Optimal Stopping Time of a Portfolio Selection Problem with Multi-assets

Expand
  • 1 School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China;
    2 Department of Mathematics, University of Macau, Macau, China;
    3 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

Received date: 2017-09-03

  Revised date: 2018-09-12

  Online published: 2021-03-11

Supported by

This work is supported by the National Natural Science Foundation of China (Nos. 11571124 and 11671158), the doctoral start-up Grant of Natural Science Foundation of Guangdong Province, China (No. 2017A030310167), the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University (No. 201808) and Unversity of Macau (No. MYGR2018-00047-FST).

Abstract

In this work, we study a right time for an investor to stop the investment among multiassets over a given investment horizon so as to obtain maximum profit. We formulate it to a two-stage problem. The main problem is not a standard optimal stopping problem due to the non-adapted term in the objective function, and we turn it to a standard one by stochastic analysis. The subproblem with control variable in the drift and volatility terms is solved first via stochastic control method. A numerical example is presented to illustrate the efficiency of the theoretical results.

Cite this article

Xian-Ping Wu, Seakweng Vong, Wen-Xin Zhou . Optimal Stopping Time of a Portfolio Selection Problem with Multi-assets[J]. Journal of the Operations Research Society of China, 2021 , 9(1) : 163 -179 . DOI: 10.1007/s40305-018-0223-5

References

[1] Shiryaev, A., Xu, Z.Q., Zhou, X.Y.:Thou shalt buy and hold. Quant. Financ. 8, 765-776(2008)
[2] Du Toit, J., Peskir, G.:Selling a stock at the ultimate maximum. Ann. Appl. Probab. 19(3), 983-1014(2009)
[3] Dai, M., Zhong, Y.F.:Optimal stock selling/buying strategy with reference to the ultimate average. Math. Financ. 22(1), 165-184(2012)
[4] Markowitz, H.:Portfolio selection. J. Financ. 7(1), 77-91(1952)
[5] Markowitz, H.:Portfolio Selection:Efticient Diversification of Investments. Wiley, New York (1959)
[6] Merton, R.C.:Lifetime portfolio selection under uncertainty:the continuous-time case. Rev. Econ. Stat. 51(3), 247-257(1969)
[7] Merton, R.C.:Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory 3(4), 373-413(1971)
[8] Merton, R.C.:Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4(1), 141-183(1973)
[9] Xu, G.L., Shreve, S.E.:A duality method for optimal consumption and investment under short-selling prohibition. I. General market coefficients. Ann. Appl. Probab. 2, 87-112(1992)
[10] Xu, G.L., Shreve, S.E.:A duality method for optimal consumption and investment under short-selling prohibition. Ⅱ. Constant market coefficients. Ann. Appl. Probab. 2, 314-328(1992)
[11] Choi, K., Koo, H., Kwak, D.:Optimal stopping of active portfolio management. Ann. Econ. Financ. 5, 93-126(2004)
[12] Steele, J.M.:Stochastic Calculus and Financial Applications. Springer, Berlin (2012)
[13] Karatzas, I., Shreve, S.E.:Methods of Mathematical Finance. Springer, New York (1998)
[14] Peskir, G., Shiryaev, A.:Optimal Stopping and Free-Boundary Problems, 2nd edn. Birkhäuser Verlag, Berlin (2006)
[15] Xu, G.L., Shreve, S.E.:A duality method for optimal consumption and investment under short-selling prohibition. Ⅱ. Constant market coefficients. Ann. Appl. Probab. 2(2), 314-328(1992)
Options
Outlines

/