Related papers: Mathematical Formulation of an Optimal Execution P…
Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model's implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision…
We use a white noise approach to study the problem of optimal inside control of a stochastic delay equation driven by a Brownian motion B and a Poisson random measure N. In particular, we use Hida-Malliavin calculus and the Donsker delta…
The paper considers the optimal control problem of inventory of a discrete product in regeneration scheme with a Poisson flow of customer requirements. In the system deferred demand is allowed, the volume of which is limited by a given…
In this note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions' Lemma for deterministic problems,…
This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances. Necessary and sufficient conditions for output agreement are derived for the class of incrementally passive…
We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on…
We consider the stochastic control problem of a financial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
We assume a continuous-time price impact model similar to Almgren-Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop…
Minimizing execution costs for large orders is a fundamental challenge in finance. Firms often depend on brokers to manage their trades due to limited internal resources for optimizing trading strategies. This paper presents a methodology…
In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…
We study optimal trade execution strategies in financial markets with discrete order flow. The agent has a finite liquidation horizon and must minimize price impact given a random number of incoming trade counterparties. Assuming that the…
This work takes up the challenges of utility maximization problem when the market is indivisible and the transaction costs are included. First there is a so-called solvency region given by the minimum margin requirement in the problem…
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are…
We study a multiplicative transient price impact model for an illiquid financial market, where trading causes price impact which is multiplicative in relation to the current price, transient over time with finite rate of resilience, and…
The main objective of this paper is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying incomplete preferences driven by externalities such as…
In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option…
We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes…
In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of…
We study discrete-time predictable forward processes when trading times do not coincide with performance evaluation times in a binomial tree model for the financial market. The key step in the construction of these processes is to solve a…