Gaussian density estimates for the solution of singular stochastic Riccati equations

Tien Dung Nguyen

Applications of Mathematics (2016)

  • Volume: 61, Issue: 5, page 515-526
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Nguyen, Tien Dung. "Gaussian density estimates for the solution of singular stochastic Riccati equations." Applications of Mathematics 61.5 (2016): 515-526. <http://eudml.org/doc/286819>.

@article{Nguyen2016,
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.},
author = {Nguyen, Tien Dung},
journal = {Applications of Mathematics},
keywords = {stochastic Riccati equation; Malliavin calculus; density estimate; stochastic Riccati equation; Malliavin calculus; density estimate},
language = {eng},
number = {5},
pages = {515-526},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Gaussian density estimates for the solution of singular stochastic Riccati equations},
url = {http://eudml.org/doc/286819},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Nguyen, Tien Dung
TI - Gaussian density estimates for the solution of singular stochastic Riccati equations
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 5
SP - 515
EP - 526
AB - 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.
LA - eng
KW - stochastic Riccati equation; Malliavin calculus; density estimate; stochastic Riccati equation; Malliavin calculus; density estimate
UR - http://eudml.org/doc/286819
ER -

References

top
  1. Aboura, O., Bourguin, S., 10.1007/s11118-012-9287-8, Potential Anal. 38 (2013), 573-587. (2013) Zbl1273.60066MR3015365DOI10.1007/s11118-012-9287-8
  2. Antonelli, F., Kohatsu-Higa, A., 10.1007/s11118-004-1324-9, Potential Anal. 22 (2005), 263-287. (2005) Zbl1082.60047MR2134722DOI10.1007/s11118-004-1324-9
  3. Cvitani{ć}, J., Zhang, J., Contract Theory in Continuous-Time Models, Springer Finance Springer, Heidelberg (2013). (2013) Zbl1319.91007MR2963805
  4. Reis, G. Dos, On Some Properties of Solutions of Quadratic Growth BSDE and Applications in Finance and Insurance, PhD thesis, Humboldt University in Berlin (2010). (2010) 
  5. Kazamaki, N., Continuous Exponential Martingales and BMO, Lecture Notes in Mathematics 1579 Springer, Berlin (1994). (1994) Zbl0806.60033MR1299529
  6. Lim, A. E. B., Zhou, X. Y., 10.1287/moor.27.1.101.337, Math. Oper. Res. 27 (2002), 101-120. (2002) Zbl1082.91521MR1886222DOI10.1287/moor.27.1.101.337
  7. Mastrolia, T., Possamaï, D., Réveillac, A., 10.1214/15-AOP1035, Ann. Probab. 44 (2016), 2817-2857. (2016) MR3531681DOI10.1214/15-AOP1035
  8. Nguyen, T. D., Privault, N., Torrisi, G. L., 10.1007/s11118-015-9472-7, Potential Anal. 43 (2015), 289-311. (2015) Zbl1321.60127MR3374113DOI10.1007/s11118-015-9472-7
  9. Nourdin, I., Viens, F. G., 10.1214/EJP.v14-707, Electron. J. Probab. 14 (2009), 2287-2309. (2009) Zbl1192.60066MR2556018DOI10.1214/EJP.v14-707
  10. Nualart, D., The Malliavin Calculus and Related Topics, Probability and Its Applications Springer, Berlin (2006). (2006) Zbl1099.60003MR2200233
  11. Privault, N., Stochastic Analysis in Discrete and Continuous Settings with Normal Martingales, Lecture Notes in Mathematics 1982 Springer, Berlin (2009). (2009) Zbl1185.60005MR2531026
  12. Shen, Y., 10.1016/j.automatica.2015.03.009, Automatica J. IFAC 55 (2015), 165-175. (2015) MR3336665DOI10.1016/j.automatica.2015.03.009
  13. Yu, Z., 10.1007/s00245-013-9209-1, Appl. Math. Optim. 68 (2013), 333-359. (2013) Zbl1288.91181MR3131499DOI10.1007/s00245-013-9209-1

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.