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January  2019, 15(1): 81-96. doi: 10.3934/jimo.2018033

## Optimal stopping investment with non-smooth utility over an infinite time horizon

 1 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China 2 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China 3 School of Finance, Guangdong University of Foreign Studies, Guangzhou 510420, China

Received  March 2017 Revised  October 2017 Published  April 2018

Fund Project: This work was partially supported by Research Grants Council of Hong Kong under grant 519913, 15224215 and 15255416; NNSF of China (No. 11601163, No.11471276, No.11771158); NSF Guangdong Province of China (No.2016A030313448, No.2015A030313574, No.2017A030313397); The Humanities and Social Science Research Foundation of the Ministry of Education of China (No.15YJAZH051)

This study addresses an investment problem facing a venture fund manager who has a non-smooth utility function. The theoretical model characterizes an absolute performance-based compensation package. Technically, the research methodology features stochastic control and optimal stopping by formulating a free-boundary problem with a nonlinear equation, which is transferred to a new one with a linear equation. Numerical results based on simulations are presented to better illustrate this practical investment decision mechanism.

Citation: Xiaoshan Chen, Xun Li, Fahuai Yi. Optimal stopping investment with non-smooth utility over an infinite time horizon. Journal of Industrial & Management Optimization, 2019, 15 (1) : 81-96. doi: 10.3934/jimo.2018033
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##### References:
The free boundaries $x^*$ and $\bar x$ change when $\alpha$ changes
The free boundaries $x^*$ and $\bar x$ change when $\alpha$ changes
The free boundaries $x^*$ and $\bar x$ change when $K$ changes
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