A MODEL FOR A LARGE INVESTOR TRADING AT MARKET INDIFFERENCE PRICES. II: CONTINUOUS-TIME CASE

被引：13
|
作者：
Bank, Peter [1 ]
Kramkov, Dmitry [2 ]
机构：
[1] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany
[2] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
来源：
ANNALS OF APPLIED PROBABILITY | 2015年 / 25卷 / 05期
基金：
美国安德鲁·梅隆基金会;
关键词：
Bertrand competition; contingent claims; equilibrium; indifference prices; liquidity; large investor; Pareto allocation; price impact; saddle functions; nonlinear stochastic integral; random field; FUNDAMENTAL THEOREM; LIQUIDITY; OPTIONS; RISK;
D O I：
10.1214/14-AAP1059
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
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页码：2708 / 2742
页数：35
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