Risk sensitive asset management with transaction costs
type: Item
instance of: scholarly article
title: Risk sensitive asset management with transaction costs
zbMATH Open document ID: 0982.91024
author: Stanley R. Pliska
author: Tomasz R. Bielecki
published in: Finance and Stochastics
publication date: 2000-05-24T00:00:00Z
review text: The mathematical problem of optimally managing a portfolio of securities when there are transaction costs has received considerable research attention in recent years. For the classical problem, where the objective is to maximize expected utility of terminal wealth, most of the attention has been devoted to the case of proportional costs, that is, to the case where the cost associated with a transaction is proportional to the amount of money that is shifted between the securities. Typically, the optimal strategy is characterized by a no-trade region with trading that is essentially continuous on its boundary used to keep a certain process contained in the region. Other approaches assumed the transaction cost has a fixed component, thereby precluding the optimality of continuous trading. Some authors applied the theories of optimal stopping and quasi-variational inequalities to two portfolio management problems, both involving two assets (a bank account with interest rate zero and a geometric Brownian motion stock) and transaction costs. In all of this researches the assets are modelled with conventional stochastic differential equations. The only physical processes being modeled are the assets themselves along with the bank account and its short term interest rate. Moreover, there is no explicit dependence of the asset processes on this interest rate. Meanwhile, several authors have developed transaction-free optimal portfolio models where the asset processes explicitly depend on underlying economic factors which are also explicitly modeled with stochastic differential equations. This paper develops a continuous time risk-sensitive portfolio optimization model with a general transaction cost structure and where the individual securities or asset categories are explicitly affected by underlying economic factors. The security prices and factors follow diffusion processes with the drift and diffusion coefficients for the securities being functions of the factor levels.…
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 49N25
zbMATH DE Number: 1452412
zbMATH Keywords: risk-sensitive impulsive stochastic control
zbMATH Keywords: quasi-variational inequalities
zbMATH Keywords: optimal portfolio selection
zbMATH Keywords: incomplete markets
zbMATH Keywords: transaction costs
MaRDI profile type: Publication
full work available at URL: s007800050001
OpenAlex ID: W1997640190
DOI: 10.1007/S007800050001
description: scientific article; zbMATH DE number 1452412