Von Neumann–Gale model, market frictions and capital growth

References

• M. Akian, A. Sulem, and M.I. Taksar, Dynamic optimization of long-term growth rate for a mixed portfolio with transactions costs, Math. Finance 11 (2001), pp. 153–188. doi: 10.1111/1467-9965.00111
   Web of Science ®Google Scholar
• C. Albanese and S. Tompaidis, Small transaction cost asymptotics and dynamic hedging, Eur. J. Oper. Res. 185 (2008), pp. 1404–1414. doi: 10.1016/j.ejor.2004.08.049
   Web of Science ®Google Scholar
• P.H. Algoet and T.M. Cover, Asymptotic optimality and asymptotic equipartition properties of log-optimum investment, Ann. Probab. 16 (1988), pp. 876–898. doi: 10.1214/aop/1176991793
   Web of Science ®Google Scholar
• W. Bahsoun, I.V. Evstigneev, and M.I. Taksar, Rapid paths in von Neumann–Gale dynamical systems, Stochastics 80 (2008), pp. 129–141. doi: 10.1080/17442500701833526
   Google Scholar
• W. Bahsoun, I.V. Evstigneev, M.I. Taksar, Growth-optimal investments and numeraire portfolios under transaction costs, in Handbook of the Fundamentals of Financial Decision Making, L.C. MacLean and W.T. Ziemba, eds., World Scientific, Singapore, 2013, pp. 789–808.
   Google Scholar
• B. Bouchard-Denize and N. Touzi, Explicit solution of the multivariate super-replication problem under transaction costs, Ann. Appl. Probab. 10 (2000), pp. 685–708.
   Web of Science ®Google Scholar
• L. Breiman, Optimal gambling systems for favorable games, Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. I, University of California Press, Berkeley, 1961, pp. 65–78.
   Google Scholar
• A. Cadenillas, Consumption–investment problems with transaction costs: Survey and open problems, Math. Methods Oper. Res. 51 (2000), pp. 43–68. doi: 10.1007/s001860050002
   Web of Science ®Google Scholar
• A. Cadenillas and S. Pliska, Optimal trading of a security when there are taxes and transaction costs, Finance Stoch. 3 (1999), pp. 137–165. doi: 10.1007/s007800050055
   Google Scholar
• C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, Vol. 580, Springer-Verlag, Berlin–Heidelberg–New York, 1977.
   Google Scholar
• P. Chalasani and S. Jha, Randomized stopping times and American option pricing with transaction costs, Math. Finance 11 (2001), pp. 33–77. doi: 10.1111/1467-9965.00107
   Web of Science ®Google Scholar
• S.A. Clark, Competitive prices for a stochastic input–output model with infinite time horizon, Econ. Theory 35 (2008), pp. 1–17. doi: 10.1007/s00199-007-0225-8
   Web of Science ®Google Scholar
• J. Cvitanić and I. Karatzas, Hedging and portfolio optimization under transaction costs: A martingale approach, Math. Finance 6 (1996), pp. 133–165. doi: 10.1111/j.1467-9965.1996.tb00075.x
   Google Scholar
• S. Dasgupta and T. Mitra, Infinite-horizon competitive programs are optimal, J. Econ. 69 (1999), pp. 217–238. doi: 10.1007/BF01231160
   Google Scholar
• F. Delbaen, Yu.M. Kabanov, and E. Valkeila, Hedging under transaction costs in currency markets: A discrete-time model, Math. Finance 12 (2002), pp. 45–61. doi: 10.1111/1467-9965.00003
   Web of Science ®Google Scholar
• M.A.H. Dempster, I.V. Evstigneev, and M.I. Taksar, Asset pricing and hedging in financial markets with transaction costs: An approach based on the von Neumann–Gale model, Ann. Finance 2 (2006), pp. 327–355. doi: 10.1007/s10436-006-0042-2
   Google Scholar
• E. Denis and Yu.M. Kabanov, Mean square error for the Leland–Lott hedging strategy: Convex pay-offs, Finance Stoch. 14 (2010), pp. 625–667. doi: 10.1007/s00780-010-0130-z
   Web of Science ®Google Scholar
• D. De Vallière, Yu.M. Kabanov, and Ch. Stricker, No-arbitrage properties for financial markets with transaction costs and incomplete information, Finance Stoch. 11 (2007), pp. 237–251. doi: 10.1007/s00780-006-0029-x
   Web of Science ®Google Scholar
• E.B. Dynkin, Some probability models for a developing economy, Soviet Math. Dokl. 12 (1971), pp. 1422–1425.
