OFFSET
0,1
COMMENTS
1) Closed-form expressions for sequences see Pfeifer (2010).
2) The median taken on partial sums of the simple random walk represents the market price in a simulation model wherein a single security among non-cooperating and asymetrically informed traders is traded (Pfeifer et al. 2009).
REFERENCES
Pfeifer, C. (2010) Probability distribution of the median taken on partial sums of the simple random walk, Submitted to Stochastic Analysis and Applications
LINKS
C. Pfeifer, K. Schredelseker, G. U. H. Seeber, On the negative value of information in informationally inefficient markets. Calculations for large number of traders, Eur. J. Operat. Res., 195 (1) (2009) 117-126.
EXAMPLE
All possible different paths (sequences of partial sums) in case of n=3:
{0,-1,-2,-3}; median=-1.5
{0,-1,-2,-1}; median=-1
{0,-1,0,-1}; median=-0.5
{0,-1,0,1}; median=0
{0,1,0,-1}; median=0
{0,1,0,1}; median=0.5
{0,1,2,1}; median=1
{0,1,2,3}; median=1.5
sequence of integers in case of n=3: 1,1,1,1
CROSSREFS
KEYWORD
fini,nonn
AUTHOR
Christian Pfeifer (christian.pfeifer(AT)uibk.ac.at), Oct 28 2008, May 04 2010
STATUS
approved