$TITLE Managing insurance policies with guarantee - The Prometeia Model - GDX Input * GuaranteeModelGDX.gms: Managing insurance policies with guarantee - The Prometeia Model - GDX Input. * Consiglio, Nielsen and Zenios. * PRACTICAL FINANCIAL OPTIMIZATION: A Library of GAMS Models, Section 8.4 * Last modified: May 2008. SETS TT Time SS Number of scenarios AA Set of Assets; ALIAS(SS,l); ALIAS(TT,t,k); ALIAS(AA,i,j); PARAMETERS ar(l,t,i) Asset Returns Scenarios abp(t) Abandon Probabilities pcf(l,t) Risk Free Periodic Capitalization Factor Scenarios cf(l) Risk Free Capitalization Factor Scenarios; $ifthen not exist GuaranteeData.gdx $ call gams GuaranteeData lo=%gams.lo% $ if errorlevel 1 $abort Inspect GuarateeData.lst $endif $gdxin GuaranteeData $load AA SS TT ar abp pcf cf $gdxin SCALARS mig Minimum Guarantee /0.04/ ptr Partecipation Rate /0.85/ ili Initial Liability /1.0/ txr Tax Rate for shareholders /0.51/ rho Equity Ratio /0.04/; POSITIVE VARIABLES HO(i) Asset holdings YP(l,t) yPlus - surplus in excess of minimum guarantee. YM(l,t) yMinus - deficit in lack of minimum guarantee.; FREE VARIABLES PRT(l,t) Portfolio Return. EUROE Expected Utility Return On Equity; EQUATIONS OFe Objective Function equation. BAe Balance equation. PRTd(l,t) Portfolio return dynamics. YPMd(l,t) Equations defining the yPlus and yMinus dynamics; OFe.. EUROE =E= 1/CARD(l)*SUM{l, LOG([(1+rho)*PROD (t, 1+PRT(l,t)) + SUM(t, ((YM(l,t) - (abp(t)*(1 + mig + YP(l,t)))) * PROD(k$(ORD(k)>ORD(t)), (1 + PRT(l,k)))* PROD(k$(ORD(k)