Geico Corp. yesterday reported a 105 percent increase in its fourth quarter earnings to $33.2 million ($1.75 a share), compared with $16.2 million (79 cents) during the same period last year.

The company, which writes risk coverage for automobiles and homes, life insurance and reinsurance, reported a 15 percent increase in its earnings for the year to $131.3 million ($6.68), compared with $113.8 million ($5.37) during 1983.

Geico's earnings reflect realized capital gains of $30.9 million during the year, according to Chairman John J. Byrne.

In another corporate earnings report:

BDM International Inc., a McLean company that performs analysis, research and testing primarily for the military, said that its fourth quarter earnings rose 20 percent to $2.35 million (47 cents), compared with $1.96 million (40 cents) during the same period last year.

Revenue for the fourth quarter climbed 32 percent to $55.1 million, up from $41.68 million during the same period in 1983.

The company's earnings for the year climbed 27 percent to $8 million ($1.63) on revenue of $191.3 million, compared with $6.34 million ($1.28) on revenue of $151.1 million during 1983.