  In this paper, we consider a generic interest rate market in the presence of
roll-over risk, which generates spreads in spot/forward term rates. We do not
require classical absence of arbitrage and rely instead on a minimal market
viability assumption, which enables us to work in the context of the benchmark
approach. In a Markovian setting, we extend the control theoretic approach of
Gombani & Runggaldier (2013) and derive representations of spot/forward spreads
as value functions of suitable stochastic optimal control problems, formulated
under the real-world probability and with power-type objective functionals. We
determine endogenously the funding-liquidity spread by relating it to the
risk-sensitive optimization problem of a representative investor.
