergence and Stability. Adv. Appl. Probab., 38(3), 729-749.
  • C. Bender (2005)
    Explicit Solutions for a Class of Linear Fractional BSDEs. Syst. Contr. Lett., 54(7), 671-680.
  • C. Bender (2005)
    The Restriction of the Fractional Ito Integral to Adapted Integrands is Injective. Stoch. Dyn., 5(1), 37-43.
  • C. Bender, R. J. Elliott (2004)
    Arbitrage in a Discrete Version of the Fractional Black-Scholes Market. Math. Oper. Res., 29(4), 935-945.
  • C. Bender, R. J. Elliott (2003)
    On the Clark-Ocone Theorem for Fractional Brownian Motion with Hurst Parameter Bigger than a Half. Stochastics Stochastics Rep., 75(6), 391-405.
  • C. Bender (2003)
    An S-Transform Approach to Integration with respect to a Fractional Brownian Motion. Bernoulli, 9(6), 955-983.
  • C. Bender (2003)
    An Ito Formula for Generalized Functionals of a Fractional Brownian Motion with Arbitrary Hurst Parameter. Stochastic Processes Appl., 104, 81-106.

Preprints

  • C. Bender, Y. Butko, M. D'Ovidio, G. Pagnini (2024)
    A Limit Theorem Clarifying the Physical Origin of Fractional Brownian Motion and Related Gaussian Models of Anomalous Diffusion.  pdf
  • C. Bender, N. T. Thuan (2024)
    Continuous Time Reinforcement Learning: a Random Measure Approach. pdf  (online supplement)
  • C. Bender, M. Thiel (2024) 
    Calibration of Non-Semimartingale Models - an Adjoint Approach.
  • C. Bender, N. T. Thuan (2024) 
    Entropy-Regularized Mean Variance Portfolio Selection with Jumps. pdf

  • C. Bender, S. Ferrando, K. Gajewski, A. Gonzalez (2023)
     Superhedging Supermartingales. pdf

     

     

Theses

  • C. Bender (2003) Integration with respect to a Fractional Brownian Motion and Related Market Models. PhD thesis. Hartung-Gorre-Verlag. 174 pages.
  • C. Bender (2001) Backward Stochastic Differential Equations and Applications to the Evaluation of Financial Derivatives (in German). Diploma thesis. 110 pages.