We discuss investment allocation to multiple alpha streams traded on the same execution platform with internal crossing of trades and point out differences with allocating investment when alpha streams are traded on separate execution platforms with no crossing. First, in the latter case allocation weights are non-nega…
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48 results for “nonlinear trading costs”
This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with …
We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well behaved initial strategy is continuously deformed to lower the expected execution cost. We find that the optimal solution is front loaded for co…
Study Nash competition among dealers quoting prices to clients with unknown trading motives.
problem Adverse selection and inventory costs in dealer-client interactions.
method Analyzes one-shot Nash competition with unknown client type and inventory constraints.
result Unique symmetric Nash equilibrium exists and can be characterized by a nonlinear ODE.
Optimal Investment and Consumption Strategies with General Cost Structure under CRRA Utilityq-fin.PM
Study optimal investment and consumption strategies with various transaction costs.
problem Investment and consumption decisions under varying transaction costs.
method Dynamic programming and singular perturbation expansion for small cost-to-wealth ratio.
result Derive leading-order asymptotic formulas for no-trade regions and trading boundaries.
In these notes we discuss investment allocation to multiple alpha streams traded on the same execution platform, including when trades are crossed internally resulting in turnover reduction. We discuss approaches to alpha weight optimization where one maximizes P&L subject to bounds on volatility (or Sharpe ratio). The…
This study optimizes trading and arbitrage in decentralized finance's CPMs, revealing convexity costs and developing efficient strategies.
problem Optimizing trading and arbitrage in decentralized finance's constant product markets (CPMs).
method Developed models for CPMs in competing centralised exchanges, CPMs, and both venues. Derived computationally efficient strategies.
result Accurately estimated convexity costs in CPMs, which are linear in trade size and nonlinear in liquidity depth and exchange rate.
Study pricing derivatives in nonlinear models with market frictions.
problem No-arbitrage pricing of derivatives in nonlinear market models with funding costs, credit risk, and trading frictions.
method Extend nonlinear pricing approach by incorporating funding costs, credit risk, and trading frictions.
result Developed a comprehensive framework for pricing derivatives in nonlinear market models.
The paper explores optimal investment and contingent claim valuation in illiquid markets using convex duality.
problem Optimal investment and contingent claim valuation in markets with nonlinear trading costs and portfolio constraints.
method Convex duality theory applied to markets with general conditions on utility functions and market models.
result Dual expressions decompose into terms for risk preferences, trading costs, and portfolio constraints.
Study asset pricing with transaction costs, showing unique equilibrium exists.
problem Risk-sharing economies with heterogeneous agents trading under quadratic transaction costs.
method Characterizes equilibrium asset prices and strategies via nonlinear, fully-coupled equations.
result Unique solution exists when agents' preferences are sufficiently similar, and empirical liquidity premia and discounts match transaction costs and volatility.
A singular stochastic control approach for optimal pairs trading with proportional transaction costsq-fin.TR
Study optimal pairs trading with transaction costs using stochastic control.
problem Finding optimal trade times and shares in pairs trading with proportional costs.
method Singular stochastic control approach to solve a nonlinear quasi-variational inequality.
result Developed a discrete time dynamic programming algorithm to compute transaction regions.
Superhedging in illiquid marketsq-fin.PR
We study contingent claims in a discrete-time market model where trading costs are given by convex functions and portfolios are constrained by convex sets. In addition to classical frictionless markets and markets with transaction costs or bid-ask spreads, our framework covers markets with nonlinear illiquidity effects…
We study super-replication of contingent claims in an illiquid market with model uncertainty. Illiquidity is captured by nonlinear transaction costs in discrete time and model uncertainty arises as our only assumption on stock price returns is that they are in a range specified by fixed volatility bounds. We provide a …
Traders are often faced with large block orders in markets with limited liquidity and varying volatility. Executing the entire order at once usually incurs a large trading cost because of this limited liquidity. In order to minimize this cost traders split up large orders over time. Varying volatility however implies t…
Study risk-sharing equilibria with general transaction costs, proving mean-reversion of returns.
problem Analyzing risk-sharing equilibria with general convex transaction costs.
method Infinite-horizon model with linear state dynamics, solved numerically using deep learning.
result Equilibrium returns mean-revert around frictionless counterparts, with different dynamics for quadratic and proportional costs.
