Modified Garch in Mean

[b.p.abdul]

I would very much appreciate it if somebody could give me advice on a modified Garch in Mean model which I am trying to estimate as part of my thesis. The equation is given by:
Y(t)=alpha+beta_1*sigma+beta_2*(sigma*Y(t-1))+u(t)
Sigma(t)=eta+lambda(1)*u(t-1)^2+lambda(2)*sigma(t-1)
(this model is estimate for example by Dean and Faff 2008 and Ciffarelli and Paladino 2010).
I followed the advice given previously in the forum. I tried to first estimate a normal Garch in Mean and use the estimated conditional variance as sigma in the first equation and then to repeat this process with the new conditional variance. Yet looping this process didn’t yield convincing results since the estimated coefficients do not converge.
I also tried to build a logl object, but here I encounter an overflow error. I would be very thankful if anybody could give me advice how to continue from here.
Thx in advance

[b.p.abdul]

PS If I set the values of the coefficients small enough I get a result, however this method seems to be quite arbitrary, so I would also appreciate any advice on the starting values. Thx

[b.p.abdul]

It seems I solved the problem. Sorry for the back and forth.