A stochastic control perspective of multi-curve term structures under the benchmark approach

The thesis gets inspiration from a paper by A. Gombani and W. J. Runggaldier (2013). By applying a convex transformation to a generic term structure, it can be shown that an interest rates derivatives pricing issue is equivalent to a stochastic control problem. We try to use the same procedure considering to model multiplicative spreads in a financial market which may not provide a martingale measure. More precisely, we combine the roll-over risk formulation for spreads with the bechmark approach. Moreover, we propose a representation of spot spreads depending on a portofolio process whose corresponding strategy solves a risk-sensitive portfolio optimization problem.