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Portfolio Choice with Transaction Costs: A User’s Guide

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2081))

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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Notes

  1. 1.

    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)

    Article  Google Scholar 

  • C. Atkinson, S. Mokkhavesa, Multi-asset portfolio optimization with transaction cost. Appl. Math. Financ. 11(2), 95–123 (2004)

    Article  MATH  Google Scholar 

  • M. Bichuch, Asymptotic analysis for optimal investment in finite time with transaction costs. SIAM J. Financ. Math. 3(1), 433–458 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • M. Bichuch, S.E. Shreve, Utility maximization trading two futures with transaction costs. Preprint (2011)

    Google Scholar 

  • P. Carr, Randomization and the American put. Rev. Financ. Stud. 11(3), 597–626 (1998)

    Article  Google Scholar 

  • J. Choi, M. Sirbu, G. Žitković, Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs. Preprint (2012)

    Google Scholar 

  • J.H. Cochrane, The dog that did not bark: A defense of return predictability. Rev. Financ. Stud. 21(4), 1533–1575 (2008)

    Article  Google Scholar 

  • G.M. Constantinides, Capital market equilibrium with transaction costs. J. Polit. Econ. 94(4), 842–862 (1986)

    Article  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • G.M. Constantinides, S. Perrakis, Stochastic dominance bounds on american option prices in markets with frictions. Rev. Financ. 11(1), 71–115 (2007)

    Article  MATH  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • G.M. Constantinides, J.C. Jackwerth, S. Perrakis, Mispricing of S&P 500 index options. Rev. Financ. Stud. 22(3), 1247–1277 (2009)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • J. Cvitanić, I. Karatzas, Hedging and portfolio optimization under transaction costs: a martingale approach. Math. Financ. 6(2), 133–165 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • M.H.A. Davis, A.R. Norman, Portfolio selection with transaction costs. Math. Oper. Res. 15(4), 676–713 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  • B. Dumas, Super contact and related optimality conditions. J. Econ. Dyn. Control 15(4), 675–685 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  • B. Dumas, E. Luciano, An exact solution to a dynamic portfolio choice problem under transactions costs. J. Financ. 46(2), 577–595 (1991)

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    MATH  Google Scholar 

  • P. Guasoni, J. Muhle-Karbe, Long horizons, high risk-aversion, and endogenous spreads. Preprint (2011)

    Google Scholar 

  • P. Guasoni, S. Robertson, Portfolios and risk premia for the long run. Ann. Appl. Probab. 22(1), 239–284 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • P. Guasoni, M. Rásonyi, W. Schachermayer, Consistent price systems and face-lifting pricing under transaction costs. Ann. Appl. Probab. 18(2), 491–520 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • A. Herzegh, V. Prokaj, Shadow price in the power utility case. Preprint (2011)

    Google Scholar 

  • K. Janeček, S.E. Shreve. Asymptotic analysis for optimal investment and consumption with transaction costs. Financ. Stoch. 8(2), 181–206 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • E. Jouini, H. Kallal, Martingales and arbitrage in securities markets with transaction costs. J. Econ. Theory 66(1), 178–197 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • J. Kallsen, J. Muhle-Karbe, On using shadow prices in portfolio optimization with transaction costs. Ann. Appl. Probab. 20(4), 1341–1358 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • T.S. Kim, E. Omberg, Dynamic nonmyopic portfolio behavior. Rev. Financ. Stud. 9(1), 141–161 (1996)

    Article  Google Scholar 

  • D. Kramkov, W. Schachermayer, The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9(3), 904–950 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • S.L. Law, C.F. Lee, S. Howison, J.N. Dewynne, Correlated multi-asset portfolio optimisation with transaction cost. Preprint (2007)

    Google Scholar 

  • H. Liu, Optimal consumption and investment with transaction costs and multiple risky assets. J. Financ. 59(1), 289–338 (2004)

    Article  Google Scholar 

  • J. Liu, Portfolio selection in stochastic enviroments. Rev. Financ. Stud. 20(1), 1–39 (2007)

    Article  Google Scholar 

  • H. Liu, M. Loewenstein, Optimal portfolio selection with transaction costs and finite horizons. Rev. Financ. Stud. 15(3), 805–835 (2002)

    Article  Google Scholar 

  • R. Liu, J. Muhle-Karbe, Portfolio selection with small transaction costs and binding portfolio constraints. Preprint (2012)

    Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • M.J.P. Magill, G.M. Constantinides, Portfolio selection with transactions costs. J. Econ. Theory 13(2), 245–263 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  • R.C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case. Rev. Econ. Stat. 51(3), 247–257 (1969)

    Article  Google Scholar 

  • R.C. Merton, Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory 3(4), 373–413 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  • K. Muthuraman, S. Kumar, Multidimensional portfolio optimization with proportional transaction costs. Math. Financ. 16(2), 301–335 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • S.E. Shreve, H.M. Soner, Optimal investment and consumption with transaction costs. Ann. Appl. Probab. 4(3), 609–692 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • A.V. Skorohod, Stochastic equations for diffusion processes with boundaries, II. Teor. Verojatnost. i Primenen. 7, 5–25 (1962)

    MathSciNet  Google Scholar 

  • H.M. Soner, N. Touzi, Homogenization and asymptotics for small transaction costs. Preprint (2012)

    Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • I. Welch, A. Goyal, A comprehensive look at the empirical performance of equity premium prediction. Rev. Financ. Stud. 21(4), 1455–1508 (2008)

    Article  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

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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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