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

doi:10.1007/s40305-018-0223-5

Journal of the Operations Research Society of China ›› 2021, Vol. 9 ›› Issue (1): 163-179.doi: 10.1007/s40305-018-0223-5

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

Xian-Ping Wu¹, Seakweng Vong², Wen-Xin Zhou³

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:2017-09-03 Revised:2018-09-12 Online:2021-03-11 Published:2021-03-11
Contact: Xian-Ping Wu, Seakweng Vong, Wen-Xin Zhou E-mail:pphappe@sina.com;swvong@umac.mo;ttabuzwx@hotmail.com
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

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.

Key words: Optimal stopping, Portfolio, Value function, Dynamic programming, Holding region

CLC Number:

60G40

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.

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References

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

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