Mortality is not significant enough with this to have any effect. Instability in the financial markets will have some effect, but I doubt it'll be enough to bring anyone down. Policies (both annuities and life insurance) that have non-guaranteed elements may see changes in rates reflecting the current environment.
+1
I was on a conference call of a major mutual life insurer last week. While obviously each company is different, where it comes to guaranteed mortality assumptions, they use the Spanish Flu for calculations. Having that kind of tragedy would mean a 50% increase in mortality, or an extra 1.5 million deaths as a result. Given the age distribution of insureds, etc. they gave the potential impact on reserves which would be miniscule.
The biggest impact is the low interest rate environment.
ETA: Japanese insurers have been operating well under zero rates for a long time. I wouldn't worry about an existing contract with guarantees. Just don't let yourself to be talked into giving up those guarantees (when it comes to Variable Annuities, which I don't think is what you have, most people simply don't know or understand the contract).