   Google Scholar
• E.B. Dynkin, Stochastic concave dynamic programming, USSR Math. Sb. 16 (1972), pp. 501–515. doi: 10.1070/SM1972v016n04ABEH001437
   Google Scholar
• E.B. Dynkin and A.A. Yushkevich, Controlled Markov Processes and their Applications, Springer, NY, 1979.
   Google Scholar
• I.V. Evstigneev and K.R. Schenk-Hoppé, Pure and randomized equilibria in the stochastic von Neumann–Gale model, J. Math. Econ. 43 (2007), pp. 871–887. doi: 10.1016/j.jmateco.2007.04.004
   Web of Science ®Google Scholar
• I.V. Evstigneev and K.R. Schenk-Hoppé, Stochastic equilibria in von Neumann–Gale dynamical systems, Trans. Amer. Math. Soc. 360 (2008), pp. 3345–3365. doi: 10.1090/S0002-9947-08-04445-0
   Web of Science ®Google Scholar
• I.V. Evstigneev and M.V. Zhitlukhin, Controlled random fields, von Neumann–Gale dynamics and multimarket hedging with risk, Stochastics 85 (2013), pp. 652–666. doi: 10.1080/17442508.2013.795565
   Web of Science ®Google Scholar
• D. Gale, A closed linear model of production, in Linear Inequalities and Related Systems, H.W. Kuhn, et al., eds., Princeton University Press, Princeton, 1956, pp. 285–303.
   Google Scholar
• D. Gale, On optimal development in a multi-sector economy, Rev. Econ. Stud. 34 (1967), pp. 1–18. doi: 10.2307/2296567
   Web of Science ®Google Scholar
• P. Guasoni, E. Lépinette, and M. Rásonyi, The fundamental theorem of asset pricing under transaction costs, Finance Stoch. 16 (2012), pp. 741–777. doi: 10.1007/s00780-012-0185-0
   Web of Science ®Google Scholar
• P. Guasoni, M. Rásonyi, and W. Schachermayer, Consistent price systems and face-lifting pricing under transaction costs, Ann. Appl. Probab. 18 (2008), pp. 491–520. doi: 10.1214/07-AAP461
   Web of Science ®Google Scholar
• N.H. Hakansson and W.T. Ziemba, Capital growth theory, in Handbooks in Operations Research and Management Science, Vol. 9, Finance, Chapter 3, R. Jarrow, A.V. Maksimovic, and W.T. Ziemba, eds., Elsevier, Amsterdam, 1995, pp. 65–86.
   Google Scholar
• D.B. Hausch and W.T. Ziemba, Transactions costs, market inefficiencies and entries in a racetrack betting model, Manag. Sci. 31 (1985), pp. 381–394. doi: 10.1287/mnsc.31.4.381
   Web of Science ®Google Scholar
• K. Janeček and S. Shreve, Asymptotic analysis for optimal investment and consumption with transaction costs, Finance Stoch. 8 (2004), pp. 181–206. doi: 10.1007/s00780-003-0113-4
   Web of Science ®Google Scholar
• D.G. Luenberger, Optimization by Vector Space Methods, Wiley, NY, 1997.
   Google Scholar
• G. Iyengar and T.M. Cover, Growth optimal investment in horse race markets with costs, IEEE Trans. Inform. Theory 46 (2000), pp. 2675–2683. doi: 10.1109/18.887881
   Web of Science ®Google Scholar
• G. Iyengar, Universal investment in markets with transaction costs, Math. Finance 15 (2005), pp. 359–371. doi: 10.1111/j.0960-1627.2005.00223.x
   Web of Science ®Google Scholar
• S. Jacka and A. Berkaoui, On the density of properly maximal claims in financial markets with transaction costs, Ann. Appl. Probab. 17 (2007), pp. 716–740. doi: 10.1214/105051606000000880
   Web of Science ®Google Scholar
• S. Jacka, A. Berkaoui, and J. Warren, No arbitrage and closure results for trading cones with transaction costs, Finance Stoch. 12 (2008), pp. 583–600. doi: 10.1007/s00780-008-0075-7
   Web of Science ®Google Scholar
• E. Jouini and H. Kallal, Martingales and arbitrage in securities markets with transaction costs, J. Econ. Theory 66 (1995), pp. 178–197. doi: 10.1006/jeth.1995.1037
   Web of Science ®Google Scholar
• Yu.M. Kabanov, Hedging and liquidation under transaction costs in currency markets, Finance Stoch.3 (1999), pp. 237–248. doi: 10.1007/s007800050061
   Google Scholar
• Yu.M. Kabanov, M. Rásonyi, and Ch. Stricker, No-arbitrage criteria for financial markets with efficient friction, Finance Stoch. 6 (2002), pp. 371–382. doi: 10.1007/s007800100062
   Web of Science ®Google Scholar
• Yu.M. Kabanov and M. Safarian, On Leland's strategy of option pricing with transaction costs, Finance Stoch. 1 (1997), pp. 239–250. doi: 10.1007/s007800050023
   Google Scholar
• Yu.M. Kabanov and M. Safarian, Markets with Transaction Costs, Springer-Verlag, Berlin, Heidelberg, 2009.
