Author: Henri Pagës

Publisher: Forgotten Books

Published: 2016-10-20

Total Pages: 34

ISBN-13: 9781334017070

Excerpt from Optimal Consumption and Portfolio Policies When Markets Are Incomplete The first question arises from the fact that when M is stictly included in X, only the marketed commodities have their price determined by arbitrage. There is an abundance of price functionals that extend 7r over all of X, and one could choose a priori any one of them. However, one candidate is of special interest to us: it is the (unique) one which is measurable with respect to the price system, i.e., such that the shadow price of consumption is itself in the price information set. With this particular valuation, it turns out that a solution 6 to the extended maximization program can always be chosen to be price measurable. And thus marketed. To see this, we have to recall a result from option pricing theory which states that the price of any contingent claim can be written as its expectation under some probability. Let. Then Q be the probability associated with our choice of the price measurable valuation, and take the conditional expectation of (3 under Q with respect to the price information set. The new consumption plan is price measurable by construction. In addition, it can be shown that it satisfies the same budget constraint and that. It is as least as preferred as 6. But 6 is Optimal by assumption, so that it. Should be clear that. The two solutions are in fact. Indifferent. Or even identical when the utility function is strictly concave. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.