Optimal investment and price dependence in a semi-static market
type: Item
instance of: scholarly article
title: Optimal investment and price dependence in a semi-static market
zbMATH Open document ID: 1312.91083
author: Pietro Siorpaes
published in: Finance and Stochastics
publication date: 2015-01-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1303.0237
review text: The author considers the problem of maximizing expected utility from terminal wealth in a semi-static market framework. A specific feature is that a general utility function defined on the positive half-line is used. It is explained that the problem under consideration does not fall under the general umbrella of utility maximization with convex constraints, because it can not be rephrased asking that the portfolio and wealth process lie in some given convex set; rather, it is demanded that the investor chooses his position at time zero arbitrarily and then keeps his position in derivatives unchanged, freely investing in stocks. The existence and uniqueness of the solution is studied as well as the dependence of the value function, of its maximizer and of other quantities of interest on the initial capital and on the price \(p\) of the derivatives. Stability, differentiability, monotonicity and convexity are established. Furthermore, the author proves the convexity in \(p\) of the largest feasible position, defined as the maximum number of shares of derivatives that the agent with given initial wealth can buy at price \(p\) and still be able to invest in the liquid stock market so as to have a nonnegative final wealth.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 60G48
zbMATH DE Number: 6387651
zbMATH Keywords: optimal investment
zbMATH Keywords: convex duality
zbMATH Keywords: incomplete market
zbMATH Keywords: semi-static market
zbMATH Keywords: price dependence
zbMATH Keywords: well-posed problem
MaRDI profile type: Publication
OpenAlex ID: W2145100155
arXiv ID: 1303.0237
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DOI: 10.1007/S00780-014-0245-8
description: scientific article