*The day and location are different from usual.
Abstract:
We develop a comprehensive mathematical finance framework for propagator models with
transient linear price impact. These models lead to infinite-dimensional, non-Markovian control
problems and fall outside the scope of classical arbitrage and duality theory. We establish a
fundamental theorem of asset pricing, a superreplication theorem with liquidity-adjusted risk
measures, and a full convex-duality approach to utility maximisation. Despite the non-linearity
of preferences and the path-dependent impact structure, we show that optimal strategies can
be obtained from an equivalent frictionless optimisation problem under a suitably constructed
shadow price.