Risk minimization under transaction costs
type: Item
instance of: scholarly article
title: Risk minimization under transaction costs
zbMATH Open document ID: 1007.91021
author: Paolo Guasoni
published in: Finance and Stochastics
publication date: 2002-11-21T00:00:00Z
review text: This paper deals with the problem of minimizing the risk of the trading position at fixed date in a market with incomplete information, proportional transaction costs, and constraints on strategies. The author considers a market with a risky asset \(X\) and a riskless asset \(B\). \(X\) is a continuous semimartingale, the transaction cost up to time \(t\) is equal to \(C_{t}(\theta)= \int_{[0,t]}k_{s} d|D\theta_{s}|\), where a cost of \(k_{t}\) is incurred for each share traded, \(\theta_{t}\) is a number of shares invested in the risky asset at time \(t\), \(D\theta\) is the Radon measure. The considered risk functionals are general enough to allow the minimization of shortfall or the minimization of the coherent risk measure and the maximization of the expected utility. A theorem on the existence of optimal strategies in markets with incomplete information and transaction costs is proved. The constrained case is studied for two types of constraints: those on the position in the risky asset (such as limits on short-selling) and those on the portfolio value (such as margin requirements).
Mathematics Subject Classification ID: 91B28
zbMATH DE Number: 1833869
zbMATH Keywords: risk minimization
zbMATH Keywords: transaction costs
zbMATH Keywords: incomplete market
zbMATH Keywords: constraints on strategies
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
full work available at URL: s780-002-8402-0
OpenAlex ID: W1966756524
DOI: 10.1007/S780-002-8402-0
description: scientific article; zbMATH DE number 1833869