On the tail distributions of the supremum and the quadratic variation of a càdlàg local martingale

2008 ◽  
pp. 401-420
Author(s):  
Shunsuke Kaji
Keyword(s):  
Quadratic Variation ◽  
Local Martingale ◽  
Tail Distributions

scholarly journals Strong approximation of continuous local martingales by simple random walks

2004 ◽  
Vol 41 (1) ◽  
pp. 101-126
Author(s):  
B. Székely ◽  
T. Szabados
Keyword(s):  
Brownian Motion ◽  
Random Walks ◽  
Rates Of Convergence ◽  
Quadratic Variation ◽  
Local Martingale ◽  
Motion Time ◽  
Time Changes ◽  
Necessary And Sufficient ◽  
Nested Sequence ◽  
The Given

The aim of this paper is to represent any continuous local martingale as an almost sure limit of a nested sequence of simple, symmetric random walk, time changed by a discrete quadratic variation process. One basis of this is a similar construction of Brownian motion. The other major tool is a representation of continuous local martingales given by Dambis, Dubins and Schwarz (DDS) in terms of Brownian motion time-changed by the quadratic variation. Rates of convergence (which are conjectured to be nearly optimal in the given setting) are also supplied. A necessary and sufficient condition for the independence of the random walks and the discrete time changes or equivalently, for the independence of the DDS Brownian motion and the quadratic variation is proved to be the symmetry of increments of the martingale given the past, which is a reformulation of an earlier result by Ocone [8].

scholarly journals Local martingale and pathwise solutions for an abstract fluids model

2011 ◽  
Vol 240 (14-15) ◽  
pp. 1123-1144 ◽  
Author(s):  
Arnaud Debussche ◽  
Nathan Glatt-Holtz ◽  
Roger Temam
Keyword(s):  
Local Martingale ◽  
Pathwise Solutions

Comparison Between the Mean-Variance Optimal and the Mean-Quadratic-Variation Optimal Trading Strategies

2013 ◽  
Vol 20 (5) ◽  
pp. 415-449 ◽  
Author(s):  
S. T. Tse ◽  
P. A. Forsyth ◽  
J. S. Kennedy ◽  
H. Windcliff
Keyword(s):  
Quadratic Variation ◽  
Trading Strategies ◽  
Optimal Trading ◽  
The Mean ◽  
Mean Variance

scholarly journals Estimating quadratic variation using realized variance

2002 ◽  
Vol 17 (5) ◽  
pp. 457-477 ◽  
Author(s):  
Ole E. Barndorff-Nielsen ◽  
Neil Shephard
Keyword(s):  
Quadratic Variation ◽  
Realized Variance
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