Rebalancing with Linear and Quadratic Costs

We consider a market consisting of one safe and one risky asset, which offer constant investment opportunities. Taking into account both proportional transaction costs and linear price impact, we derive optimal rebalancing policies for representative investors with constant relative risk aversion and a long horizon.

[1]  Johannes Muhle-Karbe,et al.  TRADING WITH SMALL PRICE IMPACT , 2014, 1402.5304.

[2]  H. Soner,et al.  Optimal Investment and Consumption with Transaction Costs , 1994 .

[3]  Pierre Collin-Dufresne,et al.  Strategic Asset Allocation with Predictable Returns and Transaction Costs , 2012 .

[4]  H. Waelbroeck,et al.  Optimal Execution of Portfolio Transactions with Short‐Term Alpha , 2013 .

[5]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[6]  Steven E. Shreve,et al.  Asymptotic analysis for optimal investment and consumption with transaction costs , 2004, Finance Stochastics.

[7]  Kent D. Daniel,et al.  Dynamic Asset Allocation with Predictable Returns and Transaction Costs , 2015 .

[8]  H. Soner,et al.  National Centre of Competence in Research Financial Valuation and Risk Management Working Paper No . 845 Homogenization and Asymptotics for Small Transaction Costs : The Multidimensional Case , 2013 .

[9]  G. Constantinides Capital Market Equilibrium with Transaction Costs , 1986, Journal of Political Economy.

[10]  M. Dai,et al.  Asymptotics for Merton Problem with Capital Gain Taxes and Small Interest Rate , 2013 .

[11]  L. Slater,et al.  Confluent Hypergeometric Functions , 1961 .

[13]  B. Dumas,et al.  An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs , 1991 .

[14]  Maxim Bichuch Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs , 2011, SIAM J. Financial Math..

[15]  T. Li to Operations Research manuscript ( Please , provide the mansucript number ! ) A Fully-Dynamic Closed-Form Solution for ∆-Hedging with Market Impact , 2011 .

[16]  Marko H. Weber,et al.  DYNAMIC TRADING VOLUME , 2012 .

[17]  E. Kamke Zur Theorie der Differentialgleichungen , 1928 .

[18]  R. C. Merton,et al.  Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case , 1969 .

[19]  Alexander Schied,et al.  Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets , 2009, Finance Stochastics.

[20]  P. Guasoni,et al.  Portfolios and Risk Premia for the Long Run , 2011, 1203.1399.

[21]  Ananth N. Madhavan Market Microstructure: A Survey , 2000 .

[22]  Ralf Korn,et al.  Portfolio optimisation with strictly positive transaction costs and impulse control , 1998, Finance Stochastics.

[23]  Sanford J. Grossman,et al.  Optimal Dynamic Trading with Leverage Constraints , 1992, Journal of Financial and Quantitative Analysis.

[24]  Nizar Touzi,et al.  Homogenization and Asymptotics for Small Transaction Costs , 2012, SIAM J. Control. Optim..

[25]  Halil Mete Soner,et al.  Asymptotics for fixed transaction costs , 2015, Finance Stochastics.

[26]  M. Dai,et al.  Finite-Horizon Optimal Investment with Transaction Costs: A Parabolic Double Obstacle Problem , 2006 .

[27]  Garleanu Nicolae,et al.  Dynamic Trading with Predictable Returns and Transaction Costs , 2009 .

[28]  Nicolae Gârleanu,et al.  Dynamic portfolio choice with frictions , 2016, J. Econ. Theory.

[29]  Robert Almgren,et al.  Option Hedging with Smooth Market Impact , 2016 .

[30]  Marko H. Weber,et al.  Nonlinear price impact and portfolio choice , 2015, Mathematical Finance.

[31]  A. R. Norman,et al.  Portfolio Selection with Transaction Costs , 1990, Math. Oper. Res..

[32]  J. Muhle‐Karbe,et al.  THE GENERAL STRUCTURE OF OPTIMAL INVESTMENT AND CONSUMPTION WITH SMALL TRANSACTION COSTS , 2013, 1303.3148.

[33]  D. Bertsimas,et al.  Optimal control of execution costs , 1998 .

[34]  Sanford J. Grossman,et al.  OPTIMAL INVESTMENT STRATEGIES FOR CONTROLLING DRAWDOWNS , 1993 .

[35]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis , 2021 .

[36]  Walter Schachermayer,et al.  Transaction costs, trading volume, and the liquidity premium , 2014, Finance Stochastics.

[37]  G. Constantinides,et al.  Portfolio selection with transactions costs , 1976 .

[38]  J. Kallsen,et al.  Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach , 2013, 1309.3479.