Financial Mathematics is a field of applied mathematics that involves defining problems in finance and providing elegant solutions using methods that draw from probability theory, partial differential equations, optimization, and numerical methods.
The primary emphasis in financial mathematics is the derivation of the mathematical models that confirm the intuition from financial economics. For example, the seminal case of the Black-Scholes-Merton model, and its many extensions, such as stochastic volatility, pure jump processes, and collateral funding, is built around the no-arbitrage assumption and assumes as given the evolution of the stock price in order to find the prices of derivative securities.
Primary Areas of Research
Hopkins Engineering faculty research in financial mathematics focuses primarily in the following areas:
Extending and proposing new models with realistic and desirable financial properties and then employing various tools from stochastic calculus to PDEs and Monte-Carlo methods to find ‘no-arbitrage’ prices of derivatives. Many problems are still open in the case of incomplete markets.
Studies of the markets of oil, metals, agriculture, and electricity, from extraction or production through delivery and usage – the so-called ‘supply chain’ and its financing issues.
Risk management focuses on quantifying various risks that financial players are subject to and defines ways to mitigate and reduce them. Examples include credit risk and systemic risk.
This area focuses on understanding and solving investors’ fundamental problem of wealth maximization in various settings, and then deriving the resulting price models, in particular in the very relevant and unsolved context of market incompleteness.
Complete descriptions appear in the course catalog.
View the semester course schedule.
- EN.553.4/627 Stochastic Processes and Applications to Finance
- EN.553.4/628 Stochastic Processes and Applications to Finance II
- EN.553.4/629 Introduction to Research in Discrete Probability
- EN.553.4/633 Monte Carlo Methods
- EN.553.4/636 Introduction to Data Science
- EN.553.4/639 Time Series Analysis
- EN.553.4/641 Equity Markets and Quantitative Trading
- EN.553.4/642 Investment Science
- EN.553.4/643 Financial Computing in C++
- EN.553.4/644 Introduction to Financial Derivatives
- EN.553.4/645 Interest Rate and Credit Derivatives
- EN.553.4/646 Risk Measurement/Management in Financial Markets
- EN.553.4/648 Financial Engineering and Structured Products
- EN.553.4/649 Advanced Equity Derivatives
- EN.553.4/661 Optimization in Finance
- EN.553.720 Probability Theory I
- EN.553.721 Probability Theory II
- EN.553.749 Advanced Financial Theory
- EN.553.753 Commodities and Commodity Markets
- EN.553.847 Financial Mathematics Masters Seminar