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If you are

Self-employed

Information on your social insurance if you are self-employed within the Nordic countries

Living and working in the same country within the Nordic countries

If you are self-employed and run your business in the country where you live, you are insured in that country.

Living in one country and running your business in another Nordic country

If you run your business in a country other than the one you live in, you are insured in the country in which you run your business and you may be entitled to receive benefits from that country.

Running your business in at least two countries within the Nordic countries

If you run your business in at least two countries, you are insured in the country you live in if part of your business operates in that country. If you are not resident in one of the countries you operate your business in, you are covered by the social insurance in the country where you do most of your work as self-employed.

Running your business in one country and being an employee in another Nordic country

You can be insured as a self-employed person in one country and an employee in the other.

Posted as self-employed

In certain cases you can run a business in one country and work temporarily as an employee or operate as self-employed in another and continue to be insured in the first country (posting). The temporary business or temporary work in the other country must not exceed a period of 12 months.

Being posted means that you will continue to be covered by the insurance in the country where you normally run your business and that social security contributions are paid to that country. There are special conditions that must be fulfilled.

Unemployment

When you are self-employed in Finland, Sweden, Greenland or Denmark you must join an unemployment benefit fund to be fully eligible for income-based compensation if you become unemployed.

In Iceland and the Faroe Islands you have to pay a premium to be covered by the unemployment insurance.
The systems for unemployment insurance are different in the different Nordic countries.  

Contact the authority in the country where you normally run your business for more information.