Faculty Experts - Klaus E. Volpert, PhD

Klaus E. Volpert, PhD

Klaus E. Volpert, PhD
Associate Professor
Department of Mathematics
Villanova University College of Liberal Arts and Sciences

Area of Expertise

  • Mathematics of Finance and Economics
  • Pricing of Financial Derivatives
  • Pedagogy of Mathematics
  • Differential Geometry
  • Algebraic Topology



Income inequality in the United States continually fluctuates, but the large gap between rich and poor remains. Dr. Volpert has done extensive research on the variation in income inequality and the mathematical causes behind its rise and fall. An expert source on applied mathematics at the intersection of finance and economics, he is also an authoritative voice on the ways in which teachers can help students understand and use mathematics.


  • Ph.D., University of Oregon
  • M.S., Physics, University of Oregon
  • M.S., Mathematics, University of Oregon
  • Vordiplom, Universität Konstanz, Germany

Selected Publications

  • “How well do bond interest rates predict stock market returns?” Journal of Investing, Summer 2013 issue.
  • Robert T. Jantzen, Klause E. Volpert, “On the Mathematics of Income Inequality: Splitting the Gini-Index in Two,” American Mathematical Monthly, June 2012.
  • “Finite spectral sequences and Massey Powers in the deformation theory of graded Lie algebras and associative algebras,” Journal of Pure and Applied Algebra, 87, p. 281-300, 1993.
  • “A Spectral Sequence Connecting the Spencer Cohomology of a Transitive Lie Algebra with is Deformation Cohomology,” Algebras, Groups and Geometries, Vol 7, p. 313-344, 1990. 


Selected Professional Experience

  • Villanova faculty member since 1989


Selected Research

  • Villanova Institute for Teaching and Learning mini grant for development of a course in Monte Carlo Methods, 2010.
  • Completion rates in PhD programs in Mathematics at U.S. institutions, 2005-present.
  • Volatility Smile and Bond Ratings, 2002-present.
  • Long-term bond yields as predictors for stock-market performance, 2004-present.
  • Math and Science Partnership of Greater Philadelphia participant, 2005.
  • Villanova Institute for Teaching and Learning mini grant for development of a course on ‘Technology in the Teaching of Mathematics,’ 1998. 


About Villanova

Since 1842, Villanova University’s Augustinian Catholic intellectual tradition has been the cornerstone of an academic community in which students learn to think critically, act compassionately and succeed while serving others. There are more than 10,000 undergraduate, graduate and law students in the University's six colleges – the College of Liberal Arts and Sciences, the Villanova School of Business, the College of Engineering, the College of Nursing, the College of Professional Studies and the Villanova University Charles Widger School of Law. As students grow intellectually, Villanova prepares them to become ethical leaders who create positive change everywhere life takes them.

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