GuaranteeModelGDX : 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.
Files: GuaranteeModelGDX.gms
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$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;
$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$(ORD(k)<ORD(t)), (1 - abp(k))*(1 + mig + YP(l,k)))))
- PROD(t, (1 - abp(t))*(1 + mig + YP(l,t)))]
/ [rho*cf(l) + SUM(t, YM(l,t)*pcf(l,t)*PROD(k$(ORD(k)<ORD(t)), (1 - abp(k))*(1 + mig + YP(l,k))))])};
BAe.. SUM(i, HO(i)) =E= 1;
PRTd(l,t).. PRT(l,t) =E= SUM(i, (HO(i) * ar(l,t,i)));
YPMd(l,t).. (ptr * PRT(l,t) - mig) =E= YP(l,t) - YM(l,t);
MODEL PrometeiaModel 'PFO 12.4.1' / ALL /;
* Guess an initial solution and set bounds on variables
HO.UP(i) = 1;
HO.L(i) = 0.0;
HO.L('AA_1') = 0.8;
HO.L('AA_2') = 0.2;
PRT.L(l,t) = SUM(i, (HO.L(i) * ar(l,t,i)));
YM.L(l,t) = - MIN ((ptr * PRT.L(l,t) - mig), 0);
YP.L(l,t) = MAX ((ptr * PRT.L(l,t) - mig), 0);
SOLVE PrometeiaModel USING NLP MAXIMIZING EUROE;
* Post Optimization Calculation and Output
SCALARS
OptimalCeXRoe Optimal certainty equivalent excess Return-On-Equity
AnnualNetCeXRoe Annual equivalent, net of tax, of the OptimalCeXRoe
ExpGuarCost Expected guarantee cost;
PARAMETERS
FinalEquity(l) Final equity level;
OptimalCeXRoe = EXP ( EUROE.L );
FinalEquity(l) = rho*cf(l)
+ SUM(t, YM.L(l,t)*pcf(l,t)*PROD(k$(ORD(k)< ORD(t)), (1 - abp(k))*(1 + mig + YP.L(l,k))));
ExpGuarCost = 1/CARD(l)*SUM(l, FinalEquity(l)/cf(l) - rho*ili);
AnnualNetCeXRoe = (OptimalCeXRoe**(1/CARD(t)) - 1)*(1 - txr);
FILE ResultHandle /"InsuranceResults.csv"/;
ResultHandle.pc = 5; ResultHandle.pw = 1048;
PUT ResultHandle;
PUT "Number of scenarios", CARD(l):0:0/;
PUT "Partecipation rate", ptr:0:3/;
PUT "Minimum guarantee", mig:0:4/;
PUT "Equity ratio", rho:0:3/;
PUT "Model status", PrometeiaModel.MODELSTAT:0:0/;
PUT "Portfolio composition" /;
LOOP ( i $HO.L(i),
PUT i.TL,i.TE(i),HO.L(i):12:8/);
PUT "CExROE","Annual net CExROE","Cost of minimum guarantee"/;
PUT OptimalCeXRoe:12:8,AnnualNetCeXRoe:12:8,ExpGuarCost:12:8/;
PARAMETER YPYM(l,t) disjoint test;
YPYM(l,t) = YP.L(l,t) * YM.L(l,t);
DISPLAY YPYM;
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