Optimal portfolios of a small investor in a limit order market: A shadow price approach

Mathematics and Financial Economics

Volumn 3, Issue 2, 2010, Pages 45-72

  Kühn, Christoph ^a   Stroh, Maximilian ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

Limit order market; Order book; Portfolio optimization; Shadow price

Indexed keywords

EID: 77953906511     PISSN: 18629679     EISSN: 18629660     Source Type: Journal    
DOI: 10.1007/s11579-010-0027-9     Document Type: Article

References (22)

1. Davis M., Norman A.: Portfolio selection with transaction costs. Math. Oper. Res. 15, 676-713 (1990).
2. Foucault T., Kadan O., Kandel E.: Limit order book as a market for liquidity. Rev. Financ. Stud. 18, 1171-1217 (2005).
3. Galtchouk L. I.: Stochastic integrals with respect to optional semimartingales and random measures. Theory Probab. Appl. 29(1), 93-108 (1985).
4. Goll T., Kallsen J.: Optimal portfolios for logarithmic utility. Stoch. Process. Appl. 89, 31-48 (2000).
5. Harris L.: Optimal dynamic order submission strategies in some stylized trading problems. Financ. Mark. Inst. Instrum. 7, 1-76 (1998).
6. Hartman P.: Ordinary Differential Equations. Wiley, New York (1964).
7. Jacod J., Shiryaev A. N.: Limit Theorems for Stochastic Processes, 2nd edn. Springer, Berlin (2002).
8. Jarrow R., Protter P.: Large traders, hidden arbitrage, and complete markets. J. Bank. Financ. 29, 2803-2820 (2005).
9. Kallsen, J., Muhle-Karbe, J.: On using shadow prices in portfolio optimization with transaction costs. Ann. Appl. Probab. (forthcoming).
10. Karatzas I., Shreve S. E.: Methods of Mathematical Finance. Springer, Berlin (1998).
11. Korn R.: Optimal Portfolios: Stochastic Models for Optimal Investment and Risk Management in Continuous Time. World Scientific, Singapore (1997).
12. Kühn C., Stroh M.: A note on stochastic integration with respect to optional semimartingales. Electron. Commun. Probab. 14, 192-201 (2009).
13. Matsumoto K.: Optimal portfolio of low liquid assets with a log-utility function. Financ. Stoch. 10, 121-145 (2006).
14. Menaldi J., Robin M.: Reflected diffusion processes with jumps. Ann. Probab. 13(2), 319-341 (1985).
15. Merton R.: Lifetime portfolio selection under uncertainty: The continuous-time case. Rev. Econ. Stat. 51, 247-257 (1969).
16. Merton R.: Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory 3, 373-413 (1971).
17. Parlour C. A., Seppi D. J.: Limit order markets: a survey. In: Thakor, A. V., Boot, A. W. A. (eds) Handbook of Financial Intermediation and Banking, pp. 63-96. North-Holland, Amsterdam (2008).
18. Pham H., Tankov P.: A model of optimal consumption under liquidity risk with random trading times. Math. Financ. 18, 613-627 (2008).
19. Protter P. E.: Stochastic Integration and Differential Equations, 2nd edn. Springer, Berlin (2004).
20. Rogers L. C. G., Zane O.: A simple model of liquidity effects. In: Sandmann, K., Schönbucher, P. J. (eds) Advances in Finance and Stochastics: Essays in Honour of Dieter Sondermann, pp. 161-176. Springer, Berlin (2002).
21. Roşu I.: A dynamic model of the limit order book. Rev. Financ. Stud. 22(11), 4601-4641 (2009).
22. Shreve S. E., Soner H. M.: Optimal investment and consumption with transaction costs. Ann. Appl. Probab. 4(3), 609-692 (1994).