  In this paper, we propose a modified Levy jump diffusion model with market
sentiment memory for stock prices, where the market sentiment comes from data
mining implementation using Tweets on Twitter. We take the market sentiment
process, which has memory, as the signal of Levy jumps in the stock price. An
online learning and optimization algorithm with the Unscented Kalman filter
(UKF) is then proposed to learn the memory and to predict possible price jumps.
Experiments show that the algorithm provides a relatively good performance in
identifying asset return trends.
