For environmental and financial reasons I have always used second hand or grey market mobile telephones. For work purposes I have general purpose computer kept as secure as possible, purchased new and running only trusted open source software, including GPG for secure communications. I maintain my security by partitioning my use, the mobile phone is only used for tasks where security is not required, and my computer for tasks where it is. This has served me well for the last 25 years, but recently my bank has been relying more and more on my telephone as a secure from of communication. I am concerned that in the case of a security breach caused by my phone being compromised I could be considered at fault and so lose money.
One thing I could do would be to inform my bank of the risk as I see it in a provable way (email, recorded delivery letter), and perhaps advise that secure information can be sent by PGP encrypted email. I have no expectation that they will change their behaviour, but I would hope that in the case of a breach I did what I could to inform the bank, so am less responsible and so have more chance of getting any lost money returned to me. However it is conceivable that it would have the opposite effect, of proving that I knew of the risk and so am more responsible and have less chance of return of the money.
In such a situation what is the best course of action? Are there any past events that could guide the decision? Is there an accepted solution to modern banking without a secure mobile telephone?