Related papers: Optimal incentives in a limit order book: a SPDE c…
We consider the problem of devising incentive strategies for viral marketing of a product. In particular, we assume that the seller can influence penetration of the product by offering two incentive programs: a) direct incentives to…
We consider impulse control problems in finite horizon for diffusions with decision lag and execution delay. The new feature is that our general framework deals with the important case when several consecutive orders may be decided before…
In this work we investigate the inefficiency of the electricity system with strategic agents. Specifically, we prove that without a proper control the total demand of an inefficient system is at most twice the total demand of the optimal…
We consider a one-period Kyle (1985) framework where the insider can be subject to a penalty if she trades. We establish existence and uniqueness of equilibrium for virtually any penalty function when noise is uniform. In equilibrium, the…
We consider a finite-horizon market-making problem faced by a dark pool that executes incoming buy and sell orders. The arrival flow of such orders is assumed to be random and, for each transaction, the dark pool earns a per-share…
Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models self-exciting behaviour of the price impact,…
This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules…
The modeling of the limit order book is directly related to the assumptions on the behavior of real market participants. This paper is twofold. We first present empirical findings that lay the ground for two improvements to these models.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…
In this paper we derive a scaling limit for an infinite dimensional limit order book model driven by Hawkes random measures. The dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume…
In this paper, we rigorously study the problem of cost optimisation of hybrid (mixed) institutional incentives, which are a plan of actions involving the use of reward and punishment by an external decision-maker, for maximising the level…
We consider optimal control of a new type of non-local stochastic partial differential equations (SPDEs). The SPDEs have space interactions, in the sense that the dynamics of the system at time $t$ and position in space x also depend on the…
We develop a mixed control framework that combines absolutely continuous controls with impulse interventions subject to stochastic execution delays. The model extends current impulse control formulations by allowing (i) the controller to…
We model incentive security in non-custodial stablecoins and derive conditions for participation in a stablecoin system across risk absorbers (vaults/CDPs) and holders of governance tokens. We apply option pricing theory to derive closed…
We consider systems of diffusion processes ("particles") interacting through their ranks (also referred to as "rank-based models" in the mathematical finance literature). We show that, as the number of particles becomes large, the process…
This paper investigates numerical methods for solving stochastic linear quadratic (SLQ) optimal control problems governed by stochastic partial differential equations (SPDEs). Two distinct approaches, the open-loop and closed-loop ones, are…
We develop dual approaches for continuous-time stochastic control problems, enabling the computation of robust dual bounds in high-dimensional state and control spaces. Building on the dual formulation proposed in [L. C. G. Rogers, SIAM…
The system operator's scheduling problem in electricity markets, called unit commitment, is a non-convex mixed-integer program. The optimal value function is non-convex, preventing the application of traditional marginal pricing theory to…
This paper conducts an empirical investigation into the effects of Designated Market Makers (DMMs) on key market quality indicators, such as liquidity, bid-ask spreads, and order fulfillment ratios. Through agent-based simulations, this…
This paper explores the bifurcative dynamics of an artificial stock market exchange (ASME) with endogenous, myopic traders interacting through a limit order book (LOB). We showed that agent-based price dynamics possess intrinsic…