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In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic value function is characterized by a fully nonlinear second…
We consider a utility maximization problem for an investment-consumption portfolio when the current utility depends also on the wealth process. Such kind of problems arise, e.g., in portfolio optimization with random horizon or with random…
In this paper, we are concerned with the classical solvability of a class of second-order Hamilton-Jacobi-Bellman equations (HJB equations) arising from stochastic optimal control problems with linear dynamics and uniformly convex cost…
We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a…
In this paper we continue the study of Bian-Miao-Zheng (2011) and extend the results there to a more general class of utility functions which may be bounded and non-strictly-concave and show that there is a classical solution to the HJB…
We introduce a novel approach to solving the optimal portfolio choice problem under Epstein-Zin utility with a time-varying consumption constraint, where analytical expressions for the value function and the dual value function are not…
We study a family of stochastic control problems arising in typical applications (such as boundary control and control of delay equations with delay in the control) with the ultimate aim of finding solutions of the associated HJB equations,…
We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to…
We study a family of stationary Hamilton-Jacobi-Bellman (HJB) equations in Hilbert spaces arising from stochastic optimal control problems. The main difficulties to treat such problems are: the lack of smoothing properties of the linear…
The aim of this paper is to study the fast computation of the lower and upper bounds on the value function for utility maximization under the Heston stochastic volatility model with general utility functions. It is well known there is a…
We study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial point. Without assuming any condition on singular…
In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…
We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity.…
We prove that outside of a closed singular set of measure zero solutions to the second boundary value problem for generated Jacobian equations are smooth.
In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB)…
A general continuous mean-variance problem is considered for a diffusion controlled process where the reward functional has an integral and a terminal-time component. The problem is transformed into a superposition of a static and a dynamic…
We present a new formulation for the computation of solutions of a class of Hamilton Jacobi Bellman (HJB) equations on closed smooth surfaces of co-dimension one. For the class of equations considered in this paper, the viscosity solution…
Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…
In optimal control problems defined on stratified domains, the dynamics and the running cost may have discontinuities on a finite union of submanifolds of RN. In [8, 5], the corresponding value function is characterized as the unique…
In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by $L^1$-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic…