Practical Financial Optimization: A Library of GAMS Models

Notation

We use throughout this book the notation introduced in S.A. Zenios, Practical Financial Optimization: Decision Making for Financial Engineers, (Blackwell Publishing, Cambridge, MA, 2007), abbreviated as PFO. To the extent possible the same notation is adopted in the accompanying software. Cross-references to chapters, sections, models, and so on from PFO are given using the notation PFO-m.n.p where m.n.p refers to PFO labels. For instance, “Section PFO-6.3” refers to Section 3 of Chapter 6, and “Model PFO-6.4.2” refers to the second model of the fourth section of Chapter 6. Readers will easily locate the cited material in PFO.

The current GAMS system, which includes the FINLIB, is available at: http://www.gams.com/download/.

The FINLIB is available at: http://www.gams.com/finlib/.

Sets and Indices

U = {1, 2, . . . , n} index set of available financial instruments or asset classes.

T = {0, 1, ..., τ, ... T} set of time periods, from today (0) until maturity (T ). Unless stated otherwise in the text all time periods are of equal duration, which is typically taken to be one month.

K = {1, 2, . . . , κ, . . . , K} index set of risk factors.

Σ_t = {1, 2, . . . , S_t } index set of states at period t .

Ω = {1, 2, . . . , N } index set of scenarios.

i index of instrument or asset class from the set U .

t index of time periods from the set T .

j index of risk factor from the set K.

l index of scenario from the set Ω.

Variables and Parameters

x n-dimensional vector of investments ...