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

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)

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  • 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.

    Mathematics Subject Classification: Primary: 34R35; Secondary: 91B28, 93E20.


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  • Figure .  The free boundaries $x^*$ and $\bar x$ change when $\alpha$ changes

    Figure .  The free boundaries $x^*$ and $\bar x$ change when $\alpha$ changes

    Figure .  The free boundaries $x^*$ and $\bar x$ change when $K$ changes

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