Mathematics for Finance

This course introduces the mathematical foundations of modern financial systems with emphasis on structure, abstraction, and rigor. Rather than providing recipes or rules, these notes develop the theoretical framework needed to understand how financial markets operate, how to quantify and manage risk, and how to value assets under uncertainty.

Instructor: Sukrit Mittal

Code: MA8.402

Semester: Spring 2026

Location: H201, Himalayan Block, IIIT Hyderabad

Part I: Foundations

• Overview of financial systems: Introduction to mathematical finance and the structure of financial systems
• Simple market model: Basic modeling frameworks for financial markets
• Time value of money: Present and future value concepts, discounting, and time-based calculations
• Money market: Money market instruments, mechanics, and short-term interest rates

Practical problems and case studies can be found in the Problem Sets.

Part II: Portfolio Theory

• Introduction to portfolios: Portfolio theory fundamentals and two securities
• Risk-free assets and preferences: Risk-free assets and preferences in portfolio optimization
• Multi-asset portfolios: Portfolio optimization with multiple assets and constraints
• CAPM model: Capital Asset Pricing Model, systematic vs. idiosyncratic risk