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Mathematical analysis of a variational inequality modelling perpetual executive stock options

Published online by Cambridge University Press:  07 January 2015

XIN LAI ,
XINFU CHEN ,
MINGXIN WANG ,
CONG QIN  and
WANGHUI YU
XIN LAI
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China email: laixin2002@163.com
XINFU CHEN
Affiliation:
Department of Mathematics, University of Pittsburgh, PA 15260, USA email: xinfu@pitt.edu
MINGXIN WANG
Affiliation:
Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, People's Republic of China email: mxwang@hit.edu.cn
CONG QIN
Affiliation:
Center for Financial Engineering, Soochow University, Suzhou 215006, People's Republic of China email: wacilee.qin@gmail.com, whyu@suda.edu.cn
WANGHUI YU
Affiliation:
Center for Financial Engineering, Soochow University, Suzhou 215006, People's Republic of China email: wacilee.qin@gmail.com, whyu@suda.edu.cn
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Abstract

In this paper, we establish the existence and uniqueness of a classical solution of a degenerate parabolic variational inequality of which a strong solution was shown to exist by Song and Yu [21]. The problem arises from optimal stochastic control of exercising continuously perpetual executive stock options (ESOs). We also characterize the basic graph, continuity, and monotonicity properties of the free boundary from which the optimal control strategy can be described precisely.

Keywords

Variational inequalityfree boundaryperpetual executive stock optionstochastic control
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 2 , April 2015 , pp. 193 - 213
Copyright
Copyright © Cambridge University Press 2015 

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