Answer: R’ Yisroel Yaakov Fisher (Even Yisrael 9:161) writes that sometimes Hashem keeps people alive in order so that they can support their family. Thus, he argues that one isn’t obligated to buy life insurance as one is removing this merit. Additionally, he argues that by buying a policy, one removes the great mitzva opportunity for others to support one’s relatives.
R’ Moshe Feinstein (Igros Moshe OC 2:111; 4:48), however disagrees, arguing that buying an insurance policy does not demonstrate a lack of belief in Hashem. As we are not supposed to rely on open miracles, it is inappropriate to daven for one. Rather, we must use the resources available to us to earn money. Hashem placed the idea of insurance in the minds of modern man and we should utilize this (See Shevet Halevi 4:1:2). R’ Moshe Stern (Baer Moshe 8:118) and R’ Moshe Sternbuch (Teshuvos Vehanhagos 4:325) add that it is particularly important to buy life insurance and do what one can for one’s family members.
R’ Ovadia Yosef (Yechave Daas 3:85) stresses that while buying a life insurance policy, one must ensure that one isn’t breaking any other halachos. Thus, one must ensure that one doesn’t give the insurance companies the right to insist on an autopsy, etc.
In conclusion, it is perfectly acceptable for one to buy a life insurance policy and it is not considered to be a lack of bitachon in Hashem.