FTAP in finite discrete time with transaction costs by utility maximization
Tóm tắt
The aim of this paper is to prove the fundamental theorem of asset pricing (FTAP) in finite discrete time with proportional transaction costs by utility maximization. The idea goes back to L.C.G. Rogers’ proof of the classical FTAP for a model without transaction costs. We consider one risky asset and show that under the robust no-arbitrage condition, the investor can maximize his expected utility. Using the optimal portfolio, a consistent price system is derived.
Tài liệu tham khảo
Barron, E.N., Cardaliaguet, P., Jensen, R.: Conditional essential suprema with applications. Appl. Math. Optim. 48, 229–253 (2003)
Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Lecture Notes in Math., vol. 580. Springer, Berlin (1977)
Campi, L., Owen, M.P.: Multivariate utility maximization with proportional transaction costs. Finance Stoch. 15, 461–499 (2011)
Cvitanić, J., Karatzas, I.: Hedging and portfolio optimization under transaction costs: a martingale approach. Math. Finance 6, 113–165 (1996)
Czichowsky, C., Muhle-Karbe, J., Schachermayer, W.: Transaction costs, shadow prices, and duality in discrete time. SIAM J. Financ. Math. 5, 258–277 (2014)
Dalang, R.C., Morton, A., Willinger, W.: Equivalent martingale measures and no-arbitrage in stochastic securities market models. Stoch. Stoch. Rep. 29, 185–201 (1990)
Delbaen, F., Schachermayer, W.: The Mathematics of Arbitrage. Springer Finance. Springer, Berlin (2006)
Deelstra, G., Pham, H., Touzi, N.: Dual formulation of the utility maximization problem under transaction costs. Ann. Appl. Probab. 11, 1353–1383 (2001)
Harrison, J.M., Kreps, D.M.: Martingales and arbitrage in multi-period securities markets. J. Econ. Theory 20, 381–408 (1979)
Harrison, J.M., Pliska, S.R.: Martingales and stochastic integrals in the theory of continuous trading. Stoch. Process. Appl. 11, 215–260 (1981)
Kabanov, Y., Rásonyi, M., Stricker, Ch.: No-arbitrage criteria for financial markets with efficient friction. Finance Stoch. 6, 371–382 (2002)
Kabanov, Y., Rásonyi, M., Stricker, Ch.: On the closedness of sums of convex cones in L 0 and the robust no-arbitrage property. Finance Stoch. 7, 403–411 (2003)
Kabanov, Y., Safarian, M.: Markets with Transaction Costs—Mathematical Theory. Springer Finance. Springer, Berlin (2010)
Pennanen, T.: Dual representation of superhedging costs in illiquid markets. Math. Financ. Econ. 5, 233–248 (2011)
Rásonyi, M., Stettner, L.: On utility maximization in discrete-time financial market models. Ann. Appl. Probab. 15, 1367–1395 (2005)
Rásonyi, M.: New methods in the arbitrage theory of financial markets with transaction costs. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, Ch. (eds.) Séminaire de Probabilités XLI. Lecture Notes in Mathematics, vol. 1934, pp. 455–462. Springer, Berlin (2008)
Rásonyi, M.: Arbitrage with transaction costs revisited. In: Delbaen, F., Rásonyi, M., Stricker, Ch. (eds.) Optimality and Risk—Modern Trends in Mathematical Finance, pp. 211–226. Springer, Berlin (2009)
Rogers, L.C.G.: Equivalent martingale measures and no-arbitrage. Stoch. Stoch. Rep. 51, 41–49 (1994)
Rokhlin, D.B.: A theorem on martingale selection for relatively open convex set-valued random sequences. Math. Notes 81, 543–548 (2007)
Rokhlin, D.B.: Constructive no-arbitrage criterion under transaction costs in the case of finite discrete time. Theory Probab. Appl. 52, 93–107 (2008)
Schachermayer, W.: A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time. Insur. Math. Econ. 11, 249–257 (1992)
Schachermayer, W.: The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time. Math. Finance 14, 19–48 (2004)