Related papers: An explicit solution for optimal investment in Hes…
In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set…
This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…
We consider a stock that follows a geometric Brownian motion (GBM) and a riskless asset continuously compounded at a constant rate. We assume that the stock can go bankrupt, i.e., lose all of its value, at some exogenous random time…
An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
This paper is concerned with a discounted optimal control problem of partially observed forward-backward stochastic systems with jumps on infinite horizon. The control domain is convex and a kind of infinite horizon observation equation is…
We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price…
We consider a finite-time stochastic drift control problem with the assumption that the control is bounded and the system is controlled until the state process leaves the half-line. Assuming general conditions, it is proved that the…
This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution…
We present a dynamic programming-based solution to a stochastic optimal control problem up to a hitting time for a discrete-time Markov control process. Firstly, we determine an optimal control policy to steer the process toward a compact…
We study time-inconsistent recursive stochastic control problems, i.e., for which the Bellman principle of optimality does not hold. For this class of problems classical optimal controls may fail to exist, or to be relevant in practice, and…
We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this…
We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod…
The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
This paper is concerned with a discrete-time mean-field stochastic linear-quadratic optimal control problem arose from financial application. Through matrix dynamical optimization method, a group of linear feedback controls is investigated.…
We study optimal investment problem for a diffusion market consisting of a finite number of risky assets (for example, bonds, stocks and options). Risky assets evolution is described by Ito's equation, and the number of risky assets can be…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
We consider long term average or `ergodic' optimal control poblems with a special structure: Control is exerted in all directions and the control costs are proportional to the square of the norm of the control field with respect to the…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…