110年第1學期-1594 保險數學 課程資訊

評分方式

評分項目	配分比例	說明
quiz 1	20
midterm	30
quiz 2	20
final	30

教育目標

課程主要目標是簡介隨機過程基本概念、理論及其應用。

課程概述

The objective of this course is to introduce basic concepts for stochastic processes. The main focus will be on studying analytical models for systems which change states stochastically with time. This is a course for studying probabilistic models rather than statistical models. Thus, background on probability and mathematical statistics are necessary. We will begin right after �onditional probability�and �onditional expectation� Students will learn concepts and techniques for characterizing models stochastically. This will help students for further study. The topics of this course include basic processes, stochastic models, and diffusion processes. Contents of this course might be adjusted according to time limitation and students�interests. They are: 1.Preliminaries: lack of memory property, transformations, inequalities, limit theorems, notations of stochastic processes 2.Markov chains: Chapman-Kolmogorov equation, classification of chains, long run behavior of Markov chains, branch processes, random walk 3.Poisson processes: Inter-arrival time distributions, conditional waiting time distributions, non-homogeneous Poisson processes 4.Continuous-time Markov chains: birth-death processes, compound Poisson processes, finite-state Markov chains 5.Renewal processes: renewal functions, limit theorems, delayed and stationary renewal processes, queueing 6.Stochastic models: Markov renewal processes, marked processes 7.Martingales: conditional expectations, filtrations, stopping time, martingale CLT 8.Diffusion Processes: Brownian motions, It�s formula, Black-Scholes Model, Girsanov Theorem

基本資料

選修課，學分數：3-0
上課時間：三/10,11,12[M155]
修課班級：統計系2-4
修課年級：年級以上
選課備註：管理群組(106-110適用)

參考書目

Shunji Osaki: Applied Stochastic System Modeling
Sheldon M. Ross: Introduction to Probability Models