TAILIEUCHUNG - Statistical Tools in Finance and Insurance

Stable laws { also called -stable or Levy-stable { are a rich family of probability distributions that allow skewness and heavy tails and have many interesting mathematical properties. They appear in the context of the Generalized Central Limit Theorem which states that the only possible non-trivial limit of normalized sums of independent identically distributed variables is -stable. The Standard Central Limit Theorem states that the limit of normalized sums of independent identically distributed terms with nite variance is Gaussian ( -stable with = 2). It is often argued that nancial asset returns are the cumulative outcome of a vast number of pieces of information and individual decisions arriving almost continuously. | 1 Statistical Tools in Finance and nsurance Pavel Cizek Wolfgang Hardle Rafal Weron November 25 2003 2 Contents I Finance 9 1 Stable distributions in finance 11 Szymon Borak Wolfgang Hardle Rafal Weron Introduction. 11 o-stable distributions. 12 Characteristic function representation. 14 Simulation of o-stable variables. 16 Tail behavior. 18 Estimation of parameters . 18 Tail exponent estimation . 19 Sample Quantiles Methods . 22 Sample Characteristic Function Methods . 23 Financial applications of o-stable laws. 26 2 Tail dependence 33 Rafael Schmidt Tail dependence and copulae . 33 Calculating the tail-dependence coefficient. .

• Ngân hàng - Tín dụng
• Stable distributions
• Tail dependence
• Trinomial Trees
• Functional data analysis
• Nonparametric Productivity Analysis
• Money Demand Modelling
• Chinas stock markets
• Stochastic volatility
• Stable Lorentz distribution
• Transition probability distribution
• Distributions of stock returns