Institute of Mathematical Statistics Lecture Notes - Monograph Series

Price systems for markets with transaction costs and control problems for some finance problems

Tzuu-Shuh Chiang, Shang-Yuan Shiu, and Shuenn-Jyi Sheu

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Abstract

In a market with transaction costs, the price of a derivative can be expressed in terms of (preconsistent) price systems (after Kusuoka (1995)). In this paper, we consider a market with binomial model for stock price and discuss how to generate the price systems. From this, the price formula of a derivative can be reformulated as a stochastic control problem. Then the dynamic programming approach can be used to calculate the price. We also discuss optimization of expected utility using price systems.

Chapter information

Source
Hwai-Chung Ho, Ching-Kang Ing, Tze Leung Lai, eds., Time Series and Related Topics: In Memory of Ching-Zong Wei (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 257-271

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196285980

Digital Object Identifier
doi:10.1214/074921706000001094

Mathematical Reviews number (MathSciNet)
MR2427853

Zentralblatt MATH identifier
1268.91161

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
dynamic programming duality method price system pricing derivatives portfolio optimization stochastic control transaction cost

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Chiang, Tzuu-Shuh; Shiu, Shang-Yuan; Sheu, Shuenn-Jyi. Price systems for markets with transaction costs and control problems for some finance problems. Time Series and Related Topics, 257--271, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000001094. https://projecteuclid.org/euclid.lnms/1196285980


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