148
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Comparison of solutions of stochastic equations and applications

&
Pages 211-229 | Published online: 03 Apr 2007

References

  • Bassan , B. , Çinlar , E. and Scarsini , M. 1993 . Stochastic comparisons of Itô Processes . Stochastic Processes Appl , 45 ( 1 ) : 1 – 11 .
  • Cox , J.T. , Fleischmann , K. and Greven , A. 1996 . Comparision of interacting diffusions and an application to their ergodic theory . Probab. Theory Related Fields , 105 ( 4 ) : 513 – 528 .
  • Day , M.V. 1983 . Comparison results for diffusions conditioned on positivity . J. Appl. Probab , 20 ( 4 ) : 766 – 777 .
  • Ferreyra G. Sundar P. Pathwise Comparison of Arithmetric Brownian Motions and Log-normal Processes Birkhauser, Boston 1999 541 546 Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming in Systems h Control: Foundations & Applications series
  • Galčhuk , L.I. 1982 . A comparison theorem for stochastic equations with integrals with respect to martingales and random measures . Teor. Veroyatnost. i Primenen , 27 ( 3 ) : 425 – 433 .
  • Galčhuk , L.I. 1981 . A note on a comparison theorem for equations with different diffusions . Stochastics , 6 ( 2 ) : 147 – 149 . 1982
  • Geiβ C. Manthey R. Comparison results for stochastic differential equations Stochastic processes and optimal control (Friedrichroda, 1992) Gordon and Breach Montreux 1993 73 81 Stochastics Monographs 7
  • Hajek , B. 1985 . Mean stochastic comparison of diffusions . Z. Wahrsch. Verw. Gebiete , 68 ( 3 ) : 315 – 329 .
  • Haugen , R. 1997 . Modern investment theory , New Jersey : Prentice Hall .
  • Heston S. A closed-form solution for options with a stochastic volatility, with Applications to bond and currency options Review of Financial Studies 1993
  • Hilliard J. Schwartz A. Binomial option pricing under stochastic volatility and correlated state variables preprint June 1998
  • Huang , Z.Y. 1984 . A comparison theorem for solutions of stochastic differential equations and its applications . Proc. Amer. Math. Soc , 91 ( 4 ) : 611 – 617 .
  • Hull , J. and White , A. 1987 . The pricing of options on assets with stochastic volatilities . J. of Finance , 42 ( 4 ) : 281 – 300 .
  • Hull , J. and White , A. 1988 . Analysis of the bias in option pricing caused by stochastic volatility . Advances in Futures and Options Research , 3 ( 4 ) : 29 – 61 .
  • Johnson , H. and Shanno , D. 1987 . Option pricing when variance is changing . J. of Financial and Quantitative Analysis , 22 ( 2 ) : 143 – 151 .
  • Karatzas , I. and Shreve , S. 1991 . “ Brownian Motion and Stochastic Calculus ” . In Graduate Texts in Math , Vol. 113 , New York : Springer-Verlag .
  • Kleptsyna , M.L. 1985 . Comparison, existence and uniqueness theorems for stochastic differential equations . Teor. Veroyatnost. i Prime-nen , 30 ( 1 ) : 147 – 152 .
  • Kloeden , P. and Platen , E. 1992 . Numerical solution of stochastic differential equations , New York : Springer-Verlag .
  • Mao , X. 1991 . A note on comparison theorems for stochastic differential equations with respect to semimartingales . Stochastics Stochastics Rep , 37 ( 1-2 ) : 49 – 59 .
  • Nakao , S. 1983 . On pathwise uniqueness and comparison of solutions of one-dimensional stochastic differential equations . Osaka J. Math , 20 ( 1 ) : 197 – 204 .
  • Obrien , G.L. 1980 . A new comparison theorem for solutions of stochastic differential equations . Stochastics , 3 ( 4 ) : 245 – 249 .
  • Ouknine Y. Sur la comparaison des solutions d’équations différentielles stochastiques (French) (On the comparison of solutions of stochastic differential equations) 1987 304,6 155 157 C. R. Acad. Sci. Paris Ser. I Math.
  • Sharpe , W. 1964 . Capital asset prices: a theory of market equilibrium under conditions of risk . J. of Finance , 19 ( 4 ) : 425 – 442 .
  • Stein , E. and Stein , J. 1991 . Stock price distributions with stochastic volatility an analytic approach . Review of Financial Studies , 4 ( 4 ) : 727 – 752 .
  • Takeuchi K. Comparison theorems for solutions of stochastic differential equations 1981 35,1 174 184 Mem. Fac. Sci. Kyushu Univ.Ser. A
  • Yamada , T. and Ogura , Y. 1981 . On the strong comparison theorems for solutions of stochastic differential equations . Z. Wahrsch. Verw. Gebiete , 56 ( 1 ) : 3 – 19 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.