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

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Listed:
  • Tzuu-Shuh Chiang
  • Shang-Yuan Shiu
  • Shuenn-Jyi Sheu

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.

Suggested Citation

  • Tzuu-Shuh Chiang & Shang-Yuan Shiu & Shuenn-Jyi Sheu, 2007. "Price systems for markets with transaction costs and control problems for some finance problems," Papers math/0702828, arXiv.org.
    • Handle: RePEc:arx:papers:math/0702828
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    References listed on IDEAS

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    1. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    2. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    3. Nizar Touzi, 1999. "Super-replication under proportional transaction costs: From discrete to continuous-time models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 297-320, October.
    4. HuyËn Pham & Nizar Touzi & Jaksa Cvitanic, 1999. "A closed-form solution to the problem of super-replication under transaction costs," Finance and Stochastics, Springer, vol. 3(1), pages 35-54.
    5. Yuri M. Kabanov & Günter Last, 2002. "Hedging under Transaction Costs in Currency Markets: a Continuous‐Time Model," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 63-70, January.
    6. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
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