qp5.gms : Standard QP Model - linear approximation

Description

```Linear approximation of qp4 operate directly on the data.
Additional information can be found at:

```

Reference

• Kalvelagen, E, Model Building with GAMS. forthcoming

Small Model of Type : LP

Category : GAMS Model library

Main file : qp5.gms   includes :  qpdata.inc

``````\$title Standard QP Model- linear Approximation (QP5,SEQ=175)

\$onText
Linear approximation of qp4 operate directly on the data.
Additional information can be found at:

Kalvelagen, E, Model Building with GAMS. forthcoming

de Wetering, A V, private communication.

Keywords: linear programming, quadratic programming, linear approximation, finance
\$offText

\$include qpdata.inc

Set
d(days)   'selected days'
s(stocks) 'selected stocks';

Alias (s,t);

* select subset of stocks and periods
d(days)   = ord(days) > 1 and ord(days) < 31;
s(stocks) = ord(stocks) < 51;

Parameter
mean(stocks)     'mean of daily return'
dev(stocks,days) 'deviations'
totmean          'total mean return';

mean(s)  = sum(d, return(s,d))/card(d);
dev(s,d) = return(s,d) - mean(s);
totmean  = sum(s, mean(s))/(card(s));

Variable
z           'objective variable'
x(stocks)   'investments'
wplus(days) 'intermediate variables'
wmin(days)  'intermediate variables';

Positive Variable x, wplus, wmin;

Equation
obj    'objective'
budget
retcon 'return constraint'
wdef(days);

obj..     z =e= sum(d, wplus(d) + wmin(d));

wdef(d).. wplus(d) - wmin(d) =e= sum(s, x(s)*dev(s,d));

budget..  sum(s, x(s)) =e= 1.0;

retcon..  sum(s, mean(s)*x(s)) =g= totmean*1.25;

Model qp5 / all /;

solve qp5 using lp minimizing z;

display x.l;
``````