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Bibliography
Aghion, P., and P. Howitt: Endogenous Growth Theory, MIT Press, Cambridge, 1998.
Akin, E.: The General Topology of Dynamical Systems, American Mathematical Society, Providence, 1993.
Algoet, P.H., and T.M. Cover: “Asymptotic optimality and asymptotic equipartition properties of log-optimum investment,” Annals of Probability 16 (1988), 876–898.
Amir, R.: “Sensitivity analysis in multisector optimal economic dynamics,” Journal of Mathematical Economics 25 (1996), 123–141.
Amir, R., and I.V. Evstigneev: “A functional central limit theorem for equilibrium paths of economic dynamics,” Journal of Mathematical Economics 33 (2000), 81–99.
Anoulova, S.V., I.V. Evstigneev, and V.M. Gundlach: “Turnpike theorems for positive multivalued stochastic operators,” Advances in Mathematical Economics 2 (2000), 1–20.
Arkin, V.I., and I.V. Evstigneev: Stochastic Models of Control and Economic Dynamics, Academic Press, London, 1987.
Arnold, L.: Random Dynamical Systems, Springer-Verlag, Berlin, 1998.
Arnold, L., I.V. Evstigneev, and V.M. Gundlach: “Convex-valued random dynamical systems: A variational principle for equilibrium states,” Random Operators and Stochastic Equations 7 (1999), 23–38.
Arnold, L., V.M. Gundlach, and L. Demetrius: “Evolutionary formalism for products of positive random matrices,” Annals of Applied Probability 4 (1994), 859–901.
Barro, R.J., and X. Sala-i-Martin: Economic Growth, McGraw-Hill, New York, 1995.
Belenky, V.Z.: “A stochastic stationary model for optimal control of an economy,” in Studies in Stochastic Control Theory and Mathematical Economics (N.Ya. Petrakov et al., eds.), pages 3–24, CEMI, Moscow, 1981 (in Russian).
Brock, W.A., and W.D. Dechert: Growth Theory, Nonlinear Dynamics and Economic Modelling: Scientific Essays of William Allen Brock (Economists of the Twentieth Century), Edward Elgar Publ., Cheltenham, 2001.
de Hek, P.: “On endogenous growth under uncertainty,” International Economic Review 40 (1999), 727–744.
de Hek, P., and S. Roy: “On sustained growth under uncertainty,” International Economic Review 42 (2001), 801–814.
Dempster, M.A.H., I.V. Evstigneev, and K.R. Schenk-Hoppé: “Exponential growth of fixed-mix strategies in stationary asset markets,” Finance and Stochastics 7 (2003), 263–276.
Dempster, M.A.H., I.V. Evstigneev, and K.R. Schenk-Hoppé: “Volatility-induced financial growth,” Working Paper No. 10/2004, Institute for Financial Research, University of Cambridge, 2004.
Dynkin, E.B.: “Some probability models for a developing economy,” Soviet Mathematics Doklady 12 (1971), 1422–1425.
Dynkin, E.B., and A.A. Yushkevich: Controlled Markov Processes and Their Applications, Springer-Verlag, New York, 1979.
Evstigneev, I.V.: “Positive matrix-valued cocycles over dynamical systems,” Uspekhi Matematicheskikh Nauk 29 (1974), 219–220 (in Russian).
Evstigneev, I.V.: “Homogeneous convex models in the theory of controlled random processes,” Soviet Mathematics Doklady 22 (1980), 108–111.
Evstigneev, I.V., and S.D. Flåm: “Rapid growth paths in multivalued dynamical systems generated by homogeneous convex stochastic operators,” Set-Valued Analysis 6 (1998), 61–82.
Evstigneev, I.V., and Yu.M. Kabanov: “Probabilistic modification of the von Neumann-Gale model,” Russian Mathematical Surveys 35 (1980), 185–186.
Evstigneev, I.V., and S.E. Kuznetsov: “Probabilistic variant of the turnpike theorem for homogeneous convex controllable models,” Mathematical Notes 33 (1983), 185–194.
Evstigneev, I.V., and K.R. Schenk-Hoppé: “From rags to riches: On constant proportions investment strategies,” International Journal of Theoretical and Applied Finance 5 (2002), 563–573.
Evstigneev, I.V., and K.R. Schenk-Hoppé: “Pure and randomized equilibria in the stochastic von Neumann-Gale model,” Discussion Paper 0507, School of Economic Studies, University of Manchester, 2005.
Evstigneev, I.V., and M.I. Taksar: “Rapid growth paths in convex-valued random dynamical systems,” Stochastics and Dynamics 1 (2001), 493–509.
Evstigneev, I.V., and M.I. Taksar: “Asset pricing and hedging under transaction costs: An approach based on the von Neumann-Gale model,” Discussion Paper 0422, School of Economic Studies, University of Manchester, 2004.
Föllmer, H., and A. Schied: Stochastic Finance: An Introduction in Discrete Time, Walter de Gruyter, Berlin, 2002.
Gale, D.: “A closed linear model of production,” in: Linear Inequalities and Related Systems (H.W. Kuhn and A.W. Tucker, eds.), pages 285–303, Princeton University Press, Princeton, 1956.
Gale, D.: “A mathematical theory of optimal economic development,” Bulletin of the American Mathematical Society 74 (1968), 207–223.
Gale, D.: “A note on the nonexistence of optimal price vectors in the general balanced-growth model of Gale: Comment,” Econometrica 40 (1972), 391–392.
