Dan Stefanica


A Linear Algebra Primer for Financial Engineering by Dan Stefanica, 2014.

It is the third book in the Financial Engineering Advanced Background Series, and covers linear algebra concepts for financial engineering applications from a numerical point of view. The book contains many such applications, as well as pseudocodes, numerical examples, and questions often asked in interviews for quantitative positions.

Financial Applications

• The Arrow—Debreu one period market model
• One period index options arbitrage
• Covariance and correlation matrix estimation from time series data
• Ordinary least squares for implied volatility computation
• Minimum variance portfolios and maximum return portfolios
• Value at Risk and portfolio VaR

Linear Algebra Topics

• Direct methods for solving linear system. LU and Cholesky decompositions.
• Optimal solvers for tridiagonal symmetric positive matrices
• The Linear Transformation Property
• Multivariate normal random variables
• Efficient cubic spline interpolation
• Ordinary least squares and linear regression
• Gershgorin’s theorem and diagonal dominance
• Sylvester’s criterion

Table of Contents (Download)

Sample Sections:

  • 8.1.1. Implied volatility computation using least squares (Download)
  • 8.1. Ordinary least squares (Download)
  • 7.4. Necessary and sufficient conditions for covariance and correlation matrices (Download)
  • 1.1. Column vectors and row vectors. Covariance matrix computation from time series data. (Download)
  • Exercises – Chapter 1 (Download)

150 Most Frequently Asked Questions on Quant Interviews by Dan Stefanica, Rados Radoicic, and Tai-Ho Wang, 2013.

A ten questions selection, with solutions, can be downloaded here.


  • Mathematics, calculus, differential equations
  • Covariance and correlation matrices. Linear algebra
  • Financial instruments: options, bonds, swaps, forwards, futures
  • C++, algorithms, data structures
  • Monte Carlo simulations. Numerical methods
  • Probability. Stochastic calculus
  • Brainteasers

A Primer for the Mathematics of Financial Engineering by Dan Stefanica, Second Edition, 2011.

Number 1 QuantNet bestselling book of 2010, 2011, 2012, and 2013.

Sample Sections:

  • Table of Contents (Download)
  • 3.6.1. Explaining the magic of Greeks computations (Download)
  • 5.2.1. The N-dimensional Newton’s Method (Download)
  • 6.5. Parallel shifts in the yield curve (Download)
  • 6.7. Dollar duration and dollar convexity; bond portfolio immunization (Download)
  • 8.6. Integrating the density function of the standard normal variable (Download)
  • 9.1. Lagrange multipliers (Download)
  • Exercises – Chapter 1 (Download)
  • Exercises – Chapter 6 (Download)

Solutions Manual – A Primer for the Mathematics of Financial Engineering by Dan Stefanica, Second Edition, 2011.

Top 3 QuantNet bestselling book in 2010, 2011, 2012, and 2013.

Sample Sections:

  • 1.1. Chapter 1 Exercises (Download)
  • 1.2. Complete Solutions to Chapter 1 Exercises (Download)


Publisher’s discount on Math Primer and Solutions Manual and worldwide shipping from FE Press

Amazon US: Math Primer; Solutions Manual

Amazon UK: Math Primer; Solutions Manual

Amazon France: Math Primer; Solutions Manual

Amazon Germany: Math Primer; Solutions Manual

The Primer and its Solutions Manual are the first books in the Financial Engineering Advanced Background Series. A third book in the series, A Numerical Linear Algebra Primer for Financial Engineering is scheduled to appear in December 2013.

Selected Papers

Domain Decomposition Methods

Dostál, Zdeněk; Horák, David; Stefanica, Dan. A scalable FETI-DP algorithm with non-penetration mortar conditions on contact interface. J. Comput. Appl. Math. 231 (2009), no. 2, 577–591

Stefanica, Dan. A balancing algorithm for mortar methods. Domain decomposition methods in science and engineering XVI, 747–754, Lect. Notes Comput. Sci. Eng., 55, Springer, Berlin, 2007

Dostál, Zdeněk; Horák, David; Stefanica, Dan. Quadratic programming and scalable algorithms for variational inequalities. Numerical mathematics and advanced applications, 62–78, Springer, Berlin, 2006

Stefanica, Dan. Lower bounds for additive Schwarz methods with mortars. C. R. Math. Acad. Sci. Paris 339 (2004), no. 10, 739–743

Stefanica, Dan. A numerical study of FETI algorithms for mortar finite element methods. SIAM J. Sci. Comput. 23 (2001), no. 4, 1135–1160

Geophysical Fluid Dynamics

Holland, David; Rosales, Rodolfo; Stefanica, Dan; Tabak, Esteban. Internal hydraulic jumps and mixing in two-layer flows. J. Fluid Mech. 470 (2002), 63–83

Graph Theory

Ismailescu, Dan; Stefanica, Dan. Minimizer graphs for a class of extremal problems. J. Graph Theory 39 (2002), no. 4, 230–240


Baruch College: Co-Director, Financial Engineering MS Program, 2002 – Present

Baruch College: Associate Professor, Department of Mathematics, 2005 – Present

Massachusetts Institute of Technology: Applied Mathematics Instructor, 2000-2002

Grant Support

NSF-DMS-0103588; PSC-CUNY 62667-00 40 (selected)

Contact for Baruch MFE Inquiries

Email: baruch.mfe at baruch.cuny.edu

Phone: +1-646-312-4001


Email: Dan.Stefanica at baruch.cuny.edu

Phone: +1-646-312-4171