Mean-Variance Optimal Adaptive Execution

Applied Mathematical Finance

Volumn 18, Issue 5, 2011, Pages 395-422

  Lorenz, Julian ^a   Almgren, Robert ^b,c  

^a ETH ZURICH   (Switzerland)

^b NEW YORK UNIVERSITY   (United States)

^c Quantitative Brokers LLC   (United States)

Author keywords

dynamic programming; Market impact; mean variance analysis; multi period portfolio choice; trading strategy

Indexed keywords

EID: 84859012704     PISSN: 1350486X     EISSN: 14664313     Source Type: Journal    
DOI: 10.1080/1350486X.2011.560707     Document Type: Article

References (26)

1. Almgren, R. F. 2003. Optimal execution with nonlinear impact functions and trading enhanced risk. Applied Mathematical Finance, 10: 1-18.
2. Almgren, R. F. 2009. Optimal trading in a dynamic market, Preprint.,
3. Almgren, R. and Chriss, N. 2000. Optimal execution of portfolio transactions. Journal of Risk, 3(2): 5-39.
4. Almgren, R. and Lorenz, J. 2006. Bayesian adaptive trading with a daily cycle. Journal of Trading, 1(4): 38-46.
5. Almgren, R. and Lorenz, J. 2007. "Adaptive arrival price". In Algorithmic Trading III, Edited by: Bruce, B. R. 59-66. New York, NY: Institutional Investor.
6. Artzner, P., Delbaen, F., Eber, J. -M. and Heath, D. 1999. Coherent measures of risk. Mathematical Finance, 9: 203-228.
7. Basak, S. and Chabakauri, G. 2010. Dynamic mean-variance asset allocation. Review of Financial Studies, 23(8): 2970-3016.
8. Bertsimas, D., Lauprete, G. J. and Samarov, A. 2004. Shortfall as a risk measure: properties, optimization and applications. Journal of Economic Dynamics and Control, 28(7): 1353-1381.
9. Bertsimas, D. and Lo, A. W. 1998. Optimal control of execution costs. Journal of Financial Markets, 1: 1-50.
10. Bielecki, T. R., Jin, H., Pliska, S. R. and Zhou, Z. Y. 2005. Continuous-time mean-variance portfolio selection with bankruptcy prohibition. Mathematical Finance, 15(2): 213-244.
11. Boyd, S. and Vandenberghe, L. 2004. Convex Optimization, Cambridge, UK: Cambridge University Press.
12. Cvitanić, J., Lazrak, A. and Wang, T. 2008. Implications of the Sharpe ratio as a performance measure in multi-period settings. Journal of Economic Dynamics and Control, 32: 1622-1649.
13. Forsyth, P. A. 2011. A Hamilton Jacobi Bellman approach to optimal trade execution. Applied Numerical Mathematics, 61(2): 241-265.
14. He, H. and Mamaysky, H. 2005. Dynamic trading policies with price impact. Journal of Economic Dynamics and Control, 29(5): 891-930.
15. Huberman, G. and Stanzl, W. 2005. Optimal liquidity trading. Review of Finance, 9(2): 165-200.
16. Kissell, R. and Malamut, R. 2005. "Understanding the profit and loss distribution of trading algorithms". In Algorithmic Trading, Edited by: Bruce, B. R. 41-49. New York, NY: Institutional Investor.
17. Kurdila, A. J. and Zabarankin, M. 2005. Convex Functional Analysis, Basel, Boston, Berlin: Birkhäuser Verlag.
18. Levy, H. 1992. Stochastic dominance and expected utility: survey and analysis. Management Science, 38(4): 555-593.
19. Li, D. and Ng, W.-L. 2000. Optimal dynamic portfolio selection: multiperiod mean-variance formulation. Mathematical Finance, 10(3): 387-406.
20. Lorenz, J. 2008. Optimal trading algorithms, Switzerland: Ph.D. thesis, ETH Zürich.
21. Perold, A. F. 1988. The implementation shortfall: paper versus reality. Journal of Portfolio Management, 14(3): 4-9.
22. Richardson, H. R. 1989. A minimum variance result in continuous trading portfolio optimization. Management Science, 35(9): 1045-1055.
23. Schied, A. and Schöneborn, T. 2009. Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets. Finance Stochastics, 13(2): 181-204.
24. Strotz, R. H. 1956. Myopia and inconsistency in dynamic utility maximization. Review of Economic Studies, 23(3): 165-180.
25. Walia, N. 2006. Optimal trading: dynamic stock liquidation strategies, Senior thesis, Princeton University, NJ, USA.
26. Zhou, X. Y. and Li, D. 2000. Continuous-time mean-variance portfolio selection: a stochastic LQ framework. Applied Mathematics and Optimization, 42: 19-33.