Hakansson, N.H., and W.T. Ziemba: “Capital growth theory,” in: Handbooks in Operations Research and Management Science, Volume 9, Finance (R.A. Jarrow, V. Maksimovic, W.T. Ziemba, eds.), Chapter 3, pages 65–86, Elsevier, Amsterdam, 1995.
Hulsmann, J., and V. Steinmetz: “A note on the nonexistence of optimal price vectors in the general balanced-growth model of Gale,” Econometrica 40 (1972), 387–389.
Iyengar, G., and T.M. Cover: “Growth optimal investment in horse race markets with costs,” IEEE Transactions on Information Theory 46 (2000), 2675–2683.
Kabanov, Yu.M.: “Hedging and liquidation under transaction costs in currency markets,” Finance and Stochastics 3 (1999), 237–248.
Kabanov, Yu.M.: “The arbitrage theory,” in: Handbooks in Mathematical Finance: Option Pricing, Interest Rates and Risk Management (E. Jouini, J. Cvitanić and M. Musiela, eds.), pages 3–42, Cambridge University Press, Cambridge, 2001.
Kabanov, Yu.M. and C. Stricker: “The Harrison-Pliska arbitrage pricing theorem under transaction costs,” Journal of Mathematical Economics 35 (2001), 185–196.
Long, J.B.: “The numeraire portfolio,” Journal of Financial Economics 26 (1990), 29–69.
Luenberger, D.G.: Optimization by Vector Space Methods, Wiley, New York, 1969.
Makarov, V.L., and A.M. Rubinov: Mathematical Theory of Economic Dynamics and Equilibria, Springer-Verlag, Berlin, 1977.
McKenzie, L.W.: “Optimal economic growth, turnpike theorems and comparative dynamics,” in Handbook of Mathematical Economics: Volume III (K.J. Arrow and M.D. Intriligator, eds.), pages 1281–1355, North-Holland, Amsterdam, 1986.
McKenzie, L.W.: “Turnpikes,” American Economic Review Papers and Proceedings 88 (1998), 1–14.
Mirman, L.J.: “One sector economic growth and uncertainty: a survey,” in Stochastic Programming (M.A.H. Dempster, ed.), pages 537–567, Academic Press, London, 1980.
Mitra, T., L. Montrucchio, and F. Privileggi: “The nature of steady states in models of optimal growth under uncertainty,” Economic Theory 23 (2003), 39–71.
Neveu, J.: Mathematical Foundations of the Calculus of Probability Theory, Holden Day, San Francisco, 1965.
Nikaido, H.: Convex Structures and Economic Theory, Academic Press, London, 1968.
Nussbaum, R.D., and S.M. Verduyn Lunel: Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps, Memoirs of the American Mathematical Society, Volume 138, American Mathematical Society, Providence, 1999.
Olson, L.J., and S. Roy: “Theory of stochastic optimal economic growth,” this volume 2005.
Presman, E.L., and A.D. Slastnikov: “Growth rates and optimal paths in stochastic models of expanding economy,” in Proceedings of the International Conference “Stochastic Optimization,” Kiev, 1984 (V.I. Arkin, A. Shiraev and R. Wets, eds.), Lecture Notes in Control and Information Sciences, pages 327–332, Spinger-Verlag, Berlin, 1986.
Radner, R.: “Balanced stochastic growth at the maximum rate,” in: Contributions to the von Neumann Growth Model (Proc. Conf., Inst. Adv. Studies, Vienna, 1970), Zeitschrift für Nationalökonomie Suppl. No. 1 (1971), 39–53.
Radner, R.: “Optimal steady-state behaviour of an economy with stochastic production and resources,” in: Mathematical Topics in Economic Theory and Computation (R.H. Day and S.M. Robinson, eds.), pages 99–112, SIAM, Philadelphia, 1972.
Ramsey, F.: “A mathematical theory of savings,” Economic Journal 38 (1928), 543–559.
Rockafellar, R.T.: Monotone Processes of Convex and Concave Type, Memoirs of the American Mathematical Society, Volume 77, American Mathematical Society, Providence, 1967.
Schachermayer, W.: “The Fundamental Theorem of Asset Pricing under proportional transaction costs in finite discrete time,” Mathematical Finance 14 (2004), 19–48.
Solow, R.M.: “A contribution to the theory of economic growth,” Quarterly Journal of Economics 70 (1956), 65–94.
Solow, R.M., and P.A. Samuelson: “Balanced growth under constant returns to scale,” Econometrica 21 (1953), 412–424.
Stachurski, J.: “Stochastic growth: asymptotic distributions,” Economic Theory 21 (2003), 913–919.
Stokey, N.L., R.E. Lucas, and E.C. Prescott: Recursive Methods in Economic Dynamics, Harvard University Press, Cambridge, 1989.
von Neumann, J.: “Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes,” in Ergebnisse eines Mathematischen Kolloquiums, No. 8, 1935–1936 (K. Menger, ed.), pages 73–83, Vienna: Franz-Deuticke, 1937 (in German). (Translated into English by C. Morgenstern: “A model of general economic equilibrium,” Review of Economic Studies 13 (1945–1946), 1–9.)
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Evstigneev, I.V., Schenk-Hoppé, K.R. (2006). The von Neumann-Gale Growth Model and Its Stochastic Generalization. In: Dana, RA., Le Van, C., Mitra, T., Nishimura, K. (eds) Handbook on Optimal Growth 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32310-4_12
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