OPTIMAL SELLING STRATEGY WITH A LARGE BLOCK OF STOCK

Yi Fu; Baojun Bian; Jizhou Zhang

doi:10.11948/2015040

2015 Volume 5 Issue 3

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Yi Fu, Baojun Bian, Jizhou Zhang. OPTIMAL SELLING STRATEGY WITH A LARGE BLOCK OF STOCK[J]. Journal of Applied Analysis & Computation, 2015, 5(3): 496-514. doi: 10.11948/2015040

Citation:

Yi Fu, Baojun Bian, Jizhou Zhang. OPTIMAL SELLING STRATEGY WITH A LARGE BLOCK OF STOCK[J]. Journal of Applied Analysis & Computation, 2015, 5(3): 496-514. doi: 10.11948/2015040

OPTIMAL SELLING STRATEGY WITH A LARGE BLOCK OF STOCK

1 Department of Finance, Shanghai Normal University, 100 Guilin RD, 200234, Shanghai, China;
2 Department of Mathematics, Tongji University, 1239 Siping Rd, 200092, Shanghai, China;
3 Department of Mathematics, Shanghai Normal University, 100 Guilin RD, 200234, Shanghai, China

Fund Project:

Abstract

Abstract

In this paper, we develop an optimal stock selling strategy with the stochastic upper bound of selling rate over an infinite time horizon. Moreover, the temporary and permanent price impact are considered. We treat the problem by using a fluid model. In the model that the number of shares is treated as fluid (continuous) and the overall liquidation is dictated by the rates of selling over time. The goal is to maximize the overall return under state constraints. The corresponding value function with the selling strategies is shown to be continuous and the unique viscosity solution to the associated HJB equation. Finally, a numerical example is given to illustrate the result.
- Optimal selling strategy /
- temporary price impact /
- HJB /
- viscosity solution
MSC: 91G80;35D40

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References

[1]	R. Almgren and N. Chriss, Optimal execution of portfolio transactions, Journal of Risk, 3(2000), 5-39. Google Scholar
[2]	R. Almgren, Optimal execution with nonlinear impact functions and trading enhanced risk, Applied Mathematical Finance, 10(2003), 1-18. Google Scholar
[3]	R. Almgren, Optimal trading in a dynamic market, (2009) WorkingPaper. Google Scholar
[4]	D. Bertsimas and A.W. Lo, Optimal control of execution costs, Journal of Financial Markets, 1(1998), 1-50. Google Scholar
[5]	B. Bian, M.Dai, L. Jiang, J. Zhang and Y.F. Zhong, Optimal decision for selling an illiquid stock, Journal of Optimization Theory and Application, 151(2)(2011), 402-417. Google Scholar
[6]	M.G. Crandall and P.L.Lions, Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, 277(1983), 1-42. Google Scholar
[7]	M.G. Crandall and P.L.Lions, User's guide to viscosity solutions of second order partial differential equations, Bulletin of the American Mathematical Society, 27(1)(1992), 1-67. Google Scholar
[8]	P.A. Forsyth and G. Labahn, Numerical methods for controlled HamiltonJacobi-Bellman PDEs in finance, Journal of Computational Finance, 11(2)(2007), 1-44. Google Scholar
[9]	P.A. Forsyth, J.S. Kennedy, S. T. Tse and H. Windcliff, Optimal trade execution:a mean-quadratic-variation approach, Journal of Economic Dynamics and Control, 36(12)(2012), 1791-1991. Google Scholar
[10]	F. Lillo, J. Farmer, and R. Manttegna, Master curve for price impact function, Nature, (2003), 421:129. Google Scholar
[11]	M. Pemy, Q. Zhang and G. Yin, Liquidation of a large block of stock, Journal of Banking and Finance, 31(2006), 295-1305. Google Scholar
[12]	M. Pemy, Q. Zhang and G. Yin, Liquidation of a large block of stock with regime switching, Mathematical Finance, 4(18)(2008), 629-648. Google Scholar
[13]	M. Pemy, Q. Zhang and G. Yin, Optimal selling rule in a regime switching levy market, International Journal of Mathematics and Mathematical Sciences, 2011(2011), 1-28. Google Scholar
[14]	M. Potters and J.-P. Bouchard, More statistical properties of order books and price impact, Physica, (2003), 133-140. Google Scholar
[15]	A. Schied and T. SchÄoneborn, Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets, Finance and Stochastics, 13(2)(2009), 181-204. Google Scholar
[16]	A. Schied and T. SchÄoneborn, Optimal basket liquidation with finite time horizon for CARA investors, Working Paper. Google Scholar
[17]	H.M. Soner, Controlled Markov processes, viscosity solutions and applications to mathematical finance, Springer Lecture Notes in Mathematics, 1660(1997), 134-185. Google Scholar
[18]	H.M. Soner, Stochastic optimal control in finance, Pisa:Scuola normale superiore, 2007. Google Scholar