A model for a large investor trading at market indifference prices. I: Single-period case

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• 作者：Peter Bank ; Dmitry Kramkov
• 关键词：Aggregate utility function ; Bertrand competition ; Demand pressure ; Equilibrium ; Large investor ; Liquidity ; Pareto allocation ; Price impact ; Risk tolerance ; Utility indifference prices ; 52A41 ; 60G60 ; 91G10 ; 91G20 ; G11 ; G12 ; G13 ; C61
• 刊名：Finance and Stochastics
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：19
• 期：2
• 页码：449-472
• 全文大小：780 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Quantitative Finance
  Finance and Banking
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Economic Theory
  Probability Theory and Stochastic Processes
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1122

文摘

We develop a single-period model for a large economic agent who trades with market makers at their utility indifference prices. We compute the sensitivities of these market indifference prices with respect to the size of the investor’s order. It turns out that the price impact of an order is determined both by the market makers-joint risk tolerance and by the variation of individual risk tolerances. On a technical level, a key role in our analysis is played by a pair of conjugate saddle functions associated with the description of Pareto optimal allocations in terms of the aggregate utility function.