Optimal position targeting with stochastic linear-quadratic costs

  title={Optimal position targeting with stochastic linear-quadratic costs},
  author={Stefan Ankirchner and Thomas Kruse},
  journal={Banach Center Publications},
We consider the dynamic control problem of attaining a target position at a finite time T , while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linearquadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T . We verify optimality of the… 

Optimal position targeting via decoupling fields

We consider a variant of the basic problem of the calculus of variations, where the Lagrangian is convex and subject to randomness adapted to a Brownian filtration. We solve the problem by reducing

Submitted to the Annals of Applied Probability OPTIMAL POSITION TARGETING VIA DECOUPLING FIELDS By

We consider a variant of the basic problem of the calculus of variations, where the Lagrangian is convex and subject to randomness adapted to a Brownian filtration. We solve the problem by reducing

A note on costs minimization with stochastic target constraints

We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal

Linear Quadratic Stochastic Control Problems with Stochastic Terminal Constraint

This work suggests that, for the minimal supersolution of the Riccati equation, the minimizers of the auxiliary problem coincide with those of the original problem, a conjecture that is confirmed in all examples understood so far.

Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience

This work proves existence and uniqueness of a solution to the BSDE system and characterize both the value function and the optimal strategy in terms of the unique solution to that system.

An Equilibrium Model for the Cross-Section of Liquidity Premia

We study a risk-sharing economy where an arbitrary number of heterogeneous agents trades an arbitrary number of risky assets subject to quadratic transaction costs. For linear state dynamics, the

Asset pricing with general transaction costs: Theory and numerics

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

Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models

We analyse an optimal trade execution problem in a financial market with stochastic liquidity. To this end, we set up a limit order book model in continuous time. Both order book depth and resilience

Asset pricing with heterogeneous beliefs and illiquidity

This paper studies the equilibrium price of an asset that is traded in continuous time between N agents who have heterogeneous beliefs about the state process underlying the asset's payoff. We



Price-Sensitive Liquidation In Continuous-Time

We consider the stochastic control problem of how to optimally close a large asset position in an illiquid market with price impact. We assume that the risk attributed to an open position depends on


We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0, T] and can trade continuously at a traditional exchange (the

When to Cross the Spread? Trading in Two-Sided Limit Order Books

The problem of optimal trading in illiquid markets is addressed when the deviations from a given stochastic target function describing, for instance, external aggregate client flow are penalized, and it is shown that the optimal control can be characterized via buy, sell, and no-trade regions.

A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions

The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is pre-specified and the solution results establish existence, uniqueness and regularity of solution results.

Optimal control of execution costs

Backward stochastic differential equations with random stopping time and singular final condition

In this paper we are concerned with one-dimensional backward stochastic differential equations (BSDE in short) of the following type: Y t =ξ-∫ τ tΛτ Y r |Y r | q dr-∫ τ tΛτ Z r dB r , t ≥ 0, where T

Curve following in illiquid markets

In this article the problem of curve following in an illiquid market is addressed. The optimal control is characterised in terms of the solution to a coupled FBSDE involving jumps via the technique

BSDEs with Singular Terminal Condition and a Control Problem with Constraints

It is proved that a solution of the BSDE exists, thus partly generalizing existence results obtained by Popier in [Stochastic Process], and a probabilistic solution of a not necessarily Markovian control problem with a state constraint by means of a backward stochastic differential equation.

Backward stochastic differential equations with singular terminal condition