Study of new models for insider trading and impulse control

This thesis presents the development and study of two stochastic models. The first one is an equilibrium model for a market involving risk-averse insider trading. In particular, the static information model is considered under new assumptions: a) the insider is risk-averse, b) the signal received by the insider is not necessarily Gaussian, and c) the price set by the market maker is a function of a weighted signal that is not necessarily Gaussian either. Conditions on the weighting and pricing functions ensuring the existence of equilibrium are discussed. Equilibrium pricing and weighting functions as well as the insider’s optimal trading strategy are derived. Furthermore, the influence of the risk aversion on the equilibrium outcome is investigated. The second model studied, we derive the explicit solution to an impulse control problem with non-linear penalisation of control expenditure. This solution has several features that are not present in impulse control problems with affine penalisation of control effort. The state dependence of the free-boundaries characterising the optimal strategy is the first one. The possibility for the so-called continuation region to not be an interval and the optimal strategy to involve multiple simultaneous jumps while the problem data is convex are further such aspects.