Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct observability continual case. Quantum theory of time continuous measurements and quantum prediction theory, developed by the author on the basis of an independent-increment model for quantum noise and nondemolition causality principle in the 80’s, solves this pr...

We consider the stochastic optimal control problem of McKean-Vlasov stochastic differential equation where the coefficients may depend upon the joint law of the state and control. By using feedback controls, we reformulate the problem into a deterministic control problem with only the marginal distribution of the process as controlled state variable, and prove that dynamic programming principle...

Multiobjective Dynamic Programming (MODP) is a general problem solving method used to determine the set of Pareto-optimal solutions in optimization problems involving discrete decision variables and multiple objectives. It applies to combinatorial problems in which Pareto-optimality of a solution extends to all its sub-solutions (Bellman principle). In this paper we focus on the determination o...

In most of the real-life applications we deal with the problem of transporting some special fruits, as banana, which has particular production and distribution processes. In this paper we restrict our attention to formulating and solving a new bi-criterion problem on a network in which in addition to minimizing the traversing costs, admissibility of the quality level of fruits is a main objecti...

The stochastic optimal control uses the differential equation of Bellman and its solution—the Bellman function. We show how the homonym function in harmonic analysis is (and how it is not) the same stochastic optimal control Bellman function. Then we present several creatures from Bellman’s Zoo: a function that proves the inverse Hölder inequality, as well as several other harmonic analysis Bel...

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features game is that weight matrix minimizer’s control cost in functional singular. Due to singularity, cannot be solved either by applying Isaacs MinMax principle, or Bellman–Isaacs equation approach. As application, introduced interception with regularized and developed dual repres...

I Bellman, R., "On the Theory of Dynamic Programming," PROC. NATL. ACAD. Sci., 38, 716-719 (1952). 2 Bellman, R., "Some Functional Equations in the Theory of Dynamic Programming," Ibid., 39, 1077-1082 (1953). ' Bellman, R., "Bottleneck Problems and Dynamic Programming," Ibid., 39, 947-951 (1953). 4 Bellman, R., "A Problem in the Theory of Dynamic Programming," Econometrica (to appear). 6 Bellma...

This paper focuses on zero-sum stochastic differential games in the framework of forward-backward equations a finite time horizon with both players adopting impulse controls. By means BSDE methods, particular that notion from Peng’s backward semigroups, authors prove dynamic programming principle for upper and lower value functions game. The are then shown to be unique viscosity solutions Hamil...

Abstract In this paper we provide a stock price model that explicitly incorporates credit risk, under stochastic optimal control system. The also the managerial of risk through policy in We explicit conditions on existence feedback controls for with risk. prove continuity value function, and then dynamic programming principle our Finally, Viscosity Solution Hamilton–Jacobi–Bellman equation. Thi...

We introduce a novel numerical method for a recently developed perspective Shape-from-Shading model. In order to discretise the corresponding partial differential equation (PDE), Prados et al. employed the dynamical programming principle yielding a Hamilton-Jacobi-Bellman equation. We reduce that model to its essential, namely to the underlying Hamilton-Jacobi equation. For this PDE, we propose...