Dynamic programming and hedging strategies in discrete time

In this chapter, we introduce four hedging strategies for path-independent contingent claims in discrete time - superhedging, local expected shortfall-hedging, local quadratic risk-minimizing and local quadratic risk-adjusted-minimizing strategies. The corresponding dynamic programming algorithms of each trading strategy are introduced for making adjustment at each rebalancing time. The hedging performances of these discrete time trading strategies are discussed in the trinomial, Black-Scholes and GARCH models. Moreover, the hedging strategies of pathdependent contingent claims are introduced in the last section, and the hedges of barrier options are illustrated as examples.