We adapt a model for bilateral counterparty risk to include transaction costs.
problem Modeling bilateral counterparty risk with transaction costs.
method Derived a nonlinear PDE, proved existence of solution, developed numerical scheme.
result Existence of solution to the PDE with transaction costs.
New method improves nonlinear filtering accuracy with reduced computation.
problem Complex nonlinear filtering with small system noise.
method Asymptotic expansion with ordinary differential equations and Edgeworth-type correction.
result Significantly lower computational cost with improved accuracy.
The paper optimizes portfolios to minimize drawdown, outperforming market indices.
problem Minimizing drawdown in financial portfolios.
method Formulated as a nonlinear program, partially linearized, solved using SCIP.
result Minimal drawdown portfolios outperform market indices in return, Sharpe ratio, maximum and average drawdown.
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dy…
The study examines pricing American options with both exogenous and endogenous transaction costs.
problem Pricing American options with transaction costs and liquidity risks.
method Modeling liquidity risks as a mean-reverting process and transaction costs as proportional to trading amount. Two nonlinear PDEs are used to characterize option values. Numerical solution via ADI method and model calibration using maximum likelihood estimation.
result The model incorporating liquidity risks significantly outperforms the Leland model.
Paper examines costs of using wrong price impact models in trading.
problem Misspecifying price impact models in trading predictions.
method Derives formulas for misspecification costs and applies to trading data.
result Misspecification costs are asymmetric, affecting profits and losses.
Investigates how trading boundaries change with transaction costs in portfolio selection.
problem Investigates how trading boundaries vary with transaction costs in portfolio selection.
method Analyzes Merton's problem with proportional transaction costs, showing monotonicity of trading boundaries.
result Cost-adjusted trading boundaries are monotone in transaction costs, with implications for the Merton line.
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.
A universal law explains trading under costs.
problem Optimal trading under proportional transaction costs.
method Universal law interpretation of various results.
result All results can be explained by a universal law.
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.
This research extends Leland's work to multi-asset options with variable transaction costs.
problem Pricing multi-asset options with variable transaction costs.
method Generalized Leland's condition, proved existence of viscosity solution using Perron method, developed numerical ADI scheme.
result Existence of a viscosity solution for the fully nonlinear initial value problem.
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.
New multi-step approach improves fiber nonlinearity compensation efficiency.
problem Fewer steps are traditionally considered better for fiber nonlinearity compensation.
method Carefully designed multi-step machine learning approaches.
result Multi-step approaches lead to better performance-complexity trade-offs.
We develop a polynomial method to optimize trading in markets with transaction costs.
problem Optimizing trading strategies in markets with proportional transaction costs.
method Polynomial approximation of the residual value function to determine optimal trading strategies.
result Identify the trade-off between trading frequency and trade sizes for satisfactory agreement with theoretically optimal strategies.
We propose a discrete time algorithm for the valuation of employee stock options based on exponential indifference prices and taking into account both the possibility of partial exercise of a fraction of the options and the use of a correlated traded asset to hedge part of their risk. We determine the optimal exercise …
Costly Tradingq-fin.PM
Optimal trading patterns adjust based on market efficiency and slippage costs.
problem Balancing active alphas and trading costs in active portfolios.
method Maximization of utility including projected alpha-based profits, slippage costs, and risk aversion.
result Optimal trading involves a no-trade zone width that scales as , differing from stochastic settings.
Study optimal trading times for mean-reverting prices with deadlines.
problem Optimal timing strategies for mean-reverting price processes with deadlines.
method Solve optimal double stopping problems with sequential deadlines using local time-space calculus.
result Derive optimal trading boundaries for long-short, short-long, and chooser strategies.
RS-PINN uses randomized smoothing to speed up high-dimensional PDE simulations without sacrificing accuracy.
problem High computational cost and bias in PINNs for high-dimensional PDEs.
method Introduces Gaussian noise for stochastic smoothing of PINNs, enabling Monte Carlo derivative approximation.
result Proposes bias correction techniques and a hybrid method to optimize the bias-variance trade-off.
