arXiv research

The paper solves a utility-based hedging problem with quadratic costs.

Study how transaction costs impact stock returns and holdings in equilibrium.

We reconsider the problem of optimal trading in the presence of linear and quadratic costs, for arbitrary linear costs but in the limit where quadratic costs are small. Using matched asymptotic expansion techniques, we find that the trading speed vanishes inside a band that is narrower than in the absence of quadratic …

In this short note, we consider mean-variance optimized portfolios with transaction costs. We show that introducing quadratic transaction costs makes the optimization problem more difficult than using linear transaction costs. The reason lies in the specification of the budget constraint, which is no longer linear. We …

Proposes a new framework for invariant quadratic P&L predictions in option books.

The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.

OMGD algorithm optimizes online convex optimization with switching costs and delayed gradients.

NOT learns optimal transport plans, kernel costs improve performance.

Optimal contracts are found for agents with quadratic effort costs.

Study cost-driven state representation learning for control from partial observations.

Schrödinger bridge solved with Weyl calculus for quadratic state cost.

Model liquidity premia using a risk-sharing economy with quadratic costs.

Paper optimizes broker performance by estimating execution costs.

RL and DTSOC for final quadratic hedging performance studied.

Study analyzes market equilibrium returns with price impact and transaction costs.

We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order $ε$ small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman eq…

Pushing a little forward an approach proposed by Villani, we are going to prove that in the Riemannian setting the condition $\nabla^2 f< g$ implies that $f$ is $c$-concave with respect to the quadratic cost as soon as it has a sufficiently small $C^1$-norm. From this, we deduce a sufficient condition for the optimalit…

Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.

We study super--replication of European contingent claims in an illiquid market with insider information. Illiquidity is captured by quadratic transaction costs and insider information is modeled by an investor who can peek into the future. Our main result describes the scaling limit of the super--replication prices wh…

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…

This paper concerns the problem of learning control policies for an unknown linear dynamical system to minimize a quadratic cost function. We present a method, based on convex optimization, that accomplishes this task robustly: i.e., we minimize the worst-case cost, accounting for system uncertainty given the observed …

A new scheme reduces global search cost by a square root factor.

Study on regularity of optimal transport maps on convex domains with quadratic cost.

Study learns state representations from observations for control, proving guarantees.

Poyiadjis et al. (2011) show how particle methods can be used to estimate both the score and the observed information matrix for state space models. These methods either suffer from a computational cost that is quadratic in the number of particles, or produce estimates whose variance increases quadratically with the am…

The study sets limits on how well systems can be controlled adaptively.

New model-free algorithm achieves similar LQR regret guarantees.

A new method matches measures across different spaces using cost-regularized optimal transport.

In this article we consider the Merton problem in a market with a single risky asset and transaction costs. We give a complete solution of the problem up to the solution of a free-boundary problem for a first-order differential equation, and find that the form of the solution (whether the problem is well-posed, whether…

Solves steering problem with continuous time, Hilbert-Schmidt cost, and matrix ODEs.

We consider a market consisting of one safe and one risky asset, which offer constant investment opportunities. Taking into account both proportional transaction costs and linear price impact, we derive optimal rebalancing policies for representative investors with constant relative risk aversion and a long horizon.

Bipartite ranking is an important supervised learning problem; however, unlike regression or classification, it has a quadratic dependence on the number of samples. To circumvent the prohibitive sample cost, many recent work focus on stochastic gradient-based methods. In this paper we consider an alternative approach, …

We study the performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the cost incurred by playing the certainty equivalent controller on the true system …

Optimal trading strategy with predictor and costs, derived equations and shape.

Policy gradient converges to globally optimal policy in nearly linear-quadratic systems.

Study high-frequency trading game with price impact, finding unique equilibrium.

The paper studies optimal transport in linear quadratic systems and derives interpolation inequalities.

We introduce a new algorithm for online linear-quadratic control in a known system subject to adversarial disturbances. Existing regret bounds for this setting scale as $\sqrt{T}$ unless strong stochastic assumptions are imposed on the disturbance process. We give the first algorithm with logarithmic regret for arbitra…

We study the variance of the REINFORCE policy gradient estimator in environments with continuous state and action spaces, linear dynamics, quadratic cost, and Gaussian noise. These simple environments allow us to derive bounds on the estimator variance in terms of the environment and noise parameters. We compare the pr…

Simple probabilistic solution for optimal liquidation with linear price impact.

The paper improves competitive and dynamic regret bounds for smoothed online learning.

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 with respect to the common noise filtration. Semi closed-loop strategies are intro…

New approach finds solutions to games with unbounded controls.

New method solves constrained stochastic optimization problems efficiently.

We study risk-sharing economies where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled forward-backward stochastic differential equations. We show that a unique solution generally…

QLA improves Bayesian uncertainty estimation for DNNs without increasing computational cost.

RL solves discrete LQ control with Gaussian optimal policy.

This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for…