Related papers: Optimal market making with persistent order flow
We study the price-setting problem of market makers under risk neutrality and perfect competition in continuous time. Thereby we follow the classic Glosten-Milgrom model that defines bid and ask prices as expectations of a true value of the…
We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…
We consider a utility maximization problem in a broad class of markets. Apart from traditional semimartingale markets, our class of markets includes processes with long memory, fractional Brownian motion and related processes, and, in…
In this paper, we consider a company can simultaneously reduce its emissions and buy carbon allowances at any time. We establish an optimal control model involving two stochastic processes with two control variables, which is a singular…
We consider a deterministic continuous time model of monopolistic firm, which chooses production and pricing strategies of a single good. Firm's goal is to maximize the discounted profit over infinite time horizon. The no-backlogging…
Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize…
Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on…
This working paper presents a comprehensive study on the development and analysis of various electricity market models, focusing on continuous, discrete, and fractional-order approaches. The continuous model captures the ongoing…
We show that non-dominated sorting of a sequence of i.i.d. random variables in Euclidean space has a continuum limit that corresponds to solving a Hamilton-Jacobi equation involving the probability density function of the random variables.…
This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss, or only on the liquidity-consuming orders like Obizhaeva and Wang,…
We develop an axiomatic theory for Automated Market Makers (AMMs) in local energy sharing markets and analyze the Markov Perfect Equilibrium of the resulting economy with a Mean-Field Game. In this game, heterogeneous prosumers solve a…
We consider a simple model for the evolution of a limit order book in which limit orders of unit size arrive according to independent Poisson processes. The frequencies of buy limit orders below a given price level, respectively sell limit…
Statistical mechanics provides a useful analog for understanding the behavior of complex adaptive systems, including electric power markets and the power systems they intend to govern. Market-based control is founded on the conjecture that…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…
We consider an optimal control problem for a non-autonomous model of ODEs that describes the evolution of the number of customers in some firm. Namely we study the best marketing strategy. Considering a $L^2$ cost functional, we establish…
In this paper, we study the optimal singular controls for stochastic recursive systems, in which the control has two components: the regular control, and the singular control. Under certain assumptions, we establish the dynamic programming…
We introduce a modular framework for market making. It combines cost-function based automated market makers with bandit algorithms. We obtain worst-case profits guarantee's relative to the best in hindsight within a class of natural…
In optimal control problems of control-affine systems, whose solutions are bang-bang or singular type, verification of optimality using the Hamilton-Jacobi-Bellman (HJB) equation involves the computation of partial derivatives of switching…
We consider an infinite horizon discounted optimal control problem for piecewise deterministic Markov processes, where a piecewise open-loop control acts continuously on the jump dynamics and on the deterministic flow. For this class of…
We focus on the problem of market making in high-frequency trading. Market making is a critical function in financial markets that involves providing liquidity by buying and selling assets. However, the increasing complexity of financial…