A discrete stochastic model for investment with an application to the transaction costs case
type: Item
instance of: scholarly article
title: A discrete stochastic model for investment with an application to the transaction costs case
zbMATH Open document ID: 0960.91038
DOI: 10.1016/S0304-4068(99)00005-1
author: Laurence Carassus
author: Elyès Jouini
published in: Journal of Mathematical Economics
publication date: 2000-04-09T00:00:00Z
review text: The authors study a model where investments are completely defined through their generated cash flows, the latter having a dynamics given by a binomial tree. The model is assumed to be stationary, i.e. each project is available at every date and in every state of the world at the same conditions. (In the deterministic case this kind of models has been studied e.g. by \textit{I. Adler} and \textit{D. Gale} [Math. Finance 7, 73-81 (1997; Zbl 0884.90011)].) Under some technical condition, the assumption of no-arbitrage implies the existence of an interest rate and a particular probability measure under which the expected value of the total investments is non-positive if there are short-selling constraints and equal to zero otherwise. In the second part of the paper an economie model is presented in which the price of the underlying asset follows a binomial process. It is assumed that there are transaction costs on the underlying asset and the options under consideration. Applying the results in the first part the authors show e.g. that at the equilibrium the Cox-Rosse-Rubinstein (CRR) price is always between the buying and selling price. In the particular case where there are only transaction costs on the underlying asset and not on the options, the options' price equals the CRR-price which is a new result about transaction costs.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 91B70
zbMATH DE Number: 1428354
zbMATH Keywords: Cox-Ross-Rubinstein price
zbMATH Keywords: investments
zbMATH Keywords: cash flows
zbMATH Keywords: no-arbitrage
zbMATH Keywords: options' price
reviewed by: Klaus Schürger
MaRDI profile type: Publication
cites work: Arbitrage and Growth Rate for Riskless Investments in a Stationary Economy
cites work: The pricing of options and corporate liabilities
cites work: Q4748596
cites work: Investment Selection with Imperfect Capital Markets
cites work: Optimal Investment Selection with a Multitude of Projects
cites work: Investment and Arbitrage Opportunities with Short Sales Constraints
cites work: Option pricing: A simplified approach
cites work: Q3941926
cites work: Martingales and arbitage in securities markets with transaction costs
full work available at URL: s0304-4068(99)00005-1
OpenAlex ID: W2077181353
Recommended article: Arbitrage and pricing in a general model with flows
Recommended article: Arbitrage and investment opportunities
Recommended article: Q4453309
Recommended article: Investment and Arbitrage Opportunities with Short Sales Constraints
Recommended article: Robust utility maximisation in markets with transaction costs
Recommended article: Hedging in the CRR model under concave transaction costs
Recommended article: Portfolio optimization under transaction costs in the CRR model
Recommended article: Transaction costs and efficiency of portfolio strategies
description: scientific article; zbMATH DE number 1428354