Elasticity approach to asset allocation in discrete time

In this paper, we apply the elasticity approach to optimal asset allocation problems in discrete-time setting. In particular, firstly, for a portfolio optimization problem, which targets to maximize the expected utility of the terminal wealth of a portfolio of an option, the underlying stock, and the risk-free bond, the elasticity approach can decompose this problem into a reduced optimization problem, consisting of only the stock and bond, and a pure delta neutral hedging problem. This decomposition provides a discrete-time version of the optimal alternative to the delta hedge, which was initially proposed in continuous time. Moreover, the general principle given by the pure delta neutral strategy is analyzed in our setting. Secondly, the same approach is applied to an optimal investment problem with defaultable securities, and show that this problem is essentially the same as the above mentioned reduced optimization problem. This work can be regarded as an extension of the elasticity approach in Kraft [Mathematical Methods of Operations Research 58(1) (2003), 159-182] to discrete-time models, and it shows that this approach can largely deduce the asset allocation problems in complete market.