   Google Scholar
• J.L. Kelly, A new interpretation of information rate, Bell Syst. Tech. J. 35 (1956), pp. 917–926. doi: 10.1002/j.1538-7305.1956.tb03809.x
   Google Scholar
• Yu. Kifer, Hedging of game options in discrete markets with transaction costs, Stochastics 85 (2013), pp. 667–681. doi: 10.1080/17442508.2013.795566
   Web of Science ®Google Scholar
• P. Koehl, H. Pham, and N. Touzi, Hedging in discrete time under transaction costs and continuous-time limit, J. Appl. Probab. 36 (1999), pp. 163–178. doi: 10.1239/jap/1032374239
   Web of Science ®Google Scholar
• P. Koehl, H. Pham, and N. Touzi, On super-replication in discrete time under transaction costs, Teoriya Veroyatnostei Primeneniya 45 (2000), pp. 783–788. English translation in Theory Probab. Appl. 45 (2002), pp. 667–673. doi: 10.4213/tvp511
   Web of Science ®Google Scholar
• H. Latané, Criteria for choice among risky ventures, J. Polit. Econ. 67 (1959), pp. 144–155. doi: 10.1086/258157
   Web of Science ®Google Scholar
• H. Leland, Option pricing and replication with transactions costs, J. Finance 40 (1985), pp. 1283–1301. doi: 10.1111/j.1540-6261.1985.tb02383.x
   Web of Science ®Google Scholar
• H. Leland, Comments on ‘Hedging errors with Leland's option model in the presence of transactions costs’, Finance Res. Lett. 4 (2007), pp. 200–202. doi: 10.1016/j.frl.2007.05.001
   Google Scholar
• E. Lépinette, Modified Leland's strategy for a constant transaction costs rate, Math. Finance 4 (2012), pp. 741–752. doi: 10.1111/j.1467-9965.2011.00498.x
   Google Scholar
• H. Liu and M. Loewenstein, Optimal portfolio selection with transaction costs and finite horizons, Rev. Finan. Stud. 15 (2002), pp. 805–835. doi: 10.1093/rfs/15.3.805
   Web of Science ®Google Scholar
• J.B. Long, The numeraire portfolio, J. Finan. Econ. 26 (1990), pp. 29–69. doi: 10.1016/0304-405X(90)90012-O
   Web of Science ®Google Scholar
• L.C. MacLean, W.T. Ziemba, and G. Blazenko, Growth versus security in dynamic investment analysis, Manag. Sci. 38 (1992), pp. 1562–1585. doi: 10.1287/mnsc.38.11.1562
   Web of Science ®Google Scholar
• L.C. MacLean, R. Sanegre, Y. Zhao, and W.T. Ziemba, Capital growth with security, J. Econ. Dyn. Control 28 (2004), pp. 937–954. doi: 10.1016/S0165-1889(03)00056-3
   Web of Science ®Google Scholar
• L.C. MacLean, W.T. Ziemba, and Y. Li, Time to wealth goals in capital accumulation, Quant. Finance5 (2005), pp. 343–355. doi: 10.1080/14697680500149552
   Web of Science ®Google Scholar
• L.C. MacLean, E.O. Thorp, and W.T. Ziemba (eds.), The Kelly Capital Growth Investment Criterion: Theory and Practice, World Scientific, Singapore, 2011.
   Google Scholar
• M.J.P. Magill and G.M. Constantinides, Portfolio selection with transactions costs, J. Econ. Theory13 (1976), pp. 245–263. doi: 10.1016/0022-0531(76)90018-1
   Web of Science ®Google Scholar
• E. Malinvaud, Capital accumulation and efficient allocation of resources, Econometrica 21 (1953), pp. 233–268. doi: 10.2307/1905538
   Web of Science ®Google Scholar
• R.C. Merton, Optimum consumption and portfolio rules in a continuous-time model, J. Econ. Theory3 (1971), pp. 373–413. doi: 10.1016/0022-0531(71)90038-X
   Web of Science ®Google Scholar
• B. Peleg, On competitive prices for optimal consumption plans, SIAM J. Appl. Math. 26 (1974), pp. 239–253. doi: 10.1137/0126021
   Web of Science ®Google Scholar
• H. Pham and N. Touzi, The fundamental theorem of asset pricing with cone constraints, J. Math. Econ. 31 (1999), pp. 265–279. doi: 10.1016/S0304-4068(97)00059-1
   Web of Science ®Google Scholar
• E. Platen and D. Heath, A Benchmark Approach to Quantitative Finance, Springer, Heidelberg, Dordrecht, London, New York, 2006.
