Bounds on process of contingent claims in an intertemporal economy with proportional transaction costs and general preferences
type: Item
instance of: scholarly article
title: Bounds on process of contingent claims in an intertemporal economy with proportional transaction costs and general preferences
zbMATH Open document ID: 0935.91014
author: George M. Constantinides
author: Thaleia Zariphopoulou
published in: Finance and Stochastics
publication date: 2000-03-01T00:00:00Z
review text: The authors consider an economy with two securities, a bond with price \(B(t)\) and stock with price \(S(t)\) at time \(t\geq 0\). The bond pays no coupons, is default free and has price dynamics \(B_{t}=e^{rt}B_0\), \(t\geq 0\), where \(r\) is the constant rate of interest. The stock price is the diffusion process \[ S_{t}=S_0\exp\left\{\left( \mu-{\sigma^2\over 2}\right)t+ \sigma W_{t}\right\}, \] where the mean rate of return \(\mu\) and the volatility \(\sigma\) are constants such that \(\mu>r\), \(\sigma\neq 0\), \(W_{t}\) is a one-dimensional standard Brownian motion. The investor holds \(x_{t}\) dollars of the bond and \(y_{t}\) dollars of the stock at date \(t\), and consumes at the rate \(c_{t}\) dollars out of the bond account. The stock account process, starting with \(y_0=y\), is \[ y_{t}=y+\int_0^{t}\mu y_{\tau} d\tau+ \int_0^{t}\sigma y_{\tau} dW_{\tau} +L_{t}-M_{t}, \] where \(L_{t}\) represents the cumulative dollar amount transferred into the stock account and \(M_{t}\) the cumulative dollar amount transferred out of the stock account, \(L_0=M_0=0\). The bond account process, starting with \(x_0=x\), is \[ x_{t}=x+\int_0^{t}\{r x_{\tau} -c_{\tau}\} d\tau-\beta L_{t}+\alpha M_{t},\quad 0<\alpha<1<\beta. \] Analytic bounds on the reservation write price of European-type contingent claims are derived. The option prices are obtained via a utility maximization approach by comparing the maximized utilities with and without the contingent claim.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 1408676
zbMATH Keywords: contingent claim prices
zbMATH Keywords: bounds on prices
zbMATH Keywords: transaction costs
zbMATH Keywords: viscosity solutions
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
full work available at URL: s007800050066
OpenAlex ID: W2114589695
DOI: 10.1007/S007800050066
description: scientific article; zbMATH DE number 1408676