This dissertation reports work where physics methods are applied to financial
and economical problems. The first part studies stock market data (chapter 1 to
5). The second part is devoted to personal income in the USA (chapter 6).
We first study the probability distribution of stock returns at mesoscopic
time lags (return horizons) ranging from about an hour to about a month. For
mesoscopic times the bulk of the distribution (more than 99% of the
probability) follows an exponential law. At longer times, the exponential law
continuously evolves into Gaussian distribution.
After characterizing the stock returns at mesoscopic time lags, we study the
subordination hypothesis. The integrated volatility V_t constructed from the
number of trades process can be used as a subordinator for a Brownian motion.
This subordination is able to describe approximatly 85% of the stock returns
for time lags that start at 1 hour but are shorter than one day. Finally, we
show that the CIR process describes well enough the empirical V_t process, such
that the corresponding Heston model is able to describe the log-returns x_t
process, with approximately the maximum quality that the subordination allows.
Finally, we study the time evolution of the personal income distribution. We
find that the personal income distribution in the USA has a well-defined
two-income-class structure. The majority of population (97-99%) belongs to the
lower income class characterized by the exponential Boltzmann-Gibb(``thermal'')
distribution, whereas the higher income class (1-3% of population) has a Pareto
power-law (``superthermal'') distribution. We show that the ``thermal'' part is
stationary in time.Comment: 24 pages and 45 figures. PhD thesis presented to the committee
members on May 10th 2005. This thesis is based on 3 published papers with one
chapter (chapter 5) with new unpublished result
