.. _literature:

Background & further reading
----------------------------


Portfolio Optimization
^^^^^^^^^^^^^^^^^^^^^^

The following resources provide additional background on mean-variance portfolio
theory, and beyond.

* Best, M.J. (2010). Portfolio Optimization (1st ed.). Chapman and Hall/CRC.
  https://doi.org/10.1201/b17178

  In this textbook, the interplay of portfolio theory and optimization is
  approached at a level appropriate for a one-semester undergraduate course.
  It features accompanying MATLAB programs, including a self-contained quadratic
  programming solver.  It details the practical importance of
  additional constraints to the classical mean-variance model, and their
  effects on the geometry of the efficient frontier.

* Cornuéjols, G., Peña, J., & Tütüncü, R. (2018). Optimization Methods in
  Finance (2nd ed.). Cambridge: Cambridge University Press.
  https://doi.org/10.1017/9781107297340

  This textbook approaches mean-variance portfolio theory and practice from an
  optimization angle.  It includes a self-contained treatment of quadratic
  optimization theory for portfolio optimization, and introduces mixed-integer
  optimization as a tool for modeling discrete decisions.  The scope of this book
  is well beyond just classical mean-variance portfolios and includes asset pricing,
  multi-period models, CVaR measures (in relation to linear
  optimization), stochastic programming and robust optimization techniques.

* Markowitz, H. (1952), PORTFOLIO SELECTION. The Journal of Finance, 7: 77-91.
  https://doi.org/10.1111/j.1540-6261.1952.tb01525.x

  This work marks the beginning of rigorous mathematical and statistical theory of
  mean-variance portfolio selection (including the "expected returns--variance of
  returns" rule).  It features intuitive, geometric arguments for the
  three-securities case. It is the first to describe portfolio selection as
  a two-stage process: (1) finding reasonable estimates for return and variance,
  and (2) selecting positions based on mathematical optimality conditions.


gurobipy
^^^^^^^^

The following resources are helpful for getting started with and using `gurobipy <https://pypi.org/project/gurobipy>`_:

* A one-page `overview
  <https://docs.gurobi.com/projects/optimizer/en/current/reference/python/overview.html>`_
  of gurobipy's modeling functionality

  Runs through key concepts, including models, variables, constraints, solution
  process, and more.  This is a good starting point to get an overview of gurobipy's
  capabilities and common usage patterns.

* gurobipy `reference documentation <https://docs.gurobi.com/projects/optimizer/en/current/reference/python.html>`_

  Detailed API reference documentation for all classes and methods.

* YouTube video on `modeling with ndarray and sparse matrices <https://youtu.be/5lDsg7KLeZI?si=5Bn_NPdbefXqKtHz>`_

  For portfolio optimization, it is natural to express matrix and
  vector expressions directly as such into a gurbipy model.  This video
  introduces gurobipy's related modeling capabilities.


Discrete aspects of portfolio optimization
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The following are a few selected research papers that touch on the interplay
between portfolio optimization and discrete decision making through
mixed-integer optimization:

* Bonami P., Lejeune M. A., (2009) An Exact Solution Approach for Portfolio
  Optimization Problems Under Stochastic and Integer Constraints. Operations
  Research 57(3):650-670.  https://doi.org/10.1287/opre.1080.0599

* Chang T.-J., Meade N., Beasley J.E., Sharaiha Y.M. 2000. Heuristics for
  Cardinality Constrained Portfolio Optimisation. Computers & Operations
  Research 27, 1271–1302.  https://doi.org/10.1016/S0305-0548(99)00074-X.

* N.J. Jobst , M.D. Horniman , C.A. Lucas & G. Mitra (2001) Computational
  aspects of alternative portfolio selection models in the presence of discrete
  asset choice constraints, Quantitative Finance, 1:5, 489-501.
  https://doi.org/10.1088/1469-7688/1/5/301