300
Views
0
CrossRef citations to date
0
Altmetric
Research Papers

Optimal solution of the liquidation problem under execution and price impact risks

ORCID Icon &
Pages 1037-1049 | Received 10 Nov 2020, Accepted 18 Feb 2022, Published online: 24 Mar 2022

References

  • Almgren, R., Optimal execution with nonlinear impact functions and trading enhanced risk. Appl. Math. Finance, 2003, 10(1), 1–18.
  • Almgren, R., Optimal trading with stochastic liquidity and volatility. SIAM J. Financ. Math., 2012, 3, 163–181.
  • Almgren, R. and Chriss, N., Optimal execution of portfolio transactions. J. Risk, 2000, 3(2), 5–39.
  • Ankirchner, S., Blanchet-Scalliet, C. and Eyraud-Loisel, A., Optimal liquidation with additional information. Math. Financ. Econ., 2016, 10(1), 1–14.
  • Avramov, D., Chordia, T. and Goyal, A., The impact of trades on daily volatility. Rev. Financ. Stud., 2006, 19(4), 1241–1277.
  • Bather, J.A. and Chernoff, H., Sequential decisions in the control of a space ship (finite fuel). J. Appl. Probab., 1967, 4(3), 584–604.
  • Becherer, D., Bilarev, T. and Frentrup, P., Optimal liquidation under stochastic liquidity. Finance Stoch., 2018, 22(1), 39–68.
  • Beneš, V.E., Shepp, L.A. and Witsenahusen, H.S., Some solvable stochastic control problems. Stochastics, 1980, 4(1), 39–83.
  • Brockett, R.W., Finite Dimensional Linear Systems, 1970 (Wiley: New York).
  • Bulthuis, B., Concha, J., Leung, T. and Ward, B., Optimal execution of limit and market orders with trade director, speed limiter, and fill uncertainty. Int. J. Financ. Eng., 2017, 4, 1–29.
  • Büyüksahin, B. and Harris, J., The role of speculators in the crude oil futures market. Working Paper, International Energy Agency, 2009.
  • Capponi, F., Cont, R. and Sani, A., Trade duration, volatility and market impact. 2019. Available at SSRN https://ssrn.com/abstract=3351736.
  • Cartea, A., Gan, L. and Jaimungal, S., Trading co-integrated assets with price impact. Math. Financ., 2019, 29(2), 542–567.
  • Cheng, X., Di Giacinto, M. and Wang, T.-H., Optimal execution with uncertain order fills in Almgren-Chriss framework. Quant. Finance, 2017, 17(1), 55–69.
  • Cheng, X., Di Giacinto, M. and Wang, T.-H., Optimal execution with dynamic risk adjustment. J. Oper. Res. Soc., 2019, 70(10), 1662–1677.
  • Cont, R. and Kukanov, A., Optimal order placement in limit order markets. Quant. Finance, 2017, 17(1), 21–39.
  • Delyon, B. and Hu, Y., Simulation of conditioned diffusion and application to parameter estimation. Stoch. Proc. Appl., 2006, 116(11), 1660–1675.
  • Du, S. and Zhu, H., What is the optimal trading frequency in financial markets? Rev. Econ. Stud., 2017, 84(4), 1606–1651.
  • Durham, G.B. and Gallant, A.R., Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes. J. Bus. Econom. Statist., 2002, 20(3), 297–338.
  • Fatone, L., Mariani, F., Recchioni, M.C. and Zirilli, F., A trading execution model based on mean field games and optimal control. Appl. Math., 2014, 5(19), 3091–3116.
  • Forsyth, P.A., Kennedy, J.S., Tse, S.T. and Windcliff, H., Optimal trade execution: A mean quadratic variation approach. J. Econ. Dyn. Control., 2012, 36(12), 1971–1991.
  • Frei, C. and Westray, N., Optimal execution of a VWAP order: A stochastic control approach. Math. Finance, 2015, 25(3), 612–639.
