We define a stochastic model of a two-sided limit order book in terms of its key quantities \textit{best bid [ask] price} and the \textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps the expected volume rate over the considered price...

This paper studies a one-sided limit order book (LOB) model, in which the order dynamics depend on both, the current best bid price and the current volume density function. For the joint dynamics of the best bid price and the standing buy volume density we derive a weak law of large numbers,...

We study a constrained optimal control problem allowing for degenerate coefficients. The coefficients can be random and then the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singular terminal condition. For this degenerate BSPDE, we...

We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a...

One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate. This agent-based viewpoint in finance goes back at least...

We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling inert investors. With a suitable scaling, we show that...

In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework within which to value derivatives under market impact in a multi-player framework by introducing strategic...

We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have exponential utility functions and the individual endowments are...

In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. The presence of ties in the agents' best-response correspondences yields...

We analyze conditional optimization problems arising in discrete time Principal-Agent problems of delegated portfolio optimization. Applying tools from Conditional Analysis to the case of linear contracts we show that most results known in the literature for very specific instances of the...