Financial Mathematics: Applications in Investment Analysis

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Course DatesLengthMeeting TimesStatusFormatInstructor(s)CRN
June 28, 2021 - August 11, 20216/28 - 8/116 WeeksOnlineOpenOnlineMehdi Khorami

Course Description

Mathematical approaches in analysis of financial markets can yield fruitful results. For example, Quantitative Analysts, who are employed by investment banks and hedge funds, design and implement complex mathematical models that help institutions price financial assets. Mathematical approaches can also be used to create portfolios of assets that balance between an investment’s risk and return characteristics.

This course provides students with techniques of Probability Theory, Markov Processes and their applications in the areas of Portfolio Theory and Risk Management. Portfolio Theory involves distribution of wealth among risky assets (such as stocks, bonds, derivative products, etc.) based on the risk tolerance and return potential. Investors, hedge funds and investment banks use this theory to construct portfolios to maximize expected return based on a given level of market risk.

This course has three parts: Discrete Probability Theory for Finance, Markov Chains, and Portfolio Theory. The course will start with a brief introduction to probability theory, covering ideas such as probability models, random variables, discrete expectations and conditional probability. Markov Processes and its applications in asset price changes are introduced. Financial simulations are used as a way of using historical data to estimate parameters in various financial situations.

These concepts are then used to provide an introduction to Portfolio Theory. This involves distribution of wealth among financial assets for investment purposes based on risk tolerance and potential gain, covering topics such as long and short positions, and portfolio rate of return.

Upon successful completion of the course students will be able to:
• Have a thorough knowledge of various types of financial assets such as stocks and bonds
• Demonstrate understanding of basic concepts in Probability such as Sample Space, Probability Models, and Expectations
• Calculate the probability of events for complex outcomes
• Employ methods of probability theory in financial applications
• Identify and differentiate Markov processes from others
• Demonstrate how to employ simulations to gauge future behaviors from historical data
• Illustrate the basic concepts in portfolio theory such as portfolio rate of return and optimal portfolio selection

Prerequisites: Students need a solid background in basic algebra. No background in finance is required.

Course Information

  • Course Code: CEMA0930

Program Information


Brown’s Pre-College Program in the liberal arts and sciences for students completing grades 9-12 by June 2021.

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