Develops SPT with price impact, deriving formulas for wealth and arbitrage conditions.
problem Tackles price impact in high-dimensional markets.
method Incorporates nonlinear price impact and impact decay models.
result Derives master formula for trading strategies and wealth dynamics.
Optimizes trading in markets with unpredictable price impacts.
problem Optimizing trading strategies in markets with stochastic price impacts.
method Singular perturbation methods to approximate optimal control problem.
result Proves approximations are accurate to specified order using sub- and super-solutions.
Modeling market makers' quoting strategies to understand price impact.
problem Understanding how price impact arises from market makers' quoting strategies.
method Modeling market making as a dynamic auction using Stochastic Differential Games and finding Nash Equilibrium.
result The price impact function derived from market makers' strategies matches the Almgren-Chriss model.
Measures price impact in order-driven markets without relying on averages.
problem Measuring price impact in order-driven markets without relying on averages.
method Modeling the limit order book using state-dependent Hawkes processes and defining price impact profile as a function of the compensator of a stochastic process.
result The clustering of sell child orders has a bigger impact on price than their sizes.
Optimizes trading strategies with price impact, predictable returns, and stochastic volatility.
problem Dynamic portfolio optimization under complex market conditions.
method Multi-scale volatility expansion, singular and regular perturbations, asymptotic approximations.
result Improved portfolio strategy with reduced profit and loss (PnL) through corrections for small price impact.
Optimal liquidation strategy with price impact and signal exploitation.
problem Maximizing revenue-risk in a market with transient and temporary price impact.
method Infinite dimensional stochastic control approach, backward stochastic differential equation, operator-valued Riccati equation.
result Explicit expression for the optimal trading strategy.
We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in a price impact model. These conditions are stated as smoothness and boundedness requirements on utility functions or Malliavin differentiability of payoffs and endowments.
Study shows how multiple traders can trade together without excessive price impact.
problem Coordination issues in trading to exploit a common signal.
method Closed-loop Nash competition model for stochastic differential games.
result Excessive trading reduced but not significantly for practical parameters.
New model shows negative resilience can improve trading efficiency.
problem Optimal trade execution in limit order books with negative resilience.
method Stochastic order book model with negative resilience.
result Negative resilience can lead to more efficient trading.
Optimal trading strategy adapts to signals in markets with price impact.
problem Optimal liquidation in markets with linear price impact and predictive signals.
method Formulated as a stochastic control problem, solved using probabilistic and convex analytic techniques.
result Explicit solution for optimal trading strategy in terms of SDEs.
Develops a framework for valuing Asian options with market impact.
problem Valuation of Asian options under price impact.
method Discrete-time quote-level model, continuous-time limits, Hamilton-Jacobi-Bellman equations, CRR-style tree-based Bellman algorithm.
result Endogenous trading volumes feed into prices and costs, leading to nontrivial bid-ask spreads.
This paper deals with an optimal position management problem for a market maker who has to face uncertain customer order flows in an illiquid market, where the market maker's continuous trading incurs a stochastic linear price impact. Although the execution timing is uncertain, the market maker can also ask its OTC cou…
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 trading strategies for a trader who desires to liquidate his inventory but faces pr…
The paper applies thermodynamics to financial markets to prove no-arbitrage constraints.
problem No arbitrage in financial markets under price impact.
method Stochastic thermodynamics applied to financial trading cycles.
result Proves any round-trip trading strategy yields non-positive expected profit.
Study on Kyle's model with stochastic liquidity impacts asset volatility.
problem Impact of stochastic volatility of noise trading on asset volatility.
method Construct equilibrium for continuous-time Kyle's model with stochastic liquidity.
result In equilibrium, Kyle's Lambda and its inverse are submartingales.
Study on energy storage's impact on electricity prices and profitability.
problem Analyzing the profitability of energy storage in electricity markets.
method Characterized optimal operating strategy for storage systems, determined equilibrium price in a market with storage, renewables, and conventional producers, and characterized price process using stochastic differential equations.
result Increased average revenues and interquantile ranges for storage assets in energy transition scenarios.
