HJB Equations with Gradient Constraint Associated with Controlled Jump-Diffusion Processes

In this paper, we guarantee the existence and uniqueness (in the almost everywhere sense) of the solution to a Hamilton--Jacobi--Bellman (HJB) equation with gradient constraint and a partial integr...

[1]  Hitoshi Ishii,et al.  Boundary regulatity and uniqueness for an elliptic equations with gradient constraint , 1983 .

[2]  Suzanne Lenhart,et al.  Integro-differential operators associated with diffusion processes with jumps , 1982 .

[3]  Hang Zhu,et al.  Generalized solution in singular stochastic control: The nondegenerate problem , 1992 .

[4]  Florin Avram,et al.  On the optimal dividend problem for a spectrally negative Lévy process , 2007, math/0702893.

[5]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[6]  Petar Popivanov,et al.  A degenerate Neumann problem for quasilinear elliptic integro-differential operators , 1999 .

[7]  Gyula Csató,et al.  The Pullback Equation for Differential Forms , 2011 .

[8]  Lawrence C. Evans,et al.  A second order elliptic equation with gradient constraint , 1979 .

[9]  P. Lions,et al.  A remark on Bony maximum principle , 1983 .

[10]  Mihail Zervos,et al.  A Pair of Explicitly Solvable Singular Stochastic Control Problems , 1998 .

[11]  L. Alvarez A class of solvable singular stochastic control problems , 1999 .

[12]  H. Soner,et al.  Regularity of the value function for a two-dimensional singular stochastic control problem , 1989 .

[13]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[14]  Michael Wiegner,et al.  The C1,1—character of solutions of second order elliptic equations with gradient constraint , 1981 .

[15]  G. Kulinich,et al.  Strong uniqueness of solutions of stochastic differential equations with jumps and non-Lipschitz random coefficients , 2014 .

[16]  Ryan Hynd,et al.  Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control ∗ , 2011, 1102.1109.

[17]  Michael I. Taksar,et al.  Optimal correction problem of a multidimensional stochastic system , 1989, Autom..

[18]  W. Rudin Principles of mathematical analysis , 1964 .

[19]  J. L. Menaldi,et al.  Singular ergodic control for multidimensional Gaussian–Poisson processes , 2013 .

[20]  Ryan Hynd,et al.  On Hamilton-Jacobi-Bellman equations with convex gradient constraints , 2014, 1412.6202.

[21]  P. Protter Stochastic integration and differential equations , 1990 .

[22]  L. Kruk Optimal policies for some n-dimensional singular stochastic control problems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[23]  Ryan Hynd,et al.  The Eigenvalue Problem of Singular Ergodic Control , 2011, 1102.1110.

[24]  Jose Luis Menaldi,et al.  Second Order Elliptic Integro-Differential Problems , 2002 .

[25]  Mihail Zervos,et al.  A singular control model with application to the goodwill problem , 2007, 0711.2143.

[26]  C. Doléans-Dade,et al.  On the existence and unicity of solutions of stochastic integral equations , 1976 .

[27]  I. Karatzas A class of singular stochastic control problems , 1983, Advances in Applied Probability.

[28]  Dimitri De Vallière,et al.  Consumption-investment problem with transaction costs for Lévy-driven price processes , 2015, Finance Stochastics.

[29]  Harold A. Moreno-Franco Solution to HJB Equations with an Elliptic Integro-Differential Operator and Gradient Constraint , 2016, 1605.04993.

[30]  Xin Guo,et al.  Optimal Execution with Multiplicative Price Impact , 2015, SIAM J. Financial Math..

[31]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[32]  Akira Yamazaki,et al.  Equilibrium Equity Price with Optimal Dividend Policy , 2015 .