Dynamic hedging of basket options under proportional transaction costs using receding horizon control

References

• Abaffy , J , Bertocchi , M , Dupacova , J and Moriaggia , V . 2000 . On Generating Scenarios for Bond Portfolios . Bulletin of the Czech Econometric Society , 11 : 13 – 27 .
   Google Scholar
• Albert , A . 1969 . Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses . SiAM Journal on Applied Mathematics , 17 : 434 – 440 .
   Web of Science ®Google Scholar
• Artzner , P , Delbaen , F , Eber , JM and Heath , D . 1999 . Coherent Measures of Risk . Mathematical Finance , 9 : 203 – 228 .
   Web of Science ®Google Scholar
• Atkinson , C and Alexandropoulos , CA . 2006 . Pricing a European Basket Option in the Presence of Proportional Transaction Costs . Applied Mathematical Finance , 13 : 191 – 214 .
   Google Scholar
• Batina , I , Stoorvogel , AA and Weiland , S . 2001a . “ Feedback Model Predictive Control by Randomized Algorithms ” . In in Proceedings of European Control Conference , 3185 – 3189 . Portugal : Porto .
   Google Scholar
• Batina , I , Stoorvogel , AA and Weiland , S . 2001b . “ Stochastic Disturbance Rejection in Model Predictive Control by Randomized Algorithms ” . In in Proceedings of American Control Conference , 732 – 737 . Virginia : Arlington .
   Google Scholar
• Batina , I , Stoorvogel , AA and Weiland , S . Model Predicitive Control of Linear, Stochastic Systems with State and Input Constraints . Proceedings of Conference on Decision and Control . pp. 1564 – 1569 . Las Vegas : Nevada .
   Google Scholar
• Black , F and Scholes , M . 1973 . The Pricing of Options and Corporate Liabilities . Journal of Political Economy , 81 : 637 – 659 .
   Web of Science ®Google Scholar
• Boyd , S , El Ghaoui , L , Feron , E and Balakrishnan , V . 1994 . Linear Matrix Inequalities in System and Control Theory , Philadelphia : SIAM .
   Google Scholar
• Boyle , P and Vorst , T . 1992 . Option Replication in Discrete Time with Transaction Costs . Journal of Finance , 47 : 271 – 293 .
   Web of Science ®Google Scholar
• Consigli , G and Dempster , MAH . 1998 . Dynamic Stochastic Programming for Asset-liability Management . Annals of Operations Research , 81 : 131 – 161 .
   Web of Science ®Google Scholar
• Couchman , PD , Cannon , M and Kouvaritakis , B . 2006 . Stochastic MPC with Inequality Stability Constraints . Automatica , 42 : 2169 – 2174 .
   Web of Science ®Google Scholar
• Couchman , PD , Kouvaritakis , B and Cannon , M . MPC on State Space Models with Stochastic Input Map . proceedings of 45th IEEE Conference on Decision and Control . pp. 3216 – 3221 .
   Google Scholar
• Davis , MHA , Panas , VG and Zariphopoulou , T . 1993 . European Option Pricing with Transaction Costs . SIAM Journal of Control and Optimization , 31 : 470 – 493 .
   Web of Science ®Google Scholar
• de la Pea , DM , Bemporad , A and Alamo , T . Stochastic Programming Applied to Model Predictive Control . Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conf . pp. 1361 – 1366 . Spain : Sevilla .
   Google Scholar
• Dupacova , J , Consigli , G and Wallace , SW . 2000 . Scenarios for Multistage Stochastic Programs . Annals of Operations Research , 100 : 25 – 53 .
   Web of Science ®Google Scholar
• Edirisinghe , C , Naik , V and Uppal , R . 1993 . Optimal Replications of Options with Transactions Costs . Journal of Financial and Quantitative Analysis , 28 : 117 – 138 .
   Web of Science ®Google Scholar
• Fleten , S-E and Lindset , S . 2008 . Optimal Hedging Strategies for Multi-period Guarantees in the Presence of Transaction Costs: A Stochastic Programming Approach . European Journal of Operational Research , 185 : 1680 – 1689 .
   Google Scholar
• Harrison , MJ and Kreps , DM . 1979 . Martingales and Arbitrage in Multiperiod Securities Markets . Journal of Economic Theory , 20 : 381 – 408 .
   Web of Science ®Google Scholar
• Harrison , MJ and Pliska , SR . 1981 . Martingales and Stochastic Integrals in the Theory of Continuous Trading . Stochastic Processes and their Applications , 11 : 215 – 260 .
   Google Scholar
• Henrotte , P . 1993 . “ Transaction Costs and Duplication Strategies ” . In Working Paper Stanford University
   Google Scholar
• Herzog , F , Dondi , G and Geering , H . 2007 . Stochastic Model Predictive Control and Portfolio Optimization . International Journal of Theoretical and Applied Finance , 10 : 203 – 233 .
