Controlled random fields, von Neumann–Gale dynamics and multimarket hedging with risk

References

• Arkin , V.I. and Evstigneev , I.V. 1987 . Stochastic Models of Control and Economic Dynamics , London : Academic Press .
   Google Scholar
• Cherny , A.S. 2008 . Pricing with coherent risk . Theory Probab. Appl. , 52 : 389 – 415 .
   Web of Science ®Google Scholar
• Clark , S.A. 1993 . The valuation problem in arbitrage price theory . J. Math. Econ. , 22 : 463 – 478 .
   Web of Science ®Google Scholar
• Cochrane , J.H. and Saa-Requejo , J. 2000 . Beyond arbitrage: good-deal asset price bounds in incomplete markets . J. Polit. Econ. , 108 : 79 – 119 .
   Web of Science ®Google Scholar
• Dempster , M.A.H. , Evstigneev , I.V. and Taksar , M.I. 2006 . Asset pricing and hedging in financial markets with transaction costs: an approach based on the von Neumann–Gale model . Ann. Finance , 2 : 327 – 355 .
   Google Scholar
• Evstigneev , I.V. 1988 . Controlled random fields on a directed graph . Theory Probab. Appl. , 33 : 433 – 445 .
   Web of Science ®Google Scholar
• Evstigneev , I.V. and Schenk-Hoppé , K.R. 2006 . “ The von Neumann–Gale growth model and its stochastic generalization ” . In Handbook on Optimal Growth , Edited by: Dana , R.-A. , Le Van , L. , Mitra , T. and Nishimura , K. Vol. 1 , 337 – 383 . Berlin : Springer .
   Google Scholar
• Evstigneev , I.V. , Schürger , K. and Taksar , M.I. 2005 . On the fundamental theorem of asset pricing: random constraints and bang-bang no-arbitrage criteria . Math. Finance , 14 : 201 – 221 .
   Web of Science ®Google Scholar
• Evstigneev , I.V. and Taksar , M.I. 1994 . Stochastic equilibria on graphs I . J. Math. Econ. , 23 : 401 – 433 .
   Web of Science ®Google Scholar
• Evstigneev , I.V. and Taksar , M.I. 1995 . Stochastic equilibria on graphs II . J. Math. Econ. , 24 : 383 – 406 .
   Web of Science ®Google Scholar
• Evstigneev , I.V. and Taksar , M.I. 2002 . Equilibrium states of random economies with locally interacting agents and solutions to stochastic variational inequalities in ⟨L1, L∞⟩ . Ann. Oper. Res. , 114 : 145 – 165 .
   Web of Science ®Google Scholar
• Evstigneev , I.V. and Taksar , M.I. 2009 . Dynamic interaction models of economic equilibrium . J. Econ. Dyn. Control , 33 : 166 – 182 .
   Web of Science ®Google Scholar
• Gale , D. 1956 . The closed linear model of production, in Linear Inequalities and Related Systems . Ann. Math. Study , 38 : 285 – 303 .
   Google Scholar
• Heath , D.C. and Jarrow , R.A. 1987 . Arbitrage, continuous trading, and margin requirements . J. Finance , XLII : 1129 – 1142 .
   Google Scholar
• Hildenbrand , W. 1974 . Core and Equilibria of a Large Economy , Princeton : Princeton University Press .
   Google Scholar
• Föllmer , H. and Schied , A. 2002 . Stochastic Finance: An Introduction in Discrete Time , Berlin : Walter de Gruyter .
   Google Scholar
• Jouini , E. and Kallal , H. 1995 . Arbitrage in securities markets with short-sales constraints . Math. Finance , 3 : 197 – 232 .
   Google Scholar
• Kabanov , Yu. and Safarian , M. 2009 . Markets with Transaction Costs. Mathematical Theory , Berlin : Springer .
   Google Scholar
• Komlós , J. 1967 . A generalization of a problem of Steinhaus . Acta Math. Hungarica , 18 : 217 – 229 .
   Web of Science ®Google Scholar
• Rockafellar , R.T. 1970 . Convex Analysis , Princeton : Princeton University Press .
   Google Scholar
• Rokhlin , D.B. 2005 . The Kreps–Yan theorem for L∞ . Int. J. Math. Math. Sci. , 17 : 2749 – 2756 .
   Google Scholar
• W. Schachermayer, Private communication (2012)
   Google Scholar
• Shiryaev , A.N. 1999 . Essentials of Stochastic Finance: Facts, Models, Theory , Singapore : World Scientific .
   Google Scholar
• von Neumann , J. 1937 . Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes . Ergebnisse eines mathematischen Kolloquiums , 8 : 73 – 83 . translated as, A model of general economic equilibrium, Rev. Econ. Studies 13 (1945), 1–9
   Google Scholar