## Coursepage of Stochastic Calculus, An Introduction with Application

### Updates

Homework 5 is now available.
### Important

Due to COVID-19, this class will be taught entirely online. All the information can be found on this webpage. Please check it regularly for updates on course/homework, etc.
**Students are REQUIRED to take contact by email directly with me AS SOON AS THEY SEE THIS WEBPAGE, and STRONGLY ADVISED to set up video call whenever necessary.** Although not giving lectures, I am fully (remotely)
available.
### Information

#### Location: Room 347B Mita campus

#### Time slot: Thursday 1:00pm-2:30pm (3rd period)

#### Semester: Spring 2020

### Description of the class

The course starts with a quick introduction to conditional expectation. Then, normal distribution, multivariate normal distribution and
Brownian motion are defined and discussed carefully. Exercises and homework are based on a setup of high-frequency financial data estimation problems.
This includes providing some basic tools of asymptotic statistics on the way.

### Prerequisites

Students must be familiar with Statistics I and II taught at Hiyoshi or the basics of probability theory (distribution, expectation, variance, Strong Law of Large Numbers, Central Limit Theorem).

### Evaluation

The evaluation will be based on five homeworks (each counting for 20% of the final grade).

### Class material

The class often follows the textbook Stochastic Calculus: An Introduction with Applications (from Gregory Lawler) book content (Ch 1-2). You can find
notes. Also, you can check
Wikipedia page on normal distribution.

### Calendar

- 2020/05/21 Homework 1 deadline
- 2020/06/04 Homework 2 deadline
- 2020/06/18 Homework 3 deadline
- 2020/07/09 Homework 4 deadline
- 2020/07/23 Homework 5 deadline

### Homework

Homework should be sent by email to me (with Object: [S2020Hi] LAST_NAME FIRST_NAME), where i is the homework index, after being converted to PDF format (with the format LastNameFirstName.pdf in Romaji/English) and not handwritten. Latex will be very appreciated, but not required. Any other typing language such as Word would work too.
You can use Sharelatex where you can code directly online (and even share it with a friend).
Also, you will have information for documentation and/or installing Latex at
The Latex Project. Graded homework will be sent back by email to students, so that they can learn from their mistakes. As much as possible, I will also provide
a detailed individual feedback in the email.

- Homework 1: read Introductory comments of textbook and Section 1.1. Do Exercise 1.1, Exercise 1.2, Exercise 1.3 and Exercise 1.4 (pp. 27-28)
Make sure you have the right book by checking the pages, and that the chapter is about conditional expectation. For your information, first two exercises should be related to dices.
- Homework 2: read the notes and Wikipedia page on Normal distribution (not everything in details, focus on moments and statistical part).
Do Homework 2.
- Homework 3: read Section 2.2 (pp. 36-39) on multivariate normal distribution. Do Exercise 2.1 (p. 75)
- Homework 4: read Section 2.4, Section 2.6 and Section 2.7. Do Exercise 2.2, Exercise 2.4, Exercise 2.6
- Homework 5: Do Homework 5.