Abstract
Recent progress in portfolio choice has made a wide class of problems involving transaction costs tractable. We review the basic approach to these problems, and outline some directions for future research.
The authors are grateful to Vicky Henderson, Ronnie Sircar, and Maxim Bichuch for useful comments, to Jens Jackwerth for additional references, and to Ren Liu for proofreading the manuscript.
Partially supported by the ERC (278295), NSF (DMS-0807994, DMS-1109047), SFI (07/MI/008, 07/SK/M1189, 08/SRC/FMC1389), and FP7 (RG-248896)
Partially supported by the National Centre of Competence in Research “Financial Valuation and Risk Management” (NCCR FINRISK), Project D1 (Mathematical Methods in Financial Risk Management), of the Swiss National Science Foundation (SNF).
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The Mathscinet database shows only nine publications with “transaction costs” in their title in the eighties (1980–1989). This figure rises to 52 in the nineties (1990–1999), and to 278 in the naughties (2000–2009).
References
C. Atkinson, P. Ingpochai, The influence of correlation on multi-asset portfolio optimization with transaction costs. J. Comput. Financ. 10(2), 53–96 (2006)
C. Atkinson, S. Mokkhavesa, Multi-asset portfolio optimization with transaction cost. Appl. Math. Financ. 11(2), 95–123 (2004)
M. Bichuch, Asymptotic analysis for optimal investment in finite time with transaction costs. SIAM J. Financ. Math. 3(1), 433–458 (2012)
M. Bichuch, S.E. Shreve, Utility maximization trading two futures with transaction costs. Preprint (2011)
P. Carr, Randomization and the American put. Rev. Financ. Stud. 11(3), 597–626 (1998)
J. Choi, M. Sirbu, G. Žitković, Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs. Preprint (2012)
J.H. Cochrane, The dog that did not bark: A defense of return predictability. Rev. Financ. Stud. 21(4), 1533–1575 (2008)
G.M. Constantinides, Capital market equilibrium with transaction costs. J. Polit. Econ. 94(4), 842–862 (1986)
G.M. Constantinides, S. Perrakis, Stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs. J. Econ. Dyn. Control 26(7–8), 1323–1352 (2002)
G.M. Constantinides, S. Perrakis, Stochastic dominance bounds on american option prices in markets with frictions. Rev. Financ. 11(1), 71–115 (2007)
G.M. Constantinides, T. Zariphopoulou, Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences. Financ. Stoch. 3(3), 345–369 (1999)
G.M. Constantinides, J.C. Jackwerth, S. Perrakis, Mispricing of S&P 500 index options. Rev. Financ. Stud. 22(3), 1247–1277 (2009)
G.M. Constantinides, M. Czerwonko, J. Jackwerth, S. Perrakis, Are options on index futures profitable for risk-averse investors? empirical evidence. J. Financ. 66(4), 1407–1437 (2011)
J. Cvitanić, I. Karatzas, Hedging and portfolio optimization under transaction costs: a martingale approach. Math. Financ. 6(2), 133–165 (1996)
M.H.A. Davis, A.R. Norman, Portfolio selection with transaction costs. Math. Oper. Res. 15(4), 676–713 (1990)
B. Dumas, Super contact and related optimality conditions. J. Econ. Dyn. Control 15(4), 675–685 (1991)
B. Dumas, E. Luciano, An exact solution to a dynamic portfolio choice problem under transactions costs. J. Financ. 46(2), 577–595 (1991)
S. Gerhold, J. Muhle-Karbe, W. Schachermayer, The dual optimizer for the growth-optimal portfolio under transaction costs. Financ. Stoch. 17(2), 325–354 (2013). doi:10.1007/s00780-011-0165-9
S. Gerhold, P. Guasoni, J. Muhle-Karbe, W. Schachermayer, Transaction costs, trading volume, and the liquidity premium. Financ. Stoch. (May 2013). doi:10.1007/s00780-013-0210-y
P. Guasoni, J. Muhle-Karbe, Long horizons, high risk-aversion, and endogenous spreads. Preprint (2011)