Estimates cross-impact on derivatives markets using E-Mini futures and options.
problem Empirical estimation of cross-impact on complex financial instruments like derivatives.
method Modeling derivatives prices as a function of stochastic factors and trades on both factors and derivatives.
result Simple framework successfully captures cross-impact on derivatives markets.
Simulates financial market orders using anomalous diffusion models.
problem Anomalous diffusion in financial market order dynamics.
method Discrete Time Random Walk with Sibuya waiting times, non-uniform sampling, and cubic spline interpolation.
result Demonstrates price impact for different forcing functions and model parameters.
A new model adds stochastic spot/volatility correlation to Heston model for better exotic pricing.
problem Improving exotic option pricing in foreign exchange markets.
method Developed a Double Heston model with stochastic spot/volatility correlation, an affine model.
result The new model increases prices of out-of-the-money knockout options and one touch options.
Study optimal stock purchases under fluctuating market resilience.
problem Optimal stock purchases over time with varying market resilience.
method Model market resilience and liquidity variations, solve optimization problem.
result Unique optimal execution strategy found.
In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modelling framework extends the Heston stochastic volatility model by including the CIR stochastic interest rate and model paramete…
In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy,…
Optimal trading strategy under market resistance and concave price impact model.
problem Optimal trading in a market with endogenous resistance and concave price impact.
method Modeling market resistance, deriving a stochastic Fredholm equation, proving existence and uniqueness, proposing an iterative scheme.
result Existence and uniqueness of optimal control under certain conditions, exponential convergence of iterative scheme.
Algorithm maximizes revenue-risk by estimating price impact kernel and optimizing control problems.
problem Maximizing revenue-risk in a risky asset liquidation with unknown price impact.
method Alternates exploration and exploitation phases, uses novel kernel estimation and stability results.
result Sublinear regret achieved with high probability.
Modeling option market making with hedging-induced price impact.
problem Tackles the challenge of market making in options markets with price impact.
method Models option order flow using Cox processes and studies the dynamics of inventory and price under hedging-induced impact.
result Establishes the well-posedness of the mixed control problem involving quoting and hedging.
The study examines how brokers' identity affects their trading strategies on the Toronto Stock Exchange.
problem Impact of anonymous trading on brokers' optimal execution strategies.
method Formulated a stochastic differential game and mean-field game to analyze the optimal execution problem of anonymous and identity-revealed trading.
result Obtained a closed-form solution for the optimal strategy under Almgren-Chris price impact framework.
Optimal portfolio choice with cross-impact propagators, solving complex equations.
problem Maximizing revenue-risk in a continuous-time portfolio choice problem with cross-impact.
method Formulated as a maximization problem, solved explicitly using operator resolvents and stochastic Fredholm equations.
result Sufficient conditions for the absence of price manipulation, providing financial insights.
Game theory models how agents trade in a risky asset considering price impact and a common signal.
problem Modeling how financial agents liquidate assets in a risky market with price impact and a common signal.
method Formulated and solved a multi-player stochastic differential game and mean field game.
result Equilibrium strategies reveal how agents adjust the predictive trading signal to price impact.
Study shows how adaptive market agents can lead to persistent overpricing in financial markets.
problem Persistent overpricing in financial markets by adaptive market agents.
method Analyzes a repeated game between market maker and market taker, decomposes the game into competitive and collaborative components, and uses projected stochastic gradient ascent.
result Decentralized learning by adaptive market agents can lead to persistent overpricing in financial markets.
We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal str…
We analyze a market impact game between n risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in t…
ICON-OCnet solves optimal execution problems with neural networks and few examples.
problem Optimal order execution in markets with unknown price impact.
method Transformer-based neural network architecture (ICON-OCnet) that learns price impact from few examples and applies it to optimal execution strategies.
result ICON-OCnet accurately infers price impact models and retrieves optimal execution strategies for various propagator kernels.
