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Least-squares Monte-Carlo methods for optimal stopping investment under CEV models |
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| Authors: | Jingtang Ma Zhengyang Lu Wenyuan Li Jie Xing |
| Affiliation: | 1. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, People's Republic of China mjt@swufe.edu.cn;3. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, People's Republic of China;4. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, People's Republic of China;5. Guiyang Institute for Big Data and Finance, Guizhou University of Finance and Economics, Guiyang 550025, People's Republic of China;6. Current address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.;7. Guiyang Institute for Big Data and Finance, Guizhou University of Finance and Economics, Guiyang 550025, People's Republic of China |
| Abstract: | The optimal stopping investment is a kind of mixed expected utility maximization problems with optimal stopping time. The aim of this paper is to develop the least-squares Monte-Carlo methods to solve the optimal stopping investment under the constant elasticity of variance (CEV) model. Such a problem has no closed-form solutions for the value functions, optimal strategies and optimal exercise boundaries due to the early exercised feature. The dual optimal stopping problem is first derived and then the strong duality between the dual and prime problems is established. The least-squares Monte-Carlo methods based on the dual control theory are developed and numerical simulations are provided. Both the power and non-HARA utilities are studied. |
| Keywords: | Optimal investment Optimal stopping CEV model Dual control approach Monte-Carlo methods |