Curve following in illiquid markets

Mathematics and Financial Economics

Volumn 4, Issue 4, 2011, Pages 299-335

  Naujokat, Felix ^a,b   Westray, Nicholas ^a,b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b Quantitative Products Laboratory   (Germany)

Author keywords

Convex analysis; Fully coupled forward backward stochastic differential equations; Stochastic maximum principle; Trading in illiquid markets

Indexed keywords

EID: 79956000519     PISSN: 18629679     EISSN: 18629660     Source Type: Journal    
DOI: 10.1007/s11579-011-0042-5     Document Type: Article

References (34)

1. Almgren R.: Optimal execution with nonlinear impact functions and trading-enhanced risk. Appl. Math. Financ. 10(1), 1-18 (2003).
2. Almgren, R.: Optimal trading in a dynamic market. preprint (2009).
3. Almgren R., Chriss N.: Optimal execution of portfolio transactions. J. Risk 3, 5-39 (2001).
4. Almgren R., Thum C., Hauptmann E., Li H.: Direct estimation of equity market impact. Risk 18(7), 58-62 (2005).
5. Applebaum D.: Lévy processes and Stochastic Calculus, Volume 116 of Cambridge Studies in Advanced Mathematics, 2nd edn. Cambridge University Press, Cambridge (2009).
6. Barles G., Buckdahn R., Pardoux E.: Backward stochastic differential equations and integral-partial differential equations. Stoch. Stoch. Rep. 60, 57-83 (1997).
7. Bayraktar E., Egami M.: An analysis of montone follower problems for diffusion processes. Math. Oper. Res. 33, 336-350 (2008) (preprint).
8. Bender C., Zhang J.: Time discretization and Markovian iteration for coupled FBSDEs. Ann. Appl. Probab. 18(1), 143-177 (2008).
9. Beneš V. E., Shepp L. A., Witsenhausen H. S.: Some solvable stochastic control problems. Stochastics 4, 39-83 (1980).
10. Beneš V. E., Karatzas I., Ocone D., Wang H.: Control with partial observations and an explicit solution of Mortensen's equation. Appl. Math. Optim. 49(3), 217-239 (2004).
11. Cadenillas A.: A stochastic maximum principle for systems with jumps, with applications to finance. Syst. Control Lett. 47, 433-444 (2002).
12. Cadenillas A., Karatzas I.: The stochastic maximum principle for linear convex optimal control with random coefficients. SIAM J. Control Optim. 33(2), 590-624 (1995).
13. Çetin U., Jarrow R., Protter P.: Liquidity risk and arbitrage pricing theory. Financ. Stoch. 8(3), 311-341 (2004).
14. Davis M., Norman A.: Portfolio selection with transaction costs. Math. Oper. Res. 15, 676-713 (1990).
15. Ekeland I., Témam R.: Convex Analysis and Variational Problems, Volume 28 of Classics in Applied Mathematics, English edn. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1999).
16. El Karoui N., Peng S., Quenez M.: Backward stochastic differential equations in finance. Math. Financ. 7(1), 1-71 (1997).
17. Emery, M.: Compensation de processus à variation finie non localement intégrables. In: Seminar on Probability, XIV (Paris, 1978/1979) (French), Volume 784 of Lecture Notes in Mathematics, pp. 152-160. Springer, Berlin (1980).
18. Friedman A.: Partial Differential Equations of Parabolic Type. Prentice-Hall Inc., Englewood Cliffs (1964).
19. Hendershott T., Mendelson H.: Crossing networks and dealer markets: competition and performance. J. Financ. 55, 2071-2115 (2000).
20. Ji S., Zhou X. Y.: A maximum principle for optimal stochastic control with terminal stated constraints, and its applications. Commun. Inf. Syst. 6(4), 321-338 (2006).
21. Karatzas I., Shreve S. E.: Brownian Motion and Stochastic Calculus, Volume 113 of Graduate Texts in Mathematics, 2nd edn. Springer, New York (1991).
22. Karatzas I., Ocone D., Wang H., Zervos M.: Finite-fuel singular control with discretionary stopping. Stoch. Stoch. Rep. 71, 1-50 (2000).
23. Ma J., Protter P., Yong J. M.: Solving forward-backward stochastic differential equations explicitly-a four step scheme. Probab. Theory Relat. Fields 98(3), 339-359 (1994).
24. Obizhaeva, A., Wang, J.: Optimal trading strategy and supply/demand dynamics. MIT Technical Report (2005).
25. Palczewski J., Zabzyck J.: Portfolio diversification with Markovian prices. Probab. Math. Stat. 25, 75-95 (2005).
26. Pardoux E., Tang S.: Forward-backward stochastic differential equations and quasilinear parabolic PDEs. Probab. Theory Relat. Fields 114, 123-150 (1999).
27. Pham H.: Continuous-Time Stochastic Control and Optimization with Financial Applications, Volume 61 of Stochastic Modelling and Applied Probability. Springer, Berlin (2009).
28. Pliska S. R., Suzuki K.: Optimal tracking for asset allocation with fixed and proportional transaction costs. Quant. Financ. 4(2), 233-243 (2004).
29. Protter, P. E.: Stochastic Integration and Differential Equations, volume 21 of Applications of Mathematics (New York), 2nd edn. Springer, Berlin (2004). Stochastic Modelling and Applied Probability.
30. Rogers L. C. G., Singh S.: The cost of illiquidity and its effects on hedging. Math. Financ. 20(4), 597-615 (2010).
31. Schied A., Schöneborn T.: Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets. Financ. Stoch. 13(2), 181-204 (2008).
32. Shreve S., Soner H. M.: Optimal investment and consumption under transactions costs. Ann. Appl. Probab. 4(3), 609-692 (1994).
33. Tang S. J., Li X. J.: Necessary conditions for optimal control of stochastic systems with random jumps. SIAM J. Control Optim. 32, 1447-1475 (1994).
34. Yong J., Zhou X. Y.: Stochastic Controls, Hamiltonian Systems and HJB Equations, Volume 43 of Applications of Mathematics (New York). Springer, New York (1999).