Optimal trading strategy derived for nonlinear price impact models.
problem Optimal trading with nonlinear price impact induced by alpha signals.
method Variational approach, nonlinear Fredholm equation, iterative scheme.
result Existence and uniqueness of optimal trading strategy under monotonicity condition.
An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth. In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general Markovian setting allowing for stochastic market, cost, and preference parameters. Thes…
Study uses machine learning to optimize stock trading strategies.
problem Optimizing stock trading strategies with machine learning.
method Dynamic programming and deep learning for nonlinear price impact.
result NN surrogates accurately approximate optimal strategies.
This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in a frictionless market, traders cannot be perfectly hedged because of execution …
The paper develops a hybrid model for optimal order execution in markets with heterogeneous market makers.
problem Optimal liquidation in markets with limited inventory and risk capacity.
method Derives a reduced form model for aggregated inventory dynamics considering price impact.
result Optimal execution can be modeled as a linear-quadratic stochastic control problem.
Model predicts BESS interactions and price impacts in energy markets.
problem Understanding BESS interactions and price formation in energy markets.
method Stochastic game-theoretic model with linear-quadratic differential game.
result Equilibrium controls and prices derived for BESSs in both heterogeneous and homogeneous settings.
Within a financial model with linear price impact, we study the problem of hedging a covered European option under gamma constraint. Using stochastic target and partial differential equation smoothing techniques, we prove that the super-replication price is the viscosity solution of a fully non-linear parabolic equatio…
We study an optimal execution problem in illiquid markets with both instantaneous and persistent price impact and stochastic resilience when only absolutely continuous trading strategies are admissible. In our model the value function can be described by a three-dimensional system of backward stochastic differential eq…
Optimizes Ethena's yield strategy by controlling stETH and ETH futures positions.
problem Maximizes Ethena's yield while managing price impacts.
method Formulates and solves stochastic control problems for Ethena's yield-generating strategy.
result Explicitly determines optimal control rates for stETH and ETH futures.
We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function we adopt a g-expectation. In contrast to the standard framework of financial engineering, a trader is no more price taker as any trade has a permanent market impact via a…
We study the effect of parameters uncertainties on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, thanks to Dirichlet Forms methods. We apply recent techniques, developed by Bouleau, to hedging procedures in order to compute the sensitivities of SDE trajectories with respect…
The paper studies projections of asset prices under equivalent martingale measures.
problem Understanding the impact of information on asset price bubbles and arbitrage opportunities.
method Analyzes optional projections of local martingales into a smaller filtration under equivalent martingale measures.
result Provides general results and specific examples like inverse Bessel process and stochastic volatility models.
We solve a complex trade execution problem by simplifying it into a known LQ control problem.
problem Optimal trade execution with stochastic price impact and resilience.
method Extending the problem to progressively measurable processes and reducing it to a LQ stochastic control problem.
result The solution to the LQ problem traces back to the solution of the original trade execution problem.
Price impact of a trade is an important element in pre-trade and post-trade analyses. We introduce a framework to analyze the market price of liquidity risk, which allows us to derive an inhomogeneous Bernoulli ordinary differential equation. We obtain two closed form solutions, one of which reproduces the linear funct…
The paper analyzes trade execution strategies for large traders in a stochastic market environment.
problem Analyzing trade execution strategies in a stochastic market with price impact.
method Formulated a Markov game model and used backward induction method of dynamic programming.
result Explicit closed-form execution strategy at Markov perfect equilibrium.
Study optimal liquidation with incomplete trend information and multiplicative price impact.
problem Optimal liquidation of assets with incomplete trend information and multiplicative price impact.
method Singular stochastic control problem with finite-fuel constraint and partial observation. Equivalent three-dimensional degenerate problem under full information. Two-dimensional optimal stopping problem with belief-dependent free boundary.
result Optimal execution rule and value function expressed in terms of a nonlinear integral equation, solved through Monte-Carlo method.