What are the reasons for a convinced metaphysical solipsist to get life insurance?
The payout may never come, but the illusory beings around them don't know that
Imagine our solipsist is married with a child. Although the solipsist does not believe that their spouse and child exist as anything more than patterns in their own perceptions, they find something of value in experiencing those patterns. The solipsist has a high-paying job, and as a family they're well off, but the spouse doesn't have reliable income, so their finances may be shaky in the event of the solipsist's death. The solipsist sees no problem with this, because the family would not exist as even an illusion in the event of their death, but the spouse is very worried. The spouse asks about getting life insurance at least once a month, and is visibly uneasy. The solipsist is uncomfortable with this as a matter of instinctive human sympathy, or at the very least finds the reminders irritating, so they buy life insurance. Problem solved.
It's not buying a policy that will never benefit anyone, it's buying peace of mind for someone who happens not to exist.
Assuming they are properly convinced (ie they do not admit the possibility of being wrong) there are two reasons.
Firstly, some life insurance policies pay out early if the insured is certified by medical professionals as being shortly to die of an incurable illness, in which case the terminally ill solipsist may blow the full amount of their cover on the purchase of more imaginary experiences.
Secondly, the solipsist might believe their mind continues in some form after their corporeal death, and that in that newly detached form it might continue to experience the imaginary and irrational emotions that plagued it during its physical life; thus the solipsist might wish to pass on the sum assured to obtain and maintain an irrational sense of pleasure at having looked after imaginary dependents.
Epistemological and methodological solipsism both roughly maintain that only one's own existence can be demonstrated to exist (the former maintains it as a belief, whereas the latter maintains it through methodology).
Such a person may still be convinced, or find it sufficiently likely, that others exist due to their perception of those people. So solipsism shouldn't affect whether they get life insurance (whether they "should" get life insurance is different question that depends on their circumstances).
Metaphysical solipsism maintains that there is nothing external to this mind. I'll leave the epistemological criticism of that to Wikipedia.
But there may be some ambiguity about what "this mind" means. If you think in the sense of how humanity understands physical reality, then "this mind" has a clear meaning. But metaphysical solipsism maintains that physical reality doesn't exist, so that argument wouldn't work.
It seems you would need some variant of metaphysical solipsism that could be one of the following:
When you "die", all of perceived existence ceases to exist.
If this is the case, then one wouldn't have much reason to get life insurance.
But this only applies if you mean "dying" in a physical sense, and if physical reality doesn't exist, dying is nothing more than some thoughts, and it's not clear why that would make your consciousness cease to exist.
One would outlive one's physical death.
There are infinitely many possibilities of what such a post-death existence would look like, and I can't address them all here. But at least for some of those getting life insurance would be to your advantage (e.g. if you next experience a deity judging you for how considerate you are towards others).
Other consciousnesses (of those you perceive as other people) exist within the same mind.
This wouldn't be functionally different from reality actually existing: those consciousnesses would presumably continue to exist after "you" die, so this shouldn't affect whether one gets life insurance.
There is also some possible pre-death benefits to getting life insurance:
There is some social utility to getting life insurance (or at least convincing others that you have life insurance). This might affect how responsible and considerate you're considered to be by other people, which informs how they treat you (whether they actually exist or not).
Any given life insurance policy may pay out early or have other benefits. Although these likely wouldn't be financially worth it if you don't care about the actual life insurance (unless the life insurance policy is just one part of a broader policy, or the insurance company relies on the fact that most people don't fully make use of those benefits, which isn't unheard of).
Solipsism does not imply the nonexistence of others (your previous comment: "there is nobody around a solipsist"). Solipsism implies the physical perception of others but the metaphysical impossibility to prove its existence as such (as others). More precisely, others exist empirically but can't be proven to exist in the external reality.
The error lies here: you write "there is nobody around a solipsist", implying that there are no human interactions (nobody around to interact with!), and therefore no possibility of the existence of insurances (what for? with who? for who?). Here, you are denying the empirical perception of others, which is just wrong. That's not solipsism. In such case, even the word "others" would not exist.
Later, you contradict yourself "others may exist". So, others are perceived as existing, and therefore, human interaction with others is perceived and existing. In such case, there are evident reasons to buy a life insurance (just google: "reasons to get a life insurance").
What are the reasons for a convinced metaphysical solipsist to get life insurance?
One reason would certainly be if a convinced metaphysical solipsist was a dear friend to you. A life insurance seems like a good idea.
Ah, you now realise that you in fact have no friend who is a convinced metaphysical solipsist. There is a good reason for this. It is that convinced metaphysical solipsists simply don't exist (funny, that).
Metaphysical solipsism is not anything any reasonable person would argue seriously. Instead, it is a thought experiment which helps us understand that we cannot rationally prove to ourselves that the world outside our own mind exists for real. Thus, all we can do is believe that it does, and hope for the best.
Metaphysical Solipsism The idea that the mind of the subject is the whole of reality, so that the external world, and other persons with it, are mere representations within this mind, thus with no independent existence.
Solipsism is the view that the only certain truth is that of one's own existence. As for the existence of others, there's no certainty - they may or may not exist. Since others may exist, getting life insurance is consistent with solipsism.
If O = Others exist, solipsism is O v ~O means others may or may not exist If L = get life insurance then L implies O means getting life insurance implies others exist.
|O v ~O||L||L implies O|
|T t F||t||T t T|
To make the long story short, there's a line in the truth table above in which all the relevant statements are true - solipsism is perfectly consistent with taking out a life insurance even if doing that implies other people exist.
EDIT: Added some basic probability calculations because many SE members see a resemblance to Pascal's wager.
P(O) = probability that others exist
P(~O) = probability that others don't exist
L = The life insurance amount
Scenario 1 If you get life insurance,
The expected value = L × P(O) - L × P(~O) = L[P(O) - P(~O)]
Scenario 2 If you don't get life insurance,
The expected value = L × P(~O) - L × P(O) = L[P(~O) - P(O)]
If P(O) = P(~O) [50%], the game is fair (niether in favor nor against you, the expected value is 0 i.e. you won't lose money, but you won't win either, break even scenario).
If P(O) > P(~O), get life insurance.
If P(~O) > P(O), don't get life insurance.
I don't really see what's special about this question for a metaphysical solipsist. The metaphysical solipsist buys (or doesn't buy) life insurance for the same reasons they do anything else.
If they don't care to better the projected lives of the zombies around them then they generally won't do anything for them including buying life insurance. But if they do care to better the projected lives (because they get personal fulfilment or something) then they will buy life insurance in the service of that.