scholarly journals Maximizing the pth moment of the exit time of planar brownian motion from a given domain

2020 ◽  
Vol 57 (4) ◽  
pp. 1135-1149
Author(s):  
Maher Boudabra ◽  
Greg Markowsky
Keyword(s):  
Brownian Motion ◽  
Conformal Invariance ◽  
Exit Time ◽  
Small Region ◽  
Geometrical Method ◽  
Planar Brownian Motion

AbstractIn this paper we address the question of finding the point which maximizes the pth moment of the exit time of planar Brownian motion from a given domain. We present a geometrical method for excluding parts of the domain from consideration which makes use of a coupling argument and the conformal invariance of Brownian motion. In many cases the maximizing point can be localized to a relatively small region. Several illustrative examples are presented.

scholarly journals Windings of planar processes, exponential functionals and Asian options

2018 ◽  
Vol 50 (3) ◽  
pp. 726-742 ◽  
Author(s):  
Wissem Jedidi ◽  
Stavros Vakeroudis
Keyword(s):  
Brownian Motion ◽  
Exit Time ◽  
Random Variable ◽  
Infinite Divisibility ◽  
Mathematical Finance ◽  
Asian Options ◽  
Product Representation ◽  
Exponential Functional ◽  
Planar Brownian Motion ◽  
Divisibility Properties

Abstract Motivated by a common mathematical finance topic, we discuss the reciprocal of the exit time from a cone of planar Brownian motion which also corresponds to the exponential functional of Brownian motion in the framework of planar Brownian motion. We prove a conjecture of Vakeroudis and Yor (2012) concerning infinite divisibility properties of this random variable and present a novel simple proof of the result of DeBlassie (1987), (1988) concerning the asymptotic behavior of the distribution of the Bessel clock appearing in the skew-product representation of planar Brownian motion, as t→∞. We use the results of the windings approach in order to obtain results for quantities associated to the pricing of Asian options.

scholarly journals The First Exit Time of Planar Brownian Motion from The Interior Of a Parabola

2001 ◽  
Vol 29 (2) ◽  
pp. 882-901 ◽  
Author(s):  
Rodrigo Bañuelos ◽  
R. Dante DeBlassie ◽  
Robert Smits
Keyword(s):  
Brownian Motion ◽  
Exit Time ◽  
First Exit Time ◽  
Planar Brownian Motion

scholarly journals Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Satya N. Majumdar ◽  
Francesco Mori ◽  
Hendrik Schawe ◽  
Grégory Schehr
Keyword(s):  
Brownian Motion ◽  
Convex Hull ◽  
Planar Brownian Motion
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