   Google Scholar
• R. Radner, Efficiency prices for infinite horizon production programmes, Rev. Econ. Stud. 34 (1967), pp. 51–66. doi: 10.2307/2296570
   Web of Science ®Google Scholar
• R. Radner, Balanced stochastic growth at the maximum rate, in Contributions to the von Neumann Growth Model (Conference Proceedings), Institute for Advanced Studies, Vienna, Zeitschrift für Nationalökonomie, Suppl. No. 1, 1970, pp. 39–53.
   Google Scholar
• R. Radner, Optimal steady-state behavior of an economy with stochastic production and resources, in Mathematical Topics in Economic Theory and Computation, R.H. Day and S.M. Robinson, eds., SIAM, Philadelphia, 1972, pp. 99–112.
   Google Scholar
• R.T. Rockafellar, Monotone Processes of Convex and Concave Type, Memoirs of the American Mathematical Society, Vol. 77, American Mathematical Society, Providence, RI, 1967.
   Google Scholar
• A. Roux, Pricing and hedging game options in currency models with proportional transaction costs, Int. J. Theor. Appl. Finance 19 (2016), p. 1650043. doi: 10.1142/S0219024916500436
   Web of Science ®Google Scholar
• A. Roux and T. Zastawniak, American options under proportional transaction costs: Pricing, hedging and stopping algorithms for long and short positions, Acta Appl. Math. 106 (2009), pp. 199–228. doi: 10.1007/s10440-008-9290-7
   Web of Science ®Google Scholar
• A. Roux and T. Zastawniak, American options with gradual exercise under proportional transaction costs, Int. J. Theor. Appl. Finance 17 (2014), p. 1450052. doi: 10.1142/S0219024914500526
   Google Scholar
• A. Roux and T. Zastawniak, American and Bermudan options in currency markets with proportional transaction costs, Acta Appl. Math. 141 (2016), pp. 187–225. doi: 10.1007/s10440-015-0010-9
   Web of Science ®Google Scholar
• A. Roux and T. Zastawniak, Game options with gradual exercise and cancellation under proportional transaction costs, Stochastics 90 (2018), pp. 1190–1220. doi: 10.1080/17442508.2018.1499102
   Web of Science ®Google Scholar
• W. Schachermayer, The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time, Math. Finance 14 (2004), pp. 19–48. doi: 10.1111/j.0960-1627.2004.00180.x
   Web of Science ®Google Scholar
• M.I. Taksar, M.J. Klass, and D. Assaf, Diffusion model for optimal portfolio selection in the presence of brokerage fees, Math. Oper. Res. 13 (1988), pp. 277–294. doi: 10.1287/moor.13.2.277
   Web of Science ®Google Scholar
• E.O. Thorp, Portfolio choice and the Kelly criterion. Proceedings of the American Statistical Association, Business and Economics Statistics Section, 1971, pp. 215–224.
   Google Scholar
• Y. Zhao and W.T. Ziemba, Hedging errors with Leland's option model in the presence of transaction costs, Finance Res. Lett. 4 (2007), pp. 49–58. doi: 10.1016/j.frl.2006.09.002
   Google Scholar
• Y. Zhao and W.T. Ziemba, Comments on and corrigendum to ‘Hedging errors with Leland's option model in the presence of transaction costs’, Finance Res. Lett. 4 (2007), pp. 196–199. doi: 10.1016/j.frl.2007.04.003
   Google Scholar
• W.T. Ziemba and R.G. Vickson (eds.), Stochastic Optimization Models in Finance, 2nd ed., World Scientific, Singapore, 2006.
   Google Scholar
• W.T. Ziemba and R.G. Vickson, Models of optimal capital accumulation and portfolio selection and the capital growth criterion, in The Kelly Capital Growth Investment Criterion: Theory and Practice, L.C. MacLean, E.O. Thorp, and W.T. Ziemba, eds., World Scientific, Singapore, 2011, pp. 473–485.
   Google Scholar
• J. von Neumann, Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes, in: Ergebnisse eines Mathematischen Kolloquiums 8 (1937) pp. 1935–1936 (Franz-Deuticke, Leipzig and Wien), pp. 73–83. [Translated: A model of general economic equilibrium, Review of Economic Studies 13 (1945–1946) 1–9.].
   Google Scholar