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

Xiaoshan Chen; Xun Li; Fahuai Yi

doi:10.3934/jimo.2018033

Article Contents

2019, Volume 15, Issue 1: 81-96. Doi: 10.3934/jimo.2018033

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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

Early access: April 2018

Published: January 2019

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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Abstract

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.

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

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

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

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

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