A Constrained Control Problem with Degenerate Coefficients and Degenerate Backward SPDEs with Singular Terminal Condition

DOI10.1137/15M1031060zbMath1334.93182arXiv1407.0108MaRDI QIDQ2799361

Ulrich Horst, Qi Zhang, Jinniao Qiu

Publication date: 11 April 2016

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0108

zbMATH Keywords

stochastic controlbackward stochastic partial differential equationportfolio liquidationsingular terminal valuedegenerate parabolic condition

Mathematics Subject Classification ID

Optimal stochastic control (93E20) Financial applications of other theories (91G80) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (11)

Weak solution for a class of fully nonlinear stochastic Hamilton-Jacobi-Bellman equations ⋮ Neumann problem for backward SPDEs with singular terminal conditions and application in constrained stochastic control under target zone ⋮ Uniqueness of viscosity solutions of stochastic Hamilton-Jacobi equations ⋮ Stochastic differential games with random coefficients and stochastic Hamilton-Jacobi-Bellman-Isaacs equations ⋮ Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience ⋮ Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models ⋮ Smooth solutions to portfolio liquidation problems under price-sensitive market impact ⋮ The link between stochastic differential equations with non-Markovian coefficients and backward stochastic partial differential equations ⋮ Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations ⋮ Optimal Trade Execution in an Order Book Model with Stochastic Liquidity Parameters ⋮ Continuous viscosity solutions to linear-quadratic stochastic control problems with singular terminal state constraint

Cites Work

• \(L ^{p }\) theory for super-parabolic backward stochastic partial differential equations in the whole space
• On the quasi-linear reflected backward stochastic partial differential equations
• Smooth solutions to portfolio liquidation problems under price-sensitive market impact
• On non-Markovian forward-backward SDEs and backward stochastic PDEs
• Backward stochastic differential equations with singular terminal condition
• On semi-linear degenerate backward stochastic partial differential equations
• \(W^{m,p}\)-solution (\(p\geqslant 2\)) of linear degenerate backward stochastic partial differential equations in the whole space
• Semi-linear degenerate backward stochastic partial differential equations and associated forward-backward stochastic differential equations
• When to Cross the Spread? Trading in Two-Sided Limit Order Books
• Utility Maximization with Habit Formation: Dynamic Programming and Stochastic PDEs
• Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions
• The Maximum Principle for Optimal Control of Diffusions with Partial Information
• Stochastic Hamilton–Jacobi–Bellman Equations
• A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions
• PORTFOLIO LIQUIDATION IN DARK POOLS IN CONTINUOUS TIME
• BSDEs with Singular Terminal Condition and a Control Problem with Constraints

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