Li, Cheng
(2016)
Three aspects of mathematical models for asymmetric information in financial market.
PhD thesis, London School of Economics and Political Science.
Abstract
The thesis consists of three parts. The first part studies the Glosten-Milgrom model [25] where the risky asset value admits an arbitrary discrete distribution. In contrast to existing results on insider model, the insiders optimal strategy in this model, if it exists, is not of feedback type. Therefore, a weak formulation of equilibrium is proposed. In this weak formulation, the inconspicuous trade theorem still holds, but the optimality for the insiders strategy is not enforced. However, the insider can employ some feedback strategies whose associated expected profit are close to the optimal value, when the order size is small. Moreover, this discrepancy converges to zero when the order size diminishes.
The second part extends Peng’s monotone convergence result [37] to backward stochastic differential equations (BSDEs in short) driven by marked point processes. We apply this result to give a stochastic representation to the value function of the insiders problem in the previous part.
The last part studies an optimal trading problem in limit order market with asymmetry information. The market consists of a strategic trader and a group of noisy traders. The strategic trader has private prediction on the fundamental value of a risk asset, and aims to maximise her expected profit. Both types of market participants are allowed to place market and limit orders. We aim to find a trading strategy for the strategic trader who uses both limit and market orders. This is formulated as a stochastic control problem that we characterise in terms of a HJB system. We also provide a numerical algorithm to obtain its solution and prove its convergence. Finally, we consider an example to illustrate the optimal trading strategy of the strategic trader.
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