Stochastic Exponential Growth and Lattice Gases Statistical Mechanics of Stochastic Compounding Processes【電子書籍】[ Dan Pirjol ]

＜p＞The book discusses a class of discrete time stochastic growth processes for which the growth rate is proportional to the exponential of a Gaussian Markov process. These growth processes appear naturally in problems of mathematical finance as discrete time approximations of stochastic volatility models and stochastic interest rates models such as the Black-Derman-Toy and Black-Karasinski models. These processes can be mapped to interacting one-dimensional lattice gases with long-range interactions.＜/p＞ ＜p＞The book gives a detailed discussion of these statistical mechanics models, including new results not available in the literature, and their implication for the stochastic growth models. The statistical mechanics analogy is used to understand observed non-analytic dependence of the Lyapunov exponents of the stochastic growth processes considered, which is related to phase transitions in the lattice gas system. The theoretical results are applied to simulations of financial models an．．．楽天市場のショップで商品詳細の続きを見る