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A model for a large investor trading at market indifference prices. II: Continuous-time case

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  • Peter Bank
  • Dmitry Kramkov

Abstract

We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In this model, the market makers compete with their quotes for the investor's orders and trade among themselves to attain Pareto optimal allocations. We first consider the case of simple strategies and then, in analogy to the construction of stochastic integrals, investigate the transition to general continuous dynamics. As a result, we show that the model's evolution can be described by a nonlinear stochastic differential equation for the market makers' expected utilities.

Suggested Citation

  • Peter Bank & Dmitry Kramkov, 2011. "A model for a large investor trading at market indifference prices. II: Continuous-time case," Papers 1110.3229, arXiv.org, revised Sep 2015.
  • Handle: RePEc:arx:papers:1110.3229
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    References listed on IDEAS

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    1. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    2. Peter Bank & Dietmar Baum, 2004. "Hedging and Portfolio Optimization in Financial Markets with a Large Trader," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 1-18.
    3. Grossman, Sanford J & Miller, Merton H, 1988. " Liquidity and Market Structure," Journal of Finance, American Finance Association, vol. 43(3), pages 617-637, July.
    4. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84.
    5. U. Çetin & R. Jarrow & P. Protter & M. Warachka, 2008. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 9, pages 185-221 World Scientific Publishing Co. Pte. Ltd..
    6. Peter Bank & Dmitry Kramkov, 2013. "The stochastic field of aggregate utilities and its saddle conjugate," Papers 1310.7280, arXiv.org.
    7. Nicolae Garleanu & Lasse Heje Pedersen & Allen M. Poteshman, 2009. "Demand-Based Option Pricing," Review of Financial Studies, Society for Financial Studies, vol. 22(10), pages 4259-4299, October.
    8. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
    9. Bank, Peter & Kramkov, Dmitry, 2013. "On a stochastic differential equation arising in a price impact model," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1160-1175.
    10. Stoll, Hans R, 1978. "The Supply of Dealer Services in Securities Markets," Journal of Finance, American Finance Association, vol. 33(4), pages 1133-1151, September.
    11. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
    12. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    13. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183 World Scientific Publishing Co. Pte. Ltd..
    14. Peter Bank & Dmitry Kramkov, 2011. "A model for a large investor trading at market indifference prices. I: single-period case," Papers 1110.3224, arXiv.org, revised Dec 2013.
    15. Kerry Back & Shmuel Baruch, 2004. "Information in Securities Markets: Kyle Meets Glosten and Milgrom," Econometrica, Econometric Society, vol. 72(2), pages 433-465, March.
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    Citations

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    Cited by:

    1. Peter Bank & Selim Gökay, 2016. "Superreplication when trading at market indifference prices," Finance and Stochastics, Springer, vol. 20(1), pages 153-182, January.
    2. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2017. "American options in an imperfect market with default," Papers 1708.08675, arXiv.org.
    3. Peter Bank & Dmitry Kramkov, 2015. "A model for a large investor trading at market indifference prices. I: Single-period case," Finance and Stochastics, Springer, vol. 19(2), pages 449-472, April.
    4. Masaaki Fukasawa, 2014. "Efficient price dynamics in a limit order market: an utility indifference approach," Papers 1410.8224, arXiv.org.
    5. Peter Bank & Selim Gökay, 2016. "Superreplication when trading at market indifference prices," Finance and Stochastics, Springer, vol. 20(1), pages 153-182, January.
    6. repec:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-017-0352-4 is not listed on IDEAS

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