Geodesic
Optimal stopping for absolute maximum of homogeneous diffusion
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2015), pp. 7-13 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article deals with the optimal stopping problem in case when the reward function depends on the absolute maximum of some homogeneous diffusion. We consider cases of infinite and finite time horizon. In both cases the differential equation for the optimal stopping boundary is obtained. Also, we prove that the maximality principle holds for reward functions which satisfy single-crossing condition. 
@article{VMUMM_2015_5_a1,
     author = {A. A. Kamenov},
     title = {Optimal stopping for absolute maximum of homogeneous diffusion},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {7--13},
     year = {2015},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_5_a1/}
}
TY  - JOUR
AU  - A. A. Kamenov
TI  - Optimal stopping for absolute maximum of homogeneous diffusion
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2015
SP  - 7
EP  - 13
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2015_5_a1/
LA  - ru
ID  - VMUMM_2015_5_a1
ER  - 
%0 Journal Article
%A A. A. Kamenov
%T Optimal stopping for absolute maximum of homogeneous diffusion
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2015
%P 7-13
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_2015_5_a1/
%G ru
%F VMUMM_2015_5_a1
A. A. Kamenov. Optimal stopping for absolute maximum of homogeneous diffusion. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2015), pp. 7-13. http://geodesic.mathdoc.fr/item/VMUMM_2015_5_a1/

[1] Shiryaev A., Xu Z., Zhou X. Y., “Thou shalt buy and hold”, Quant. Finance, 8:8 (2008), 765–776 | DOI | MR | Zbl

[2] du Toit J., Peskir G., “Selling a stock at the ultimate maximum”, Ann. Appl. Probab., 19:3 (2009), 983–1014 | DOI | MR | Zbl

[3] Dai M., Jin H., Zhong Y. et al., “Buy low and sell high”, Contemp. Quant. Finance, 2010, no. 1, 317–333 | DOI | MR | Zbl

[4] Graversen S. E., Peskir G., Shiryaev A. N., “Stopping Brownian motion without anticipation as close as possible to its ultimate maximum”, Theory Probab. and Its Appl., 45:1 (2001), 41–50 | DOI | MR

[5] du Toit J., Peskir G., “The trap of complacency in predicting the maximum”, Ann. Probab., 35:1 (2007), 340–365 | DOI | MR | Zbl

[6] Pedersen J. L., “Optimal prediction of the ultimate maximum of Brownian motion”, Stochastics and Stochast. Repts., 75:4 (2003), 205–219 | DOI | MR | Zbl

[7] Peskir G., “Optimal stopping of the maximum process: the maximality principle”, Ann. Probab., 26:4 (1998), 1614–1640 | DOI | MR | Zbl

[8] Milgrom P., Segal I., “Envelope theorems for arbitrary choice sets”, Econometrica, 70:2 (2002), 583–601 | DOI | MR | Zbl