110年第1學期-1594 保險數學 課程資訊

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評分方式

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

選課分析

本課程名額為 70人,已有135 人選讀,尚餘名額-65人。

授課教師

陳志賢

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

課程資訊

參考書目

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