The thesis describes an extension of O. Schramm's SLE processes to complicated plane domains and Riemann surfaces. First, three kinds of new SLEs are defined for simple conformal types. They have properties similar to traditional SLEs. Then harmonic random Loewner chains (HRLC) are defined in finite Riemann surfaces. They are measures on the space of Loewner chains, which are increasing families of closed subsets satisfying certain properties. An HRLC is first defined on local charts using Loewner's equation. Since the definitions in different charts agree with each other, these local HRLCs can be put together to construct a global HRLC. An HRLC in a plane domain can be described by differential equations involving canonical plane domains. Those old and new SLEs are special cases of HRLCs. An HRLC is determined by a parameter [kappa] >= 0, a starting point and a target set. When [kappa] = 6, the HRLC satisfies the locality property.
Households can allocate their savings in many ways. Not only are there several broad asset classes, but within any one class there is often a huge variety of choices. With so many alternatives to choose from, it is not surprising that some households have difficulty choosing a portfolio. Evidence of these difficulties takes several forms. Researchers have looked at micro-level data on household portfolios and found that some households allocate savings in ways that are hard to rationalize with standard economic models. For example, households may not allocate any savings to equities or they may hold under-diversified portfolios (for examples see Haliassos and Bertaut [1995] and Calvet, Campbell and Sodini [2007]). Surveys of financial literacy have also found that many households do not understand some fundamental financial concepts such as the difference between bonds and stocks (van Rooij, Lusardi and Alessie [2007]).
The current financial and economic crisis has quickly spread from the housing and credit markets in the United States resulting in the worst global recession since World War II. As a consequence of the downturn, millions of workers have been laid off, while for those lucky enough to hold on to their jobs, many have experienced cuts in hours worked, wages and others benefits as enterprises seek to reduce labour costs in order to remain afloat.
Although there is some evidence that the global economy has reached a trough, history shows that synchronized and global crises, like the current one, result in recessions that are more severe and longer in duration (IMF 2009). The ongoing destruction of jobs and increased duration of joblessness will ensure that unemployment rates across the world will continue to rise and stay stubbornly high for some time to come, well after the economy has begun to recover.
