\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

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)

Abstract Full Text(HTML) Figure(3) Related Papers Cited by
  • 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.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • 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

  •   A. Bensoussan , A. Cadenillas  and  H. K. Koo , Entrepreneurial decisions on effort and project with a nonconcave objective function, Mathematics of Operations Research, 40 (2015) , 901-914.  doi: 10.1287/moor.2014.0702.
      A. Berger  and  G. F. Udell , The economics of small business finance: The roles of private equity and debt markets in the financial growth cycle, Journal of Banking and Finance, 22 (1998) , 613-673.  doi: 10.2139/ssrn.137991.
      J. N. Carpenter , Does option compensation increase managarial risk appetite?, The Journal of Finance, 50 (2000) , 2311-2331. 
      S. Carter, C. Mason and S. Tagg, Lifting the barriers to growth in UK small businesses: The FSB biennial membership survey, Federation of Small Businesses, London, 2004.
      C. Ceci  and  B. Bassan , Mixed optimal stopping and stochastic control problems with semicontinuous final reward for diffusion processes, Stochastics and Stochastics Reports, 76 (2004) , 323-337.  doi: 10.1080/10451120410001728436.
      M. H. bChang , T. Pang  and  J. Yong , Optimal stopping problem for stochastic differential equations with random coefficients, SIAM Journal on Control and Optimization, 48 (2009) , 941-971.  doi: 10.1137/070705726.
      K. J. Choi , H. K. Koo  and  D. Y. Kwak , Optimal stopping of active portfolio management, Annals of Economics and Finance, 5 (2004) , 93-126. 
      J. Chua , J. Chrisman , F. Kellermanns  and  Z. Wu , Family involvement and new venture debt financing, Journal of Business Venturing, 26 (2011) , 472-488.  doi: 10.1016/j.jbusvent.2009.11.002.
      D. Cumming  and  U. Walz , Private equity returns and disclosure around the world, Journal of International Business Studies, 41 (2010) , 727-754. 
      S. Dayanik  and  I. Karatzas , On the optimal stopping problem for one-dimensional diffusions, Stochastic Processes and their Applications, 107 (2003) , 173-212.  doi: 10.1016/S0304-4149(03)00076-0.
      R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, Springer-Verlag, New York, 1999.
      W. Fleming and H. Soner, Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York, 1993.
      V. Henderson  and  D. Hobson , An explicit solution for an optimal stopping/optimal control problem which models an asset sale, The Annals of Applied Probability, 18 (2008) , 1681-1705.  doi: 10.1214/07-AAP511.
      X. Li , X. Y. Zhou  and  A. E. B. Lim , Dynamic mean-variance portfolio selection with no-shorting constraints, SIAM Journal on Control and Optimization, 40 (2002) , 1540-1555.  doi: 10.1137/S0363012900378504.
      X. Li  and  X. Y. Zhou , Continuous-time mean-variance efficiency: The 80 % rule, The Annals of Applied Probability, 16 (2006) , 1751-1763.  doi: 10.1214/105051606000000349.
      G. Peskir and A. Shiryaev, Optimal Stopping and Free-Boundary Problems, 2nd edition. Birkhäuser Verlag, Berlin, 2006.
      A. Shiryaev , Z. Q. Xu  and  X. Y. Zhou , Thou shalt buy and hold, Quantitative Finance, 8 (2008) , 765-776.  doi: 10.1080/14697680802563732.
      J. Sparrow  and  P. Bentley , Decision tendencies of entrepreneurs and small business risk management practices, Risk Management, 2 (2000) , 17-26.  doi: 10.1057/palgrave.rm.8240037.
      G. L. Xu  and  S. E. Shreve , A duality method for optimal consumption and investment under short-selling prohibition: Ⅱ. constant market coefficients, Annals of Applied Probability, 2 (1992) , 314-328.  doi: 10.1214/aoap/1177005706.
      J. Yong and X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999.
  • 加载中

Figures(3)

SHARE

Article Metrics

HTML views(2398) PDF downloads(462) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return