  • Gatheral, J. and Schied, A., Optimal trade execution under geometric brownian motion in the Almgren and Chriss framework. Int. J. Theo. Appl. Finance, 2011, 14(3), 353–368.
  • Graewe, P. and Horst, U., Optimal trade execution with instantaneous price impact and stochastic resilience. SIAM J. Control Optim., 2017, 55(6), 3707–3725.
  • Guéant, O. and Lehalle, C.A., General intensity shapes in optimal liquidation. Math. Finance, 2015, 25(3), 457–495.
  • Huang, X., Jaimungal, S. and Nourian, M., Mean-field game strategies for optimal execution. Appl. Math. Finance, 2019, 26(2), 153–185.
  • Huanga, R.D. and Masulis, R.W., Trading activity and stock price volatility: Evidence from the London stock exchange. J. Empir. Finance, 2003, 10(3), 249–269.
  • Hull, J. and White, A., Pricing interest-rate-derivative securities. Rev. Financial Stud., 1990, 3(4), 573–592.
  • Jiang, Y., Cao, Y., Liu, X. and Zhai, J., Volatility modeling and prediction: The role of price impact. Quant. Finance, 2019, 19(12), 2015–2031.
  • Kallsen, J. and Muhle-Karbe, J., On using shadow prices in portfolio optimization with transaction costs. Ann. Appl. Probab., 2010, 20(4), 1341–1358.
  • Karatzas, I., Probabilistic aspects of finite-fuel stochastic control. Proc. Natl. Acad. Sci., USA, 1985, 82(17), 5579–5581.
  • Klebaner, F.C., Introduction to Stochastic Calculus with Applications (3rd ed.), 2012 (Imperial College Press: London).
  • Kyle, A.S., Obizhaeva, A.A. and Wang, Y., Smooth trading with overconfidence and market power. Rev. Econ. Stud., 2018, 1, 611–662.
  • Lorenz, C. and Schied, A., Drift dependence of optimal trade execution strategies under transient price impact. Finance Stoch., 2013, 17(4), 743–777.
  • Ma, G., Siu, C.C., Zhu, S.P. and Elliott, R.J., Optimal portfolio execution problem with stochastic price impact. Automatica, 2020, 112, 108739.
  • Mariani, F., Recchioni, M.C. and Ciommi, M., Merton's portfolio problem including market frictions: A closed-form formula supporting the shadow price approach. Eur. J. Oper. Res., 2019, 275(3), 1178–1189.
  • Moro, E., Vicente, J., Moyano, L.G., Gerig, A., Farmer, J.D., Vaglica, G., Lillo, F. and Mantegna, R.N., Market impact and trading profile of hidden orders in stock markets. Phys. Rev. E, 2009, 80, 066102.
  • Sannikov, Y. and Skrzypacz, A., Dynamic trading: Price inertia and front-running. Stanford Univ. Grad. School of Business Research Paper, No. 3487, 2016, 1–59.
  • Schied, A., A control problem with fuel constraint and Dawson-Watanabe superprocesses. Ann. Appl. Probab., 2013, 23(6), 2472–2499.
  • Schied, A., Schöneborn, T. and Tehranchi, M., Optimal basket liquidation for CARA investors is deterministic. Appl. Math. Finance, 2010, 17(6), 471–489.
  • Tse, S.T., Forsyth, P.A., Kennedy, J.S. and Windcliff, H., Comparison between the mean-variance optimal and the mean-quadratic-variation optimal trading strategies. Appl. Math. Finance, 2013, 20(5), 415–449.
  • Tsoukalas, G., Wang, J. and Giesecke, K., Dynamic portfolio execution. Manag. Sci., 2019, 65(5), 1949–2443.
  • Whitaker, G.A., Golightly, A., Boys, R.J. and Sherlock, C., Improved bridge constructs for stochastic differential equations. Stat. Comput., 2017, 27, 885–900.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.