Dr Ben Goldys

Position Held

School of Mathematics, The University of New South Wales

Employment

2000-Senior Lecturer, School of Mathematics, The University of New South Wales
1991-Lecturer, School of Mathematics, The University of New South Wales

Graduate Students

PhD (3), Hons/Dip. (14).

Research Interests

Quantitative Finance, Options, Interest rate models, Stochastic volatility models, Stochastic Differential Equations and analysis of differential operators, Stochastic Control, Ergodic theory of diffusion processes in finite and infinite dimensions

Selected Research Grants

1994-1996 Large ARC Grant: Martingale Problem on Hilbert Spaces. ($144,000).
2003 ARC Discovery Grant: Optimal Control of Stochastic Partial Differential Equations. ($50,000).

Professional Activities

Reviewer of grant applications in Analysis, Probability, Stochastic Processes and Finance for ARC and analogous Dutch (SWON) and Czech (GACR) institutions
Referee for Annals of Probability, Stochastic Processes and their Applications, Finance and Stochastics, Mathematical Finance, SIAM Journal on Control and Optimisation

Industry Experience

Various consulting & collaborative projects in the
Finance area, 1993-2003.

Invited Talks at Congresses

Stochastic Evolution Equations and Applications, Oberwolfach 2001
Stochastic Analysis and Related Topics, Pisa, June 2001
Mathematic of Finance, Bedlewo, 2001
Stochastic Partial Differential Equations and Applications, Trento, 2002, 2004
Stochastic Control and its Applications, Bedlewo, 2002
Dynamics and Applications of Stochastic Partial Differential Equations, Oberwolfach 2002
Probabilistic Methods in Fluids, Swansea, April 2002
RISK Conference, Sydney, August 2002
International Congress on Industrial and Applied Mathematics, ICIAM, Sydney, 2003

Selected Recent Publications

  • Chojnowska-Michalik A. and Goldys B.: Existence, uniqueness and invariant measures for stochastic semilinear equations on Hilbert spaces, Probab. Theory Related Fields 102 (1995), 331-356
  • Goldys, B.: On pricing interest rate derivatives when the forward LIBOR rates are lognormal, Finance and Stochastics 1 (1997), 345-352
  • Goldys B., Maslowski B.: Ergodic control of semilinear stochastic equations and Hamilton-Jacobi equations, J. Math. Analysis Applications 234 (1999), 592-631
  • Goldys B., Musiela M. and Sondermann D.: Lognormality of rates and term structure models, Stochastic Analysis Applications 18 (2000), 375-396
  • Chojnowska, A., Goldys, B.: Symmetric Mehler semigroups in Lp: Littlewood-Paley-Stein inequalities and domains of generators, J. Funct. Analysis 182 (2001), 243-279
  • Goldys B., Kocan M.: Diffusion semigroups in spaces of continuous functions with mixed topology, J. Differential Equations 173 (2001), 17-39
  • Goldys B., Musiela M.: Infinite dimensional diffusions, Kolmogorov equations and interest rate models, in: Jouini E., Cvitanic J., Musiela M.: Option Pricing, Interest Rates and Risk Management, Series: Handbooks in Mathematical Finance}, Cambridge University Press 2001, 314-335
  • Goldys B., Maslowski B.: Uniform Exponential Ergodicity of Stochastic Dissipative Systems, Czechoslovak Mathematical J. 51 (2001), 745-762
  • Da Prato G., Debusche A., Goldys B: Some Properties of Invariant Measures of Non-Symmetric Dissipative Stochastic Systems, Probab. Theory Related Fields 123 (2002), 355-380
  • Chojnowska, A., Goldys, B.: Symmetric Ornstein-Uhlenbeck Semigroups and their Generators, Probab. Theory Related Fields 124 (2002), 459-486