Optional : Indonesia
After taking this subject students are expected to understand and apply the concept in probability theory and stochastic processes in finance theory. These concepts include a change of measure (theorem Girsanov), the reflection principle, random walks, Brownian motion, Markov chains, Poisson processes, martingales, risk-neutral method, self-financing portfolio, no-arbitrage opportunity, forward-neutral method. The course material will present the theory of stochastic processes and its use in financial theory. The emphasis on this course lies in the use of a simple discrete stochastic process as a means to explain the idea of other stochastic processes. Discrete stochastic process is intuitively easier to understand than the continuous stochastic process. As an illustration, a continuous stochastic process called Brownian motion can be regarded as the limit of the discrete stochastic process called random walks. In this case the discrete stochastic process can be viewed as an approximation of a continuous stochastic process. The results are important from a discrete stochastic process will be transferred to the results in continuous stochastic processes. Such approach allows the course material can be presented to the college participants with background knowledge of mathematics is not too high.