Model calculates optimal trading time for derivatives orders.
problem Balancing execution costs and market risks in large order execution.
method Time Is Money model using Bachelier model and central limit order book.
result Demonstrates a continuous-time Arrival Price framework.
A new model for heterogeneous populations optimizes consumption and investment over short horizons.
problem Optimizing consumption and investment in economies with a heterogeneous population over short time periods.
method Continuous-time general equilibrium framework with Brownian flow on a type space, solving vanishing-horizon problems under relative-income criteria.
result Existence and characterization of short-horizon Duesenberry equilibrium, with sharp asset-pricing implications.
For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We identify these quantities as…
Study on optimal trading in a finite population with market frictions and asymmetric information.
problem Optimal trading in a finite population with market frictions and asymmetric information.
method Investigates stochastic differential games with asymmetric information and market frictions, proving existence and uniqueness of Nash and Stackelberg-Nash equilibria.
result Existence and uniqueness of Nash and Stackelberg-Nash equilibria in both unconstrained and constrained trading scenarios.
Study Nash equilibrium between broker and informed trader in dealer and lit markets.
problem Nash equilibrium between broker and informed trader in dealer and lit markets with partial information.
method Convex analysis, FBSDEs, polynomial approximation.
result Existence and uniqueness of Nash equilibrium for short time horizons.
Enhanced pairs trading with Black-Litterman model outperforms market indexes.
problem Underperformance of pairs trading in volatile or distressed markets.
method Integrated Black-Litterman model with pairs trading strategy.
result Superior performance compared to S\&P 500 index under various market conditions.
We study in detail and explicitly solve the version of Kyle's model introduced in a specific case in \cite{BB}, where the trading horizon is given by an exponentially distributed random time. The first part of the paper is devoted to the analysis of time-homogeneous equilibria using tools from the theory of one-dimensi…
Equilibrium found for multi-agent trading with transaction costs.
problem Designing a trading equilibrium for multiple agents with transaction costs.
method Proving the existence of a continuous-time Radner equilibrium with incentives and transaction costs.
result Each agent optimally trades for a specific time interval before stopping, influenced by transaction costs.
Kyle's equilibrium model stability proven for 1-2 trading times, but not for 3 or more.
problem Stability of Kyle's equilibrium model in a dynamic trading setting.
method Proof of stability for 1-2 trading times, non-stability for 3 or more trading times, independent of input parameters.
result Kyle's equilibrium model is stable for 1-2 trading times but not for 3 or more trading times.
Generalizes insider trading model to multiple assets.
problem Modeling informed trading in a multi-asset context.
method Formulated an infinite-dimensional Bayesian trading game.
result Obtained a parsimonious equilibrium with closed-form solutions.
Model predicts trading strategies based on latent demand and price impact.
problem Predicting strategic trading behavior of investors with private targets.
method Equilibrium model of dynamic trading, learning, and pricing by strategic investors.
result Trading strategies are a combination of target following, liquidity provision, and front-running based on latent demand and price pressure.
Study how transaction costs impact stock returns and holdings in equilibrium.
problem Impact of quadratic transaction costs on equilibrium stock returns and holdings.
method Developed a continuous-time risk-sharing model with FBSDEs to characterize equilibrium stock holdings and trading rates.
result Equilibrium stock holdings and trading rates are uniquely determined by FBSDEs, and equilibrium return by a system of coupled FBSDEs.
Modeling trading behavior with information signals and limit order books, showing market impact and equilibrium properties.
problem Analyzing the impact of information signals on trading behavior and market equilibrium in limit order books.
method Static equilibrium model with profit-maximizing investors and competitive dealers, using iterative algorithms and asymptotic analysis.
result The market impact of large trades follows a power law with fat tails and a logarithmic law with lighter tails, and the order book flattens as noise trading increases.
The paper analyzes trade dynamics among G7 countries, revealing unequal exchange and degenerate equilibrium states.
problem Unequal exchange and degenerate equilibrium states in international trade among G7 countries.
method Analysis based on a model of international trade with supply and demand structures.
result Found relative equilibrium price vector is very degenerate, indicating unequal exchange.
The paper finds optimal levels for traders in mean-reverting markets.
problem Determining optimal levels for traders in mean-reverting markets.
method Analytical framework using heat potentials.
result Developed an analytical solution for optimal levels.
In this paper, we propose an equilibrium pricing model in a dynamic multi-period stochastic framework with uncertain income streams. In an incomplete market, there exist two traded risky assets (e.g. stock/commodity and weather derivative) and a non-traded underlying (e.g. temperature). The risk preferences are of expo…
We propose a stylized model of production and exchange in which long-term investors set their production decision over a horizon τ , the "time to produce", and are liquidity constrained, while financial investors trade over a much shorter horizon δ (<< τ ) and are therefore more duly informed on the exogenous shocks af…
Since they were authorized by the U.S. Security and Exchange Commission in 1998, electronic exchanges have boomed, and by 2010 high frequency trading accounted for over 70% of equity trades in the US. Such markets are thought to increase liquidity because of the presence of market makers, who are willing to trade as co…
Study Nash equilibrium between broker and trader in a lit exchange with price impact.
problem Optimizing trading strategies between informed and uninformed traders with broker's inventory penalties.
method Characterized Nash equilibrium through FBSDEs, solved explicitly.
result Explicit solution to trading strategies of broker and informed trader.
Insider trading is reduced when penalized, affecting expected penalties in a non-monotone way.
problem Reducing insider trading behavior when insiders face legal penalties.
method Characterized via a backward stochastic differential equation (BSDE) with a non-linear operator.
result The insider's expected penalties are non-monotone in the fee structure and determined by relative entropy.
