Optimal control of deteriorating production inventory systems.
Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations
In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude with an application to optimal stationary feedback control.
Optimal control of impulsive stochastic evolution inclusions
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
Optimal control of linear stochastic evolution equations in Hilbert spaces and uniform observability
In this paper we study the existence of the optimal (minimizing) control for a tracking problem, as well as a quadratic cost problem subject to linear stochastic evolution equations with unbounded coefficients in the drift. The backward differential Riccati equation (BDRE) associated with these problems (see [chen], for finite dimensional stochastic equations or [UC], for infinite dimensional equations with bounded coefficients) is in general different from the conventional BDRE (see [1990], [ukl])....
Optimal control under discrete observation of continuous stochastic systems with time delay
Optimal control with partial information for stochastic Volterra equations.
Optimal guaranteed cost filtering for Markovian jump discrete-time systems.
Optimal investment strategy for a non-life insurance company: quadratic loss
The aim of this paper is to construct an optimal investment strategy for a non-life insurance business. We consider an insurance company which provides, in exchange for a single premium, full coverage to a portfolio of risks which generates losses according to a compound Poisson process. The insurer invests the premium and trades continuously on the financial market which consists of one risk-free asset and n risky assets (Black-Scholes market). We deal with the insurer's wealth path dependent disutility...
Optimal investment under stochastic volatility and power type utility function
2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.In this work we will study a problem of optimal investment in financial markets with stochastic volatility with small parameter. We used the averaging method of Bogoliubov for limited development for the optimal strategies when the small parameter of the model tends to zero and the limit for the optimal strategy and demonstrated the convergence of these optimal strategies.
Optimal multivariable PID regulator
A continuous version of optimal LQG design under presence of Wiener disturbances is solved for MIMO controlled plant. Traditional design tools fail to solve this problem due to unstability of the augmented plant. A class of all optimality criteria, which guarantee existence of an asymptotical solution, is defined using a plant deviation model. This class is utilized in design of an optimal state and an error feedback regulator which is presented here. The resultant optimal error regulator is interpreted...
Optimal position targeting with stochastic linear-quadratic costs
We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linear-quadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T. We verify optimality of the candidate...
Optimal premium pricing for a heterogeneous portfolio of insurance risks.
Optimal resource allocation in stochastic activity networks via the electromagnetism approach: a platform implementation in Java
Optimal sequential multiple hypothesis testing in presence of control variables
Suppose that at any stage of a statistical experiment a control variable that affects the distribution of the observed data at this stage can be used. The distribution of depends on some unknown parameter , and we consider the problem of testing multiple hypotheses , , allowing the data to be controlled by , in the following sequential context. The experiment starts with assigning a value to the control variable and observing as a response. After some analysis, another value for...
Optimal singular stochastic problem on harvesting system.
Optimal solutions to stochastic differential inclusions
A martingale problem approach is used first to analyze compactness and continuous dependence of the solution set to stochastic differential inclusions of Ito type with convex integrands on the initial distributions. Next the problem of existence of optimal weak solutions to such inclusions and their dependence on the initial distributions is investigated.
Optimal stationary policies inrisk-sensitive dynamic programs with finite state spaceand nonnegative rewards
This work concerns controlled Markov chains with finite state space and nonnegative rewards; it is assumed that the controller has a constant risk-sensitivity, and that the performance ofa control policy is measured by a risk-sensitive expected total-reward criterion. The existence of optimal stationary policies isstudied within this context, and the main resultestablishes the optimalityof a stationary policy achieving the supremum in the correspondingoptimality equation, whenever the associated...
Optimal stopping and impulsive control of one-dimensional diffusion processes
Optimal stopping with advanced information flow: selected examples
We study optimal stopping problems for some functionals of Brownian motion in the case when the decision whether or not to stop before (or at) time t is allowed to be based on the δ-advanced information , where is the σ-algebra generated by Brownian motion up to time s, s ≥ -δ, δ > 0 being a fixed constant. Our approach involves the forward integral and the Malliavin calculus for Brownian motion.
Optimal transmission of Gaussian signals through a feedback channel.