Is an alternative other than negative interest rate possible?
Negative interest rates means that if you take a 1.000 loan, you will pay 900 to the lender. At the same time, if you deposit this same 1.000 in a savings accounts, you will withdraw 900. This is an expansionary monetary policy. In other words, low or negative interest rates estimulates the consumption and destimulates the savings. 

It also weaken a country’s currency, which boost the exports and pushing up import costs. Like Japan and USA, Denmark is a big exporter. One of Trump strategies - along with direct taxations into imported goods - is to decrease interest rates to gain advantage against China.

The stimulus for comsumption is to boost the economy and increase the aggregate demand. An investor would prefer to invest in a company or enterprise rather than government bonds, and a family would rather buy a new house today than save for 5 years.

Other monetary policies could be the reduction of the reserve ratio or quantitative easing, but all expansionary policies can lead to bad consequences in the future, like high inflation rates.