We consider the problem of maximizing expected power utility from consumption
over an infinite horizon in the Black-Scholes model with proportional
transaction costs, as studied in Shreve and Soner [Ann. Appl. Probab. 4 (1994)
609-692]. Similar to Kallsen and Muhle-Karbe [Ann. Appl. Probab. 20 (2010)
1341-1358], we derive a shadow price, that is, a frictionless price process
with values in the bid-ask spread which leads to the same optimal policy.Comment: Published at http://dx.doi.org/10.1214/14-AAP1058 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Tanaka equation $dX_t={\operatorname{sign}}(X_t)\,dB_t$ is an example of
a stochastic differential equation (SDE) without strong solution. Hence
pathwise uniqueness does not hold for this equation. In this note we prove that
if we modify the right-hand side of the equation, roughly speaking, with a
strong enough additive noise, independent of the Brownian motion B, then the
solution of the obtained equation is pathwise unique.Comment: Published in at http://dx.doi.org/10.1214/11-AOP716 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Please cite this article as: Prokaj, V., Unfolding the Skorohod reflection of a semimartingale. Statistics and Probability Letters (2008Letters ( ), doi:10.1016Letters ( /j.spl.2008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT
Unfolding the Skorohod reflection of a semimartingaleVilmos Prokaj a,b , a Department of Probability Theory and Statistics, Eötvös Loránd University, 1117 Budapest, Pázmány P. sétány 1/C, Hungary b Computer and Automation Institute of the Hungarian Academy of Sciences, 1111Budapest, Kende utca 13-17, Hungary
AbstractIt is well-known that the Skorohod reflection of a Wiener-process is the absolute value of another Wiener process with finer filtration. In other words it can be unfolded to obtain a Wiener process. In this short note a similar statement is proved for continuous semimartingales.
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