Related papers: Trading constraints in continuous-time Kyle models
This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This…
We study a continuous time economy where throughout time, insiders receive private signals regarding the risky assets' terminal payoff. We prove existence of a partial communication equilibrium where, at each private signal time, the public…
We study superreplication of European contingent claims in discrete time in a large trader model with market indifference prices recently proposed by Bank and Kramkov. We introduce a suitable notion of efficient friction in this framework,…
A new definition of events of game-theoretic probability zero in continuous time is proposed and used to prove results suggesting that trading in financial markets results in the emergence of properties usually associated with randomness.…
We study a time-inconsistent singular control problem originating from irreversible reinsurance decisions with non-exponential discount. A novel definition of equilibrium for time-inconsistent singular control problems is introduced. For…
In this paper, which is a continuation of the previously published discrete time paper we develop a theory for continuous time stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a…
In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
We investigate a market with a normal-speed informed trader (IT) who may employ mixed strategy and multiple anticipatory high-frequency traders (HFTs) who are under different inventory pressures, in a three-period Kyle's model. The pure-…
We study a multi-player stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed-loop Nash equilibrium…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…
In real-world control applications, actuator constraints and output constraints (specifically in tracking problems) are inherent and critical to ensuring safe and reliable operation. However, generally, control strategies often neglect…
We present a mathematical model of a market with $m$ shares traded across $n$ investor groups, each one with similar motivations and trading strategies. The market of each asset consists of a fixed amount of cash and shares (no additions…
The flow of contracting systems contracts 1-dimensional parallelotopes, i.e., line segments, at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…
We study $N$-player optimal execution games in an Obizhaeva--Wang model of transient price impact. When the game is regularized by an instantaneous cost on the trading rate, a unique equilibrium exists and we derive its closed form. Whereas…
In a fixed time horizon, appropriately executing a large amount of a particular asset -- meaning a considerable portion of the volume traded within this frame -- is challenging. Especially for illiquid or even highly liquid but also highly…
The paper develops no arbitrage results for trajectory based models by imposing general constraints on the trading portfolios. The main condition imposed, in order to avoid arbitrage opportunities, is a local continuity requirement on the…
We study optimal liquidation of a trading position (so-called block order or meta-order) in a market with a linear temporary price impact (Kyle, 1985). We endogenize the pressure to liquidate by introducing a downward drift in the…