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Graduate Seminar2006-2007 Schedule2005-2006 Schedule - 2004-2005 Schedule - Spring 04 Schedule - Fall 2003 Schedule
AbstractsHung-Ching (Justin) Chen - NN-OPT: Neural Network for Option Pricing Using Multinomial Tree Abstract: We provide a framework for learning to price complex options by learning risk-neutral measures (Martingale measures).In a simple geometric Brownian motion model, the price volatility, fixed interest rate and a no-arbitrage condition suffice to determine a unique risk-neutral measure. On the other hand, in our framework, we relax some of these assumptions to obtain a class of allowable risk-neutral measures. We then propose a framework for learning the appropriate risk-neural measure. In particular, we provide an efficient algorithm for backpropagating gradients through multinomial pricing trees. Since the risk-neutral measure prices all options simultaneously, we can use all the option contracts on a particular stock for learning. Finally, We demonstrate the performance of these models on historical data. Specially, we show that both learning without a no-arbitrage condition and a no-arbitrage condition without learning are worse than our framework; however the combination of learning with a no-arbitrage condition has the best result. These results indicate the potential to learn Martingale measures with a no-arbitrage condition providing just the right constraint. Abstract: Mapping --- construction of an environment model from sensory information --- is a fundamental capability for any autonomous mobile robot. Most mapping research employs high-fidelity sensors such as scanning laser rangefinders. These sensors provide accurate and dense information about the world but consume significant computational and energy resources, and typically cost several thousand US dollars. Our research aims to instead develop mapping algorithms for inexpensive sensors such as small arrays of infrared rangefinders. We have addressed a number of practical challenges, from simply collecting enough data to observe useful environment features, to performing consistent map and trajectory estimation under large uncertainty, to exploiting prior knowledge about the environment when it is available. We have also analytically characterized the relationship between sensing capabilities and map quality and determined, under reasonable assumptions, conditions for map convergence and bounds on map error in terms of the sensor used for mapping. In this talk I will introduce the basic robot mapping problem, give an overview of our research on mapping with limited sensing, and discuss in some detail our convergence and error bound results. |
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