Stochastic Process
                 Brownian motion and the heat equation
            An introduction to elementary stochastic calculus
               MATH4210 - Financial Mathematics
                                       MATH4210 - Financial Mathematics
                                                       Stochastic Process        Motivation
                                   Brownian motion and the heat equation         Basic probability theory, recalling
                          An introduction to elementary stochastic calculus      Brownian motion
      Samples of Stock Price
            Stock price of Cheung Kong from 2006 to 2011
                                           scource: http://hk.finance.yahoo.com/
                                                                                 MATH4210 - Financial Mathematics
                                                       Stochastic Process        Motivation
                                   Brownian motion and the heat equation         Basic probability theory, recalling
                          An introduction to elementary stochastic calculus      Brownian motion
      Samples of Stock Price
            Stock price of Hong Kong Electric from 2006 to 2011
                                           scource: http://hk.finance.yahoo.com/
                                                                                 MATH4210 - Financial Mathematics
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          drift
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Wesee fluctuation of the stock price.                                                                      volatility
                                                       Stochastic Process        Motivation
                                   Brownian motion and the heat equation         Basic probability theory, recalling
                          An introduction to elementary stochastic calculus      Brownian motion
      Model of Stock Price
            Key observation
                     Stock price has a trend.
                                                                                 MATH4210 - Financial Mathematics