Advertisement

Applications of Mathematics

, Volume 61, Issue 5, pp 515–526 | Cite as

Gaussian density estimates for the solution of singular stochastic Riccati equations

  • Tien Dung NguyenEmail author
Article
  • 104 Downloads

Abstract

Stochastic Riccati equation is a backward stochastic differential equation with singular generator which arises naturally in the study of stochastic linear-quadratic optimal control problems. In this paper, we obtain Gaussian density estimates for the solutions to this equation.

Keywords

stochastic Riccati equation Malliavin calculus density estimate 

MSC 2010

60H10 60H07 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    O. Aboura, S. Bourguin: Density estimates for solutions to one dimensional backward SDE’s. Potential Anal. 38 (2013), 573–587.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    F. Antonelli, A. Kohatsu-Higa: Densities of one-dimensional backward SDEs. Potential Anal. 22 (2005), 263–287.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    J. Cvitanić, J. Zhang: Contract Theory in Continuous-Time Models. Springer Finance, Springer, Heidelberg, 2013.CrossRefzbMATHGoogle Scholar
  4. [4]
    G. Dos Reis: On Some Properties of Solutions of Quadratic Growth BSDE and Applications in Finance and Insurance. PhD thesis, Humboldt University in Berlin, 2010.Google Scholar
  5. [5]
    N. Kazamaki: Continuous Exponential Martingales and BMO. Lecture Notes in Mathematics 1579, Springer, Berlin, 1994.zbMATHGoogle Scholar
  6. [6]
    A. E. B. Lim, X. Y. Zhou: Mean-variance portfolio selection with random parameters in a complete market. Math. Oper. Res. 27 (2002), 101–120.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    T. Mastrolia, D. Possamaï, A. Réveillac: Density analysis of BSDEs. Ann. Probab. 44 (2016), 2817–2857.MathSciNetCrossRefGoogle Scholar
  8. [8]
    T. D. Nguyen, N. Privault, G. L. Torrisi: Gaussian estimates for the solutions of some one-dimensional stochastic equations. Potential Anal. 43 (2015), 289–311.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    I. Nourdin, F. G. Viens: Density formula and concentration inequalities with Malliavin calculus. Electron. J. Probab. 14 (2009), 2287–2309.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    D. Nualart: The Malliavin Calculus and Related Topics. Probability and Its Applications, Springer, Berlin, 2006.zbMATHGoogle Scholar
  11. [11]
    N. Privault: Stochastic Analysis in Discrete and Continuous Settings with Normal Martingales. Lecture Notes in Mathematics 1982, Springer, Berlin, 2009.zbMATHGoogle Scholar
  12. [12]
    Y. Shen: Mean-variance portfolio selection in a complete market with unbounded random coefficients. Automatica J. IFAC 55 (2015), 165–175.MathSciNetCrossRefGoogle Scholar
  13. [13]
    Z. Yu: Continuous-time mean-variance portfolio selection with random horizon. Appl. Math. Optim. 68 (2013), 333–359.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  1. 1.Department of MathematicsFPT University, Hoa Lac High Tech ParkHanoiVietnam

Personalised recommendations