P. Guasoni, S. Robertson, Portfolios and risk premia for the long run. Ann. Appl. Probab. 22(1), 239–284 (2012)
P. Guasoni, M. Rásonyi, W. Schachermayer, Consistent price systems and face-lifting pricing under transaction costs. Ann. Appl. Probab. 18(2), 491–520 (2008)
A. Herzegh, V. Prokaj, Shadow price in the power utility case. Preprint (2011)
K. Janeček, S.E. Shreve. Asymptotic analysis for optimal investment and consumption with transaction costs. Financ. Stoch. 8(2), 181–206 (2004)
E. Jouini, H. Kallal, Martingales and arbitrage in securities markets with transaction costs. J. Econ. Theory 66(1), 178–197 (1995)
J. Kallsen, J. Muhle-Karbe, On using shadow prices in portfolio optimization with transaction costs. Ann. Appl. Probab. 20(4), 1341–1358 (2010)
T.S. Kim, E. Omberg, Dynamic nonmyopic portfolio behavior. Rev. Financ. Stud. 9(1), 141–161 (1996)
D. Kramkov, W. Schachermayer, The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9(3), 904–950 (1999)
S.L. Law, C.F. Lee, S. Howison, J.N. Dewynne, Correlated multi-asset portfolio optimisation with transaction cost. Preprint (2007)
H. Liu, Optimal consumption and investment with transaction costs and multiple risky assets. J. Financ. 59(1), 289–338 (2004)
J. Liu, Portfolio selection in stochastic enviroments. Rev. Financ. Stud. 20(1), 1–39 (2007)
H. Liu, M. Loewenstein, Optimal portfolio selection with transaction costs and finite horizons. Rev. Financ. Stud. 15(3), 805–835 (2002)
R. Liu, J. Muhle-Karbe, Portfolio selection with small transaction costs and binding portfolio constraints. Preprint (2012)
M. Loewenstein, On optimal portfolio trading strategies for an investor facing transactions costs in a continuous trading market. J. Math. Econ. 33(2), 209–228 (2000)
M.J.P. Magill, G.M. Constantinides, Portfolio selection with transactions costs. J. Econ. Theory 13(2), 245–263 (1976)
R.C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case. Rev. Econ. Stat. 51(3), 247–257 (1969)
R.C. Merton, Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory 3(4), 373–413 (1971)
K. Muthuraman, S. Kumar, Multidimensional portfolio optimization with proportional transaction costs. Math. Financ. 16(2), 301–335 (2006)
L.C.G. Rogers, Why is the effect of proportional transaction costs O(δ 2 ∕ 3)? in Mathematics of Finance. Contemporary Mathematics, vol. 351 (American Mathematical Society, Providence, 2004), pp. 303–308
S.E. Shreve, H.M. Soner, Optimal investment and consumption with transaction costs. Ann. Appl. Probab. 4(3), 609–692 (1994)
A.V. Skorohod, Stochastic equations for diffusion processes with boundaries, II. Teor. Verojatnost. i Primenen. 7, 5–25 (1962)
H.M. Soner, N. Touzi, Homogenization and asymptotics for small transaction costs. Preprint (2012)
H.M. Soner, S.E. Shreve, J. Cvitanić, There is no nontrivial hedging portfolio for option pricing with transaction costs. Ann. Appl. Probab. 5(2), 327–355 (1995)
M. Taksar, M.J. Klass, D. Assaf, A diffusion model for optimal portfolio selection in the presence of brokerage fees. Math. Oper. Res. 13(2), 277–294 (1988)
I. Welch, A. Goyal, A comprehensive look at the empirical performance of equity premium prediction. Rev. Financ. Stud. 21(4), 1455–1508 (2008)
A.E. Whalley, P. Wilmott, An asymptotic analysis of an optimal hedging model for option pricing with transaction costs. Math. Financ. 7(3), 307–324 (1997)
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Guasoni, P., Muhle-Karbe, J. (2013). Portfolio Choice with Transaction Costs: A User’s Guide. In: Paris-Princeton Lectures on Mathematical Finance 2013. Lecture Notes in Mathematics, vol 2081. Springer, Cham. https://doi.org/10.1007/978-3-319-00413-6_3
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