   Google Scholar
• Herzog , F , Dondi , G , Keel , S , Schumann , L and Geering , H . 2007 . Solving ALM Problems via Sequential Stochastic Programming . Quantitative Finance , 7 : 231 – 244 .
   Web of Science ®Google Scholar
• Hodges , SD and Neuberger , A . 1989 . Optimal Replication of Contingent Claims Under Transaction Costs . The Review of Futures Markets , 8 : 222 – 239 .
   Google Scholar
• Hoggard , T , Whalley , AE and Wilmott , P . 1994 . Hedging Option Portfolios in the Presence of Transaction Costs . Advances in Futures and Options Research , 7 : 21 – 35 .
   Google Scholar
• Hoyland , K and Wallace , SW . 2001 . Generating Scenario Trees for Multistage Decision Problems . Management Science , 47 : 295 – 307 .
   Web of Science ®Google Scholar
• Hull , J . 2000 . Options, Futures, and Other Derivatives , 4th , Upper Saddle River, NJ : Prentice Hall .
   Google Scholar
• Kabanov , Y and Safarian , MM . 1997 . On Leland's Strategy of Option Pricing with Transaction Costs . Finance and Stochastics , 1 : 238 – 250 .
   Google Scholar
• Klaassen , P . 2002 . Comment on Generating Scenario Trees for Multistage Decision Problems . Management Science , 48 : 1512 – 1516 .
   Web of Science ®Google Scholar
• Kouvaritakis , B , Cannon , M and Tsachouridis , V . 2004 . Recent Developments in Stochastic MPC and Sustainable Development . Annual Reviews in Control , 28 : 23 – 35 .
   Google Scholar
• Kouwenberg , R . 2001 . Scenario Generation and Stochastic Programming Models for Asset Liability Management . European Journal of Operational Research , 134 : 279 – 292 .
   Web of Science ®Google Scholar
• Kusy , MI and Ziemba , WT . 1986 . A Bank Asset and Liability Model . Operations Research , 34 : 356 – 376 .
   Web of Science ®Google Scholar
• Lee , JH and Ricker , NL . 1994 . Extended Kalman Filter Based Nonlinear Model Predictive Control . Industrial and Engineering Chemistry Research , 33 : 1530 – 1541 .
   Web of Science ®Google Scholar
• Leland , H . 1985 . Option Pricing and Replication with Transaction Costs . Journal of Finance , 40 : 1283 – 1301 .
   Web of Science ®Google Scholar
• McNeil , AJ , Frey , R and Embrechts , P . 2005 . Quantitative Risk Management: Concepts, Techniques, and Tools , Princeton, NJ : Princeton University Press .
   Google Scholar
• Meindl , P and Primbs , JA . 2008 . Dynamic Hedging of Single and Multi-Dimensional Options with Transaction Costs: a Generalized Utility Maximization Approach . Quantitative Finance , 8 : 299 – 312 .
   Web of Science ®Google Scholar
• Merton , RC . 1973 . Theory of Rational Option Pricing . Bell Journal of Economics and Management Science , 4 : 142 – 183 .
   Google Scholar
• Mulvey , JM and Vladimirou , H . 1992 . Stochastic Network Planning for Financial Planning Problems . Management Science , 38 : 1642 – 1664 .
   Web of Science ®Google Scholar
• Nevistic , V and Morari , M . 1996 . “ MPC-based Methods for Constrained Control of Non-linear Systems ” . In World Automation Congress Montpellier, , France
   Google Scholar
• Peaucelle , D , Henrion , D , Labit , Y and Taitz , K . 2002 . User's Guide for SeDuMi Interface 1.04 , September
   Google Scholar
• Primbs , JA . Stochastic Receding Horizon Control of Constrained Linear Systems with State and Control Multiplicative Noise . Proceedings of the American Control Conference . July . pp. 4470 – 4475 . New York, NY
   Google Scholar
• Rockafellar , RT and Uryasev , S . 2000 . Optimization of Conditional Value-at-risk . The Journal of Risk , 2 : 21 – 41 .
   Google Scholar
• Sturm , J . 2004 . SeDuMi: Version 1.05 , October
   Google Scholar
• van Hessem , DH and Bosgra , OH . A Full Solution to the Constrained Stochastic Closed-loop MPC Problem via State and Innovations Feedback and Its Receding Horizon Implementation . Proceedings of the 2003 Conference on Decision and Control . December . Hawaii, , USA : Maui .
   Google Scholar
• van Hessem , DH and Bosgra , OH . Closed-loop Stochastic Model Predictive Control in a Receding Horizon Implementation on a Continuous Polymerization Reactor Example . Proceedings of the 2004 American Control Conference . Boston, MA
   Google Scholar
• Vandenberghe , L and Boyd , S . 1996 . Semidefinite Programming . SIAM Review , 38 : 49 – 95 .
   Web of Science ®Google Scholar
• Zhao , Y and Ziemba , WT . 2007 . Hedging Errors with Leland's Option Model in the Presence of Transaction Costs . Finance Research Letters , 4 : 49 – 58 .
   Google Scholar