Two men and a woman, all in their 40s, are being held by police.
Guy Hedger, 61, was shot in the early hours of 30 April after intruders entered his home in Ringwood, Dorset.
The insurance executive was pronounced dead shortly after arriving at hospital and it is believed jewellery, including designer watches, was stolen from his home.
A 41-year-old man from Bournemouth has been arrested on suspicion of murder and aggravated burglary.
Police are also questioning a 44-year-old man and a woman, 40, on suspicion of conspiracy to commit murder and conspiracy to commit aggravated burglary.
Officers are searching homes in Winterborne Stickland, near Blandford, and West Howe, Bournemouth, for evidence.
Superintendent Kevin Connolly said: “We have worked tirelessly on this investigation which still continues even though arrests have been made.
“Our appeal still stands for anyone with information that could aid our investigation to come forward as any small detail may be important.”
A post-mortem has found Mr Hedger died as a consequence of gunshot wounds, Dorset Police said.
The 61-year-old’s civil partner witnessed the attack and was said to have been left “deeply affected”.
In a statement, Mr Hedger’s family said he was “a caring and compassionate partner, son, brother and uncle who lived life to its full and enriched the lives of all those who knew him”.
They added: “We are devastated that Guy’s life has been cut short in this way.
“Guy will be sorely missed by family, friends and colleagues, but he will live in our hearts forever.”
Anyone with information is asked to contact Dorset Police at www.dorset.police.uk, via email [email protected] or by calling 101, quoting incident number 30:53. Alternatively contact Crimestoppers anonymously on 0800 555111 or via www.crimestoppers-uk.org.