# Linear Quadratic Stochastic Control Problems with Stochastic Terminal Constraint

@article{Bank2016LinearQS, title={Linear Quadratic Stochastic Control Problems with Stochastic Terminal Constraint}, author={Peter Bank and Moritz Vo{\ss}}, journal={SIAM J. Control. Optim.}, year={2016}, volume={56}, pages={672-699} }

We study a linear quadratic optimal control problem with stochastic coefficients and a terminal state constraint, which may be in force merely on a set with positive, but not necessarily full, probability. Under such a partial terminal constraint, the usual approach via a coupled system of a backward stochastic Riccati equation and a linear backward equation breaks down. As a remedy, we introduce a family of auxiliary problems parametrized by the supersolutions to this Riccati equation alone…

## 20 Citations

### Stochastic Linear-quadratic Control Problems with Affine Constraints

- Mathematics
- 2022

In this paper, we investigate the stochastic linear-quadratic control problems with affine constraints in random coefficients case. With the help of the Pontryagin maximum principle and stochastic…

### Continuous Viscosity Solutions to Linear-Quadratic Stochastic Control Problems with Singular Terminal State Constraint

- MathematicsApplied Mathematics & Optimization
- 2020

This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a linear-quadratic stochastic control problem with singular terminal…

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

- Mathematics
- 2019

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…

### Backward stochastic differential equations with non-Markovian singular terminal conditions for general driver and filtration

- Mathematics
- 2019

We consider a class of Backward Stochastic Differential Equations with superlinear driver process f adapted to a filtration supporting at least a d dimensional Brownian motion and a Poisson random…

### Optimal Investment with Transient Price Impact

- EconomicsSIAM J. Financial Math.
- 2019

It is optimal to trade towards the frictionless Merton position, taking into account the initial bid-ask spread as well as the optimal liquidation of the accrued position when approaching terminal time, leading to a surprisingly rich phenomenology of possible trajectories for the optimal share holdings.

### Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems

- Mathematics
- 2022

We start with a stochastic control problem where the control process is of finite variation (possibly with jumps) and acts as integrator both in the state dynamics and in the target functional.…

### Asymptotic approach for backward stochastic differential equation with singular terminal condition

- MathematicsStochastic Processes and their Applications
- 2019

### Optimal execution with dynamic risk adjustment

- EconomicsJ. Oper. Res. Soc.
- 2019

It is shown that, under a quadratic specification of the driver of a backward stochastic differential equation, it is possible to find a closed form solution and an explicit expression of the optimal liquidation policies.

### Limit behaviour of the minimal solution of a BSDE with singular terminal condition in the non Markovian setting

- Mathematics
- 2020

We use the functional Itô calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: liminf t → T Y ( t ) = ξ = Y ( T ) $\liminf _{t\to T} Y(t) =…

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

- Mathematics, EconomicsFinance and Stochastics
- 2021

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…

## References

SHOWING 1-10 OF 28 REFERENCES

### Linear Quadratic Optimal Stochastic Control with Random Coefficients

- Mathematics
- 1976

The purpose of this paper is to apply the methods developed in [1] and [2] to solve the problem of optimal stochastic control for a linear quadratic system.After proving some preliminary existence…

### BSDEs with Singular Terminal Condition and a Control Problem with Constraints

- MathematicsSIAM J. Control. Optim.
- 2014

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.

### Global Adapted Solution of One-Dimensional Backward Stochastic Riccati Equations, with Application to the Mean-Variance Hedging

- Mathematics
- 2002

### Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting

- Mathematics
- 2015

### Limit behaviour of BSDE with jumps and with singular terminal condition

- Mathematics
- 2016

We study the behaviour at the terminal time T of the minimal solution of a backward stochastic differential equation when the terminal data can take the value +$\infty$ with positive probability. In…

### A control problem with fuel constraint and Dawson-Watanabe superprocesses

- Mathematics
- 2013

We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of $J$-functionals of Dawson-Watanabe superprocesses. This solution is related to the superprocess…

### Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach

- Mathematics, Computer Science
- 2015

The existence of asymptotic lower bounds for this problem, depending on the cost structure, can be related to the time-average control of Brownian motion, which is characterized as a deterministic linear programming problem.

### Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience

- MathematicsSIAM J. Control. Optim.
- 2017

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.

### OPTIMAL EXECUTION OF A VWAP ORDER: A STOCHASTIC CONTROL APPROACH

- Computer Science
- 2015

A new model for the relative volume curve is introduced which allows simultaneously for accurate data fit, economic justification, and mathematical tractability, and an explicit characterization of the optimal trading rate and liquidation trajectory.