Stochastic Finance, 4th Edition

9Hedging under constraints

So far, we have focussed on frictionless market models, where asset transactions can be carried out with no limitation. In this chapter, we study the impact of market imperfections generated by convex trading constraints. Thus, we develop the theory of dynamic hedging under the condition that only trading strategies from a given convex class S may be used. In Section 9.1 we characterize those market models for which S does not contain arbitrage opportunities. Then we take a direct approach to the superhedging duality for American options. To this end, we first derive a uniform Doob decomposition under constraints in Section 9.2. The appropriate upper Snell envelopes are analyzed in Section 9.3. In Section 9.4 we derive ...