Topics in Mathematics with Applications in Finance

Problem Sets

Problem Sets

Problem Set 1 (PDF)

Problem Set 2 (PDF)

Problem Set 3 (PDF)

• The following paper is referenced in problem 2: Gron, Anne. “Optimal Portfolio Choice and Stochastic Volatility.” Applied Stochastic Models in Business and Industry, 2012. https://doi.org/10.1002/asmb.898
• The following readings relate to problem 4 and principal components analysis:
  • Principal Components Analysis in Finance Modeling the Dynamics of Interest Rates (PDF)
  • Sample R Code from the reading “Principal Components Analysis in Finance Modeling the Dynamics of Interest Rates (2016)” and Principal Components Analysis (PCA) of US Treasury Yields over a 5-Year Period (PDF)

Problem Set 4 (PDF)

Problem Set 5 (PDF)

• The following paper is referenced in this problem set: Parkinson, Michael. “The Extreme Value Method for Estimating the Variance of the Rate of Return.” The Journal of Business 53, no. 1 (1980): 61–65. http://www.jstor.org/stable/2352357 
• Volatility Case Study R Markdown (ZIP)