A Partitioning Algorithm for Markov Decision Processes with Applications to Market Microstructure

Published Online:https://doi.org/10.1287/mnsc.2016.2639

References

  • Ahn HJ, Bae KH, Chan K (2001) Limit orders, depth, and volatility: Evidence from the stock exchange of Hong Kong. J. Finance 56(2):767–788.CrossrefGoogle Scholar
  • Aïd R, Gruet P, Pham H (2016) An optimal trading problem in intraday electricity markets. Math. Financial Econom. 10(1):49–85.CrossrefGoogle Scholar
  • Alfonsi A, Fruth A, Schied A (2010) Optimal execution strategies in limit order books with general shape functions. Quant. Finance 10(2):143–157.CrossrefGoogle Scholar
  • Almgren R (2012) Optimal trading with stochastic liquidity and volatility. SIAM J. Financial Math. 3(1):163–181.CrossrefGoogle Scholar
  • Almgren R, Chriss N (2001) Optimal execution of portfolio transactions. J. Risk 3(2):5–39.CrossrefGoogle Scholar
  • Anupindi R, Morton TE, Pentico D (1996) The nonstationary stochastic lead-time inventory problem: Near-myopic bounds, heuristics, and testing. Management Sci. 42(1):124–129.LinkGoogle Scholar
  • Athans M (1971) The role and use of the stochastic linear-quadratic-gaussian problem in control system design. Automatic Control, IEEE Trans. 16(6):529–552.CrossrefGoogle Scholar
  • Bemporad A, Morari M, Dua V, Pistikopoulos EN (2002) The explicit linear quadratic regulator for constrained systems. Automatica 38(1):3–20.CrossrefGoogle Scholar
  • Bertsekas DP (1995) Dynamic Programming and Optimal Control, Vol. 1 (Athena Scientific, Belmont, MA).Google Scholar
  • Bertsimas D, Lo AW (1998) Optimal control of execution costs. J. Financial Markets 1(1):1–50.CrossrefGoogle Scholar
  • Biais B, Hillion P, Spatt C (1995) An empirical analysis of the limit order book and the order flow in the Paris Bourse. J. Finance 50(5):1655–1689.CrossrefGoogle Scholar
  • Birge JR, Louveaux FV (2011) Introduction to Stochastic Programming (Springer, New York).CrossrefGoogle Scholar
  • Blair Jr WPJ, Sworder DD (1975) Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria. Internat. J. Control 21(5):833–841.CrossrefGoogle Scholar
  • Bradley JR, Robinson LW (2005) Improved base-stock approximations for independent stochastic lead times with order crossover. Manufacturing Service Oper. Management 7(4):319–329.LinkGoogle Scholar
  • Brogaard J, Hendershott T, Riordan R (2014) High-frequency trading and price discovery. Rev. Financial Stud. 27(8):2267–2306.CrossrefGoogle Scholar
  • Cao C, Hansch O, Wang X (2008) Order placement strategies in a pure limit order book market. J. Financial Res. 31(2):113–140.CrossrefGoogle Scholar
  • Chen J, Feng L, Peng J, Ye Y (2014) Analytical results and efficient algorithm for optimal portfolio deleveraging with market impact. Oper. Res. 62(1):195–206.LinkGoogle Scholar
  • Chiyachantana CN, Jain PK, Jiang C, Wood RA (2004) International evidence on institutional trading behavior and price impact. J. Finance 59(2):869–898.CrossrefGoogle Scholar
  • Chizeck HJ, Willsky AS, Castanon D (1986) Discrete-time Markovian-jump linear quadratic optimal control. Internat. J. Control 43(1):213–231.CrossrefGoogle Scholar
  • Cont R, Stoikov S, Talreja R (2010) A stochastic model for order book dynamics. Oper. Res. 58(3):549–563.LinkGoogle Scholar
  • Ehrhardt R (1984) (s, S) policies for a dynamic inventory model with stochastic lead times. Oper. Res. 32(1):121–132.LinkGoogle Scholar
  • Fodra P, Pham H (2015a) High frequency trading and asymptotics for small risk aversion in a Markov renewal model. SIAM J. Financial Math. 6(1):656–684.CrossrefGoogle Scholar
  • Fodra P, Pham H (2015b) Semi-Markov model for market microstructure. Appl. Math. Finance 22(3):261–295.CrossrefGoogle Scholar
  • Forsyth PA, Kennedy JS, Tse ST, Windcliff H (2012) Optimal trade execution: A mean quadratic variation approach. J. Econom. Dynam. Control 36(12):1971–1991.CrossrefGoogle Scholar
  • Foucault T (1999) Order flow composition and trading costs in a dynamic limit order market. J. Financial Markets 2(2):99–134.CrossrefGoogle Scholar
  • Foucault T, Kadan O, Kandel E (2005) Limit order book as a market for liquidity. Rev. Financial Stud. 18(4):1171–1217.CrossrefGoogle Scholar