Unified Asymptotics For Investment Under Illiquidity: Transaction Costs And Search Frictionsq-fin.MF
Unified asymptotics for investment in markets with transaction costs and search frictions.
problem Investment in markets with transaction costs and search frictions.
method Power-utility maximization problem with proportional transaction costs and Poisson-triggered trades, analyzed using a novel asymptotic framework.
result Explicit asymptotics for the no-trade region and value function derived.
Study examines trading costs after Hong Kong-Shanghai Connect.
problem Estimating trading costs in China's securities market.
method Developed a novel methodology to compensate for lack of data.
result Trading costs on Shanghai may have increased after Connect.
Optimizes trading pairs of stocks to reduce cross-impact costs.
problem Minimizing costs from trades of one stock affecting another.
method Develops a strategy to minimize cross-impacts by optimizing trading rates and periods.
result An optimal trading strategy for stock pairs is found.
Optimal trading speeds are reduced by small quadratic costs, with specific velocity regimes identified.
problem Optimal trading speeds in the presence of linear and quadratic costs.
method Matched asymptotic expansion techniques to analyze the effects of small quadratic costs.
result Trading speeds inside a band are reduced by the one-third power of quadratic costs, with specific velocity regimes identified.
Study examines trading costs on Uniswap, finding adversarial slippage is significant for large trades and certain assets.
problem Analyzing costs and slippage in decentralized exchanges (DEXs).
method Empirical evaluation of Uniswap's USDC-ETH and PEPE-ETH pools, calculating slippage and reordering slippage.
result Adversarial slippage is significant for large trades and certain assets like PEPE.
Paper optimizes broker performance by estimating execution costs.
problem Minimizing execution costs for large trades.
method Intraday modeling of execution cost components (linear and quadratic).
result Substantial improvements in estimating execution costs.
Paper solves complex investment-consumption problem with numerical methods.
problem Optimal investment and consumption strategies with proportional transaction costs.
method Monte Carlo simulation and finite difference method for approximating gradients.
result Numerical results validate optimal trading strategies and properties.
Optimal trade execution strategies show adaptive methods reduce costs.
problem Optimal trade execution with short-term price predictive signals.
method Comparison of static and adaptive strategies with transient and instantaneous market impacts.
result Adaptive strategies significantly reduce transaction costs compared to static strategies.
Machine learning predicts Bitcoin returns but trading performance drops with costs.
problem Trading Bitcoin predictions with transaction costs.
method XGBoost, LSTM, iTransformer models evaluated in walk-forward protocol; cost-aware execution filter implemented.
result Cost-aware execution filter restores profitability; XGBoost strategy outperforms.
Paper proposes a deep reinforcement learning model for forex trading that considers transaction costs.
problem Trading in forex markets with high transaction costs and non-stationary data.
method Deep reinforcement learning model considering transaction costs and online learning.
result Maximizes profit while keeping transaction costs low in non-stationary markets.
A protocol reduces transaction costs for portfolio managers.
problem Transaction costs reduce portfolio returns over time.
method Distributed convex optimization protocol.
result Trades converge to optimal for the firm with adjustments.
A posteriori multi-stage optimal trading under transaction costs and a diversification constraintq-fin.PM
This paper optimizes trading strategies with costs and diversification constraints.
problem Optimizing trading strategies with transaction costs and diversification constraints.
method Historical multi-stage optimal trading with graph generation and search.
result Developed methods for multi-variate multi-stage optimal trading under constraints.
New trading policies preserve robust gains in presence of transaction costs.
problem Maintaining robust gains in asset trading with transaction costs.
method Proposed double linear trading policies, analyzed with Monte Carlo simulations and historical data.
result Desired robust positive expected gain can be preserved under certain conditions.
The paper analyzes option pricing with variable transaction costs using a nonlinear model.
problem Analyzing option pricing under variable transaction costs with nonlinear dynamics.
method Transformation of a fully nonlinear parabolic equation into a quasilinear one, existence of classical smooth solutions, numerical approximation.
result Existence of classical smooth solutions and useful bounds on option prices.
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.