交通大學、清華大學 統計學研究所 專題演講 題　目：Risk Patterns and Correlated Brain Activities 主講人：Prof. Wolfgang Karl Hardle (Humboldt-Universit?t zu Berlin, Germany) 時　間：99年2月26日(星期五)上午10:10-11:00 (上午9:50-10:10茶會於交大統計所429室舉行) 地　點：交大綜合一館427室 Abstract Many decisions people make can be described as decisions under risk. Understanding which part of our brain is activated during risky decisions and whether there is a significant reaction to specific stimuli in the hemodynamic response (neural processes underlying investment decisions) are important goals in decision neuroscience. Functional magnetic resonance imaging (fMRI) is a noninvasive technique of recording brain signals on spatial area in every particular time period. Here we used a novel investment decision task that uses streams of (past) returns as stimuli to the exercised subjects and obtain a series of three-dimensional images of the blood-oxygen-level-dependent (BOLD) fMRI signals. The challenge here is to get a grip on the dynamic behavior of this high-dimensional fMRI time series, by a factor approach resulting in a low dimensional representation. We considered the dynamic semiparametric factor model (DSFM) given in Park et al. (2009). DSFM helps identify the corresponding brain's activation areas. Additionally we classify the risk attitudes of different subjects based on the recovered low-dimensional time series, which performed quite well compared to the classic risky decision making model (risk - return model) which is based on the subjects' answers directly. 敬 請 公 佈 歡 迎 參 加 交通大學、清華大學 統計學研究所 專題演講 題　目：Uniform Confidence Band for Empirical Pricing Kernels 主講人：Ms. Weining Wang (Humboldt-Universit?t zu Berlin, Germany) 時　間：99年2月26日(星期五)上午11:10-12:00 (上午9:50-10:10茶會於交大統計所429室舉行) 地　點：交大綜合一館427室 Abstract The pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The former density can be represented as the second derivative of the option price, which we estimate by a nonparametric regression. The subjective density is estimated nonparametrically too. In this framework we develop the asymptotic distribution theory of the EPK. Particularly, to evaluate the overall variation of the pricing kernel we develop a uniform confidence band of EPK by a strong approximation of the empirical process. Furthermore, as an alternative to the asymptotic approach we study the bootstrap confidence bands. The developed theory is helpful for testing parametric specifications of pricing kernels and has a direct extension to the estimated risk aversion. The established results are assessed and compared in a Monte-Carlo study. 敬 請 公 佈 歡 迎 參 加 --

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