  The main purpose of this work is to derive a partial differential equation
for the reserves of life insurance liabilities subject to stochastic interest
rates where the benefits and premiums depend directly on changes in the
interest rate curve. In particular, we allow the payment streams to depend on
the performance of an overnight technical interest rate, making them stochastic
as well. This opens up for considering new types of contracts based on the
performance of the insurer's returns on their own investments. We provide
explicit solutions for the reserves when the premiums and benefits vary
according to interest rate levels or averages under the Vasicek model and
conduct some simulations computing reserve surfaces numerically. We also give
an example of a reinsurance treaty taking over pension payments when the
insurer's average returns fall under some specified threshold.
