Research Interests and Publications
A. Journal Articles
R. H. Liu, Optimal Investment and Consumption with Proportional Transaction Costs in Regime-Switching Model. Journal of Optimization Theory and Applications (2014), Vol 163, No. 2, 614-641. DOI 10.1007/s10957-013-0445-y.
R. H. Liu, A Finite-Horizon Optimal Investment and Consumption Problem Using Regime-Switching Models. Int. J. Theor. Appl. Finance Vol. 17, No. 4 (2014) 1450027 (18 pages). DOI: 10.1142/S0219024914500277.
I. Florescu, R. H. Liu, M. Mariani & G. Sewell, Numerical Schemes for Option Pricing in Regime-Switching Jump Diffusion Models. Int. J. Theor. Appl. Finance Vol. 16, No. 8 (2013) 1350046 (25 pages). DOI: 10.1142/S0219024913500465.
R. H. Liu & J.L. Zhao, A Lattice Method for Option Pricing with Two Underlying Assets in Regime-Switching Model. Journal of Computational and Applied Mathematics (2013), Vol. 250, 96-106.
I. Florescu, R. H. Liu & M. Mariani, Solutions to a partial integro-differential parabolic system arising in the pricing of financial options in regime-switching jump diffusion models. Electron. J. Diff. Equ., Vol. 2012 (2012), No. 231, 1-12.
R. H. Liu, A new tree method for pricing financial derivatives in a regime-switching mean-reverting model, Nonlinear Analysis: Real World Applications, 13 (2012), 2609-2621.
A.Q.M. Khaliq, B. Kleefeld & R. H. Liu, Solving complex PDE systems for pricing American options with regime-switching by efficient exponential time differencing schemes, Numerical Methods for Partial Differential Equations (2012), Vol. 29, No. 1, 320-336.
P. Eloe & R. H. Liu, Upper and lower solutions for regime-switching diffusions with applications in financial mathematics, SIAM Journal on Applied Mathematics (SIAP) (2011), Vol. 71, No. 4, 1354-1373.
R. H. Liu & Q. Zhang, Valuation of guaranteed equity-linked life insurance under regime-switching model, Dynamic Systems and Applications (2011), Vol. 20, 101-128.
R. H. Liu, Regime-switching recombining tree for option pricing, Int. J. Theor. Appl. Finance (2010), Vol. 13, No. 3, 479-499.
R. H. Liu & Y. Raffoul, Boundedness and exponential stability of highly nonlinear stochastic differential equations, Electron. J. Diff. Equ., Vol. 2009 (2009), No. 143, 1-10.
R. H. Liu, Analytical approximation method of option pricing under geometric mean-reverting process, International Journal of Computer Mathematics (2009), Vol. 86, No. 6, 1082-1092.
P. Eloe, R. H. Liu, & J.Y. Sun, Double barrier option under regime-switching exponential mean-reverting process, International Journal of Computer Mathematics (2009), Vol. 86, No. 6, 964-981.
A.Q.M. Khaliq & R. H. Liu, New Numerical Scheme for Pricing American Option with Regime-Switching, Int. J. Theor. Appl. Finance (2009), Vol. 12, No. 3, 319-340.
P. Eloe, R. H. Liu, M. Yatsuki, G. Yin & Q. Zhang, Optimal selling rules in a regime-switching exponential Gaussian diffusion model, SIAM Journal on Applied Mathematics (SIAP) (2008), Vol. 69, No. 3, 810-829.
R. H. Liu, Q. Zhang & G. Yin, Option pricing in a regime switching model using the Fast Fourier Transform, Journal of Applied Mathematics and Stochastic Analysis Vol. (2006), Article ID 18109, doi:10.1155/JAMSA/2006/18109.
Alain Bensoussan, R. H. Liu & Suresh P. Sethi, Optimality of an (s, S) Policy with Compound Poisson and Diffusion Demands: A QVI Approach, SIAM Journal on Control and Optimization (2006), Vol. 44, No. 5, 1650-1676.
G. Yin, Q. Zhang, F. Liu, R. H. Liu & Y. Cheng, Stock liquidation via stochastic approximation using NASDAQ daily and intra-day data, Mathematical Finance (2006), Vol.16, No.1, 217-236.
Q. Zhang, G. Yin & R. H. Liu, A Near-optimal selling rule for a two-time-scale market model, SIAM Journal on Multiscale Modeling & Simulation (2005),Vol. 4, No. 1, 172-193.
G. Yin, R. H. Liu & Q. Zhang, Recursive algorithms for stock liquidation: a stochastic optimization approach, SIAM Journal on Optimization (2002), Vol. 13, No. 1, 240-263.
R. H. Liu, Q. Zhang & G. Yin, Asymptotically optimal controls of hybrid linear quadratic regulators in discrete time, Automatica (2002), Vol.38, 409-419.
R. H. Liu, Q. Zhang & G. Yin, Nearly optimal control of singularly perturbed Markov decision processes in discrete time, Applied Mathematics and Optimization (2001), Vol.44, 105-129.
R. H. Liu & Q. Zhang, Nonlinear filtering: a hybrid approximation scheme, IEEE Trans. Aerospace & Electronic System (2001), Vol. 37, No. 4, 470-480.
R. H. Liu, Q. Zhang & G. Yin, Nearly optimal control of nonlinear Markovian systems subject to weak and strong interactions, Stoch. Anal. Appl (2001), Vol.19, No.3, 361-386.
