An Optimal Control Problem Associated with SDEs Driven by Lévy-Type Processes

DOI10.1080/07362990802007004zbMath1144.60036OpenAlexW1972939169MaRDI QIDQ3506297

Jiang-Lun Wu, Jonathan Bennett

Publication date: 12 June 2008

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362990802007004

zbMATH Keywords

Hamilton-Jacobi-Bellman equationjumpsLévy processesviscosity solutionstochastic differential equationsoptimal control problemsfinancial market modelsLévy generators

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Optimal stochastic control (93E20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items

Stochastic control of drill-heads driven by Lévy processes ⋮ Stochastic control of SDEs associated with Lévy generators and application to financial optimization ⋮ Inverse optimal control of stochastic systems driven by Lévy processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Applied stochastic control of jump diffusions.
• Uniqueness in law for pure jump Markov processes
• Dirichlet forms and symmetric Markov processes
• Invariant measures and symmetry property of Lévy type operators
• Continuous dependence estimates for viscosity solutions of integro-PDEs
• A ``maximum principle for semicontinuous functions applicable to integro-partial differential equations
• Lévy measure with generalized polar decomposition and the associated sde with jumps
• User’s guide to viscosity solutions of second order partial differential equations
• [https://portal.mardi4nfdi.de/wiki/Publication:4043914 Diffusion processes associated with L�vy generators]
• [https://portal.mardi4nfdi.de/wiki/Publication:4131394 Repr�sentation des processus ponctuels multivari�s � l'aide d'un processus de Poisson]
• Markov Processes from K. Ito's Perspective (AM-155)
• Symmetric Stable Laws and Stable-Like Jump-Diffusions
• Lévy Processes and Stochastic Calculus
• Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach
• Optimal portfolio management rules in a non-Gaussian market with durability and intertemporal substitution