  • Fruth A, Schöneborn T, Urusov M (2014) Optimal trade execution and price manipulation in order books with time-varying liquidity. Math. Finance 24(4):651–695.CrossrefGoogle Scholar
  • Glosten LR, Milgrom PR (1985) Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. J. Financial Econom. 14(1):71–100.CrossrefGoogle Scholar
  • Goettler RL, Parlour CA, Rajan U (2005) Equilibrium in a dynamic limit order market. J. Finance 60(5):2149–2192.CrossrefGoogle Scholar
  • Goettler RL, Parlour CA, Rajan U (2009) Informed traders and limit order markets. J. Financial Econom. 93(1):67–87.CrossrefGoogle Scholar
  • Gould MD, Porter MA, Williams S, McDonald M, Fenn DJ, Howison SD (2013) Limit order books. Quant. Finance 13(11):1709–1742.CrossrefGoogle Scholar
  • Guilbaud F, Pham H (2013) Optimal high-frequency trading with limit and market orders. Quant. Finance 13(1):79–94.CrossrefGoogle Scholar
  • Guo X, Zervos M (2015) Optimal execution with multiplicative price impact. SIAM J. Financial Math. 6(1):281–306.CrossrefGoogle Scholar
  • Guo X, de Larrard A, Ruan Z (2013) Optimal placement in a limit order book. Working paper, University of California, Berkeley, Berkeley.LinkGoogle Scholar
  • Henriot A (2014) Market design with centralized wind power management: Handling low-predictability in intraday markets. Energy J. 35(1):99–117.CrossrefGoogle Scholar
  • Horst U, Naujokat F (2014) When to cross the spread? Trading in two-sided limit order books. SIAM J. Financial Math. 5(1):278–315.CrossrefGoogle Scholar
  • Huberman G, Stanzl W (2004) Price manipulation and quasi-arbitrage. Econometrica 72(4):1247–1275.CrossrefGoogle Scholar
  • Kavajecz KA (1999) A specialist’s quoted depth and the limit order book. J. Finance 54(2):747–771.CrossrefGoogle Scholar
  • Kempf A, Korn O (1999) Market depth and order size. J. Financial Markets 2(1):29–48.CrossrefGoogle Scholar
  • Kyle AS (1985) Continuous auctions and insider trading. Econometrica 53(6):1315–1335.CrossrefGoogle Scholar
  • Louveaux FV (1980) A solution method for multistage stochastic programs with recourse with application to an energy investment problem. Oper. Res. 28(4):889–902.LinkGoogle Scholar
  • Moore JB, Zhou XY, Lim AE (1999) Discrete time lqg controls with control dependent noise. Systems Control Lett. 36(3):199–206.CrossrefGoogle Scholar
  • Obizhaeva AA, Wang J (2013) Optimal trading strategy and supply/Demand dynamics. J. Financial Markets 16(1):1–32.CrossrefGoogle Scholar
  • O’Hara M (1995) Market Microstructure Theory, Vol. 108 (Blackwell, Cambridge, MA).Google Scholar
  • Parlour CA, Seppi DJ (2008) Limit order markets: A survey. Thakor AV, Boot A, eds. Handbook of Financial Intermediation and Banking, Handbooks in Finance, Vol. 5 (Elsevier, Amsterdam), 63–96.CrossrefGoogle Scholar
  • Powell WB (2007) Approximate Dynamic Programming: Solving the Curses of Dimensionality, Vol. 703 (John Wiley & Sons, Hoboken, NJ).CrossrefGoogle Scholar
  • Predoiu S, Shaikhet G, Shreve S (2011) Optimal execution in a general one-sided limit-order book. SIAM J. Financial Math. 2(1):183–212.CrossrefGoogle Scholar
  • Puterman ML (2009) Markov Decision Processes: Discrete Stochastic Dynamic Programming, Vol. 414 (John Wiley & Sons, Hoboken, NJ).Google Scholar
  • Ranaldo A (2004) Order aggressiveness in limit order book markets. J. Financial Markets 7(1):53–74.CrossrefGoogle Scholar
  • Roşu I (2009) A dynamic model of the limit order book. Rev. Financial Stud. 22(11):4601–4641.CrossrefGoogle Scholar
  • Saar G (2001) Price impact asymmetry of block trades: An institutional trading explanation. Rev. Financial Stud. 14(4):1153–1181.CrossrefGoogle Scholar
  • Schmalensee R (2012) Evaluating policies to increase electricity generation from renewable energy. Rev. Environ. Econom. Policy 6(1):45–64.CrossrefGoogle Scholar
  • Tse ST, Forsyth PA, Kennedy JS, Windcliff H (2013) Comparison between the mean-variance optimal and the mean-quadratic-variation optimal trading strategies. Appl. Math. Finance 20(5):415–449.CrossrefGoogle Scholar
  • Tsoukalas G, Wang J, Giesecke K (2016) Dynamic portfolio execution. Working paper, University of Pennsylvania, Philadelphia.Google Scholar
  • Zipkin PH (2000) Foundations of Inventory Management, 1st ed. (McGraw-Hill, New York).Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.