R. H. Liu, Q. Zhang & G. Yin, Singularly perturbed Markov decision processes with inclusion of transient states, J. Systems Science and Complexity (2001), Vol.14, No.2, 199-211.
R. H. Liu & F.S. Tu, Local function expression approach of a class of tandem queueing networks, Acta Automatica Sinica (1997, Chinese), Vol. 23, No. 3, 418-420.
R. H. Liu & F.S. Tu, A new approach to estimate the gradient of the GI/G/m queueing systems, Acta Automatica Sinica (1995, Chinese), Vol. 21, No. 6, 696-705.
R. H. Liu & F.S. Tu, Modelling and stability of fork-join queueing networks, Journal of Control and Decision (1994, Chinese), Vol. 9, No. 3, 161-166.
R. H. Liu & F.S. Tu, Critical path and new perturbation analysis algorithm for a class of tandem processing networks, Journal of Systems Engineering (1994, Chinese), Vol. 1, No. 9, 12-21.
Z.Q. Chen, R. H. Liu & Z.Z. Yuan, Some aspects on the applications of predictive control to industrial processes, Journal of Automatic Instruments and Meters (1994, Chinese), No. 1, 1-6.
Z.Q. Chen, R. H. Liu & Z.Z. Yuan, Self-tuning control system of a ring-shape heating furnace, Journal of Information and Control (1991, Chinese), No. 3, 14-19.
B. Book Chapters
R. H. Liu, Recombining tree for regime-switching model: algorithm and weak convergence, Stochastic Analysis, Stochastic Systems, and Applications to Finance (2011), Allanus Tsoi et. al. Eds., 211-232, World Sci. Publishing.
G. Yin, J.W. Wang, Q. Zhang, Y.J. Liu & R. H. Liu, Pricing American put options using stochastic optimization methods, Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems (2006), H.M. Yan et. al. Eds., 301-329, Springer.
Q. Zhang, R. H. Liu & G. Yin, Nearly optimal controls of Markovian Systems, in Stochastic Modeling and Optimization (2003), D. Yao, H. Q. Zhang, & X. Y. Zhou eds., 43-86, Springer Verlag.
G. Yin, Q. Zhang & R. H. Liu, Using stochastic approximation algorithms in stock liquidation, Recent developments in mathematical finance (Shanghai, 2001), 238-248, World Sci. Publishing, River Edge, NJ, 2002.
C. Book Review
Hybrid Switching Diffusions: Properties and Applications (Yin, G.G. and Zhu, C.; 2010), IEEE Control Systems Magazine, Vol. 30, No. 5 (2010), 74-75. Reviewer: R.H. Liu.
D. Papers in Refereed Conference Proceedings
R.T. Thiab & R. H. Liu, Parallel split-step Fourier methods for the CMKdV equation, Proceedings of the international conference on parallel and distributed processing techniques and applications, PDPTA '03, June 23 - 26, 2003, Las Vegas, Volume 3, 1317-1323.
R. H. Liu, & Q. Zhang, Nonlinear filtering: a hybrid approximation scheme, The proc. of the 38th IEEE Conference on Decision and Control (1999), Phoenix, 4917-4922.
R. H. Liu & F.S. Tu, A control policy for fork-join queueing networks, The proc. of the 34th IEEE Conference on Decision and Control (1995), New Orleans, Vol. 4, 3648-3649.
R. H. Liu & F.S. Tu, Modelling and infinitesimal perturbation analysis of a class of fork-join manufacturing systems, Proc. of the international conference on Data and Knowledge Systems for Manufacturing and Engineering (1994), Hong Kong, Vol. 2, 566-571.
R. H. Liu & F.S. Tu, A new approach to analyze the unbiasedness of the sampled derivatives for the GI/G/m queues, Proc. of the first Asian Control Conference (1994), Japan, Vol. 3, 571-574.
R. H. Liu & F.S. Tu, Study of serial production lines with stochastic processing times, Proc. of the international conference on Computer Integrated Manufacturing (1993), Beijing, 110-114.
Z.Z. Yuan & R. H. Liu, Recursive synthetic generalized predictive self-tuning controller, Proc. of the 8th IFAC/IFORS Symposium on Identification and System Parameter Estimation (1988), Beijing, Vol. 1, 414-419.
Z.Z. Yuan & R. H. Liu, A practical software package of identification and self-tuning control system, Proc. of the 8th IFAC/IFORS Symposium on Identification and System Parameter Estimation (1988), Beijing, Vol. 3, 1986-1989.
Z.Z. Yuan & R. H. Liu, Recursive generalized predictive STC and its application to a power plant, Proc. of IEEE Asian Electronics Conference (1987), Hong Kong, 566-570.
E. Papers Submitted and in Progress
R. H. Liu, Optimal Stopping of Switching Diffusions with State Dependent Switching Rates. Submitted.
Pricing Multi-Asset American Options with Regime-Switching by Efficient L-stable Exponential Time Differencing Method. Work in progress.
Efficient L-stable Exponential Time Differencing Method for Pricing American Options with Regime-Switching. Work in progress.
Optimal Investment and Consumption Problems with State-Dependent Regime-Switching. Work in progress.
A Tree Method for Option Pricing in Switching Models with State Dependent Switching Rates. Work in progress.