Stochastic Portfolio Theory
In this chapter we introduce the basic definitions for stocks and portfolios, and prove preliminary results that are used throughout the later chapters. The mathematical definitions and notation that we use can be found in Karatzas and Shreve (1991), and the model for continuous stock prices can be found in, e.g., Karatzas (1997), Karatzas and Shreve (1998), and Duffle (1992). The definitions, notation, and stock price model are all fairly standard in current mathematical finance, and we make a number of fairly standard assumptions to simplify the presentation.
KeywordsPortfolio Optimization Local Martingale Market Portfolio Short Sale Logarithmic Model
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