Modeling insider trading with transaction costs and fair pricing.
problem Maximizing profits for an informed trader in a market with transaction costs and fair pricing.
method Single auction model and continuous time analogue, analyzing equilibrium behavior with polynomial and differential equations.
result Equilibrium trading strategy and pricing rules are affected by transaction costs, revealing an information gap.
We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon and analyze the effect of transaction costs on the endogenously determined interest rate. Two agents receive exogenous, unspanned income and choose between consumption and investing into an annuity.…
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.
We analyze a family of portfolio management problems under relative performance criteria, for fund managers having CARA or CRRA utilities and trading in a common investment horizon in log-normal markets. We construct explicit constant equilibrium strategies for both the finite population games and the corresponding mea…
This paper investigates the equilibrium interactions between trading targets and private information in a multi-period Kyle (1985) market. There are two investors who each follow dynamic trading strategies: A strategic portfolio rebalancer who engages in order splitting to reach a cumulative trading target and an uncon…
Model shows how price impact and transaction costs affect trading behavior and profits.
problem Analyzing trading behavior and profits in markets with transaction costs and price impact.
method Proves the existence of an equilibrium in a model with transaction costs and price impact.
result Existence of a strictly positive optimal transaction cost from the exchange's perspective.
Continuous-time model shows insider trading constraints impact market dynamics.
problem Trading constraints faced by insiders in continuous-time models.
method Proved global existence of equilibrium with terminal trading constraint.
result Equilibrium model aligns with empirical market behaviors.
In this paper, we introduce a novel, non-recursive, maximal matching algorithm for double auctions, which aims to maximize the amount of commodities to be traded. It differs from the usual equilibrium matching, which clears a market at the equilibrium price. We compare the two algorithms through experimental analyses, …
Study optimal execution in a transient price impact model with multiple traders.
problem Optimal execution among multiple traders with transient price impact.
method Analyzed N-player optimal execution games in an Obizhaeva--Wang model with and without regularization. Derived equilibrium solutions and explained their behavior. result Existence of equilibrium restored with a specific time-dependent cost on block trades, and equilibrium is tractable.
The study examines when large trades are considered news or liquidity shocks in a market model.
problem Understanding when large trades are news or liquidity shocks in a market model.
method A sequential competitive limit order book model with asymmetric information and Student-t tails for liquidity demand.
result Heavy-tailed liquidity demand flattens and concavifies price impact, delaying price discovery.
Solves expert prediction problem for 4 experts in finite time horizon.
problem Expert prediction problem in finite horizon with 4 experts.
method Solves nonlinear PDE, shows C2 solution, proves Nash equilibrium and regret conjectures. result Proves Finite vs Geometric regret conjecture for N=4 and shows comb strategies are optimal. Mathematical model predicts international trade and global economy dynamics.
problem Understanding complex international trade and economy interactions.
method Developed a mathematical model for non-equilibrium processes in open systems.
result Predicted model accurately reflects international trade and economy.
We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function induces decreasing impatience, we establish the existence of an equilibrium through …
Paper proposes a new model to prevent tariff wars by balancing trade balances.
problem Inequality in trade relations and tariff wars.
method Developed an algorithm to achieve zero trade balance for each country.
result Achieving zero trade balance prevents tariff wars and recession.
Model explains periodic trading in financial markets through game theory.
problem Understanding periodic trading activities in financial markets.
method Mean-field liquidation game with major-minor players.
result Existence and uniqueness of Nash equilibrium established.
We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time 1 value satisfies a specific constraint. This construction allows us to show the existence of Glosten-Milgrom equilibrium and its as…
We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts - the deviation has Ornstein-Uhlenbeck dynamics for quadr…
We consider a time-consistent mean-variance portfolio selection problem of an insurer and allow for the incorporation of basis (mortality) risk. The optimal solution is identified with a Nash subgame perfect equilibrium. We characterize an optimal strategy as solution of a system of partial integro-differential equatio…
We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled…
Two strategic agents track their portfolios, influencing each other's trading targets.
problem Strategic competition in portfolio tracking with price impact.
method Stochastic linear quadratic differential game with terminal state constraints.
result Unique open-loop Nash equilibrium strategies emerge based on price impact types.
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.
AI simplifies trading strategies, potentially making markets more efficient.
problem Efficient market hypothesis (EMH) relies on traders optimising trading strategies based on information.
method Generalised notion of market efficiency, distinguishing model complexity through investor beliefs and trading strategies.
result Increased availability of low-cost AI systems may push towards more advanced trading strategies, potentially harder for inefficient traders.
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,…
A game-theoretic analysis of DEX competition through dynamic trading fees.
problem Competition between decentralized exchanges (DEXs) and their impact on trading fees and slippage.
method Characterization of an approximate Nash equilibrium via coupled system of partial differential equations and closed-form expressions for equilibrium fees.
result The equilibrium trading fees shift from the oracle price to a weighted average of the oracle and competitors' exchange rates under competition.
New paper finds strategic trade centralization benefits firms, while naive centralization often harms them.
problem Finding optimal trading strategies in competitive markets.
method Complete solution to finding equilibrium strategies in competition using Fourier Series methods.
result Firms that strategically centralize trades generally benefit, while naive centralization often harms them.
We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain aroun…
Study high-frequency trading game with price impact, finding unique equilibrium.
problem Optimal execution in a trading game with transient price impact.
method Analyzes high-frequency limit of an n-trader optimal execution game. result High-frequency limit converges to a continuous-time model with quadratic costs.
This paper presents a continuous-time model of intraday trading, pricing, and liquidity with dynamic TWAP and VWAP benchmarks. The model is solved in closed-form for the competitive equilibrium and also for non-price-taking equilibria. The intraday trajectories of TWAP trading targets cause predictable intraday pattern…