A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the free boundary between the control and no-action regions is approximately linear away from the state constraining boundaries. Proof of this result relies on connections with related optimal stopping problems. We provide an explicit solution to one such optimal stopping problem. Results of ...

1. Abstract We consider an optimal control problem of optimal hydrothermal scheduling. The model, already discussed in [1], is deterministic and takes into account the dependence of efficiency of hydroelectric energy with respect to the volume of water in dams. The thermal cost is a strongly convex and nondecreasing function of the thermal power. We study the possible occurrence of a singular a...

We consider a model of a nancial corporation which has to nd an optimal policy balancing its risk and expected proots. The example treated in this paper is related to an insurance company with the risk control method known in the industry as excess-of-loss reinsurance. Under this scheme the insurance company divert part of its premium stream to another company in exchange of an obligation to pi...

where λ ∈ IR denotes the adjoint variable and μ is the multiplier for the control-state constraint. For this control problem, second–order sufficient conditions, sensitivity analysis and real– time control techniques have been extensively studied in the literature under the assumption that the strict Legendre condition Huu[t] ≥ cIm , c > 0, holds; c.f., e.g., Dontchev, Hager [3], Malanowski, Ma...

This study concentrates on time-optimal operation of a general batch diafiltration process. The process model consists of a set of input affine differential equations. We apply Pontryagin’s minimum principle to formulate necessary conditions of optimality. These are then used to identify the shape of optimal control as well as singular surface in concentration space. Comparison is made between ...

We study partial information, possibly non-Markovian, singular stochastic control of jump diffusions and obtain general maximum principles. The results are used to find connections between singular stochastic control, reflected BSDEs and optimal stopping in the partial information case. Mathematics Subject Classification 2010: 93E20, 60H07, 60H10, 60HXX, 60J75

A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the free boundary between the control and no-action regions is approximately linear away from the state constraining boundaries. Proof of this result relies on connections with related optimal stopping problems. We provide an explicit solution to one such optimal stopping problem. Results of ...

We consider a problem of maximization of the distance traveled by a material point in the presence of a nonlinear friction under a bounded thrust and fuel expenditure. Using the maximum principle we obtain the form of optimal control and establish conditions under which it contains a singular subarc. This problem seems to be the simplest one having a mechanical sense in which singular subarcs a...

The goal of this paper consists in showing how a recently developed sufficient theorem appropriate for certain classes of optimal control problems containing mixed state-control constraints could be applied. The existence of a singular solution to a practical application involving an economic model with population growth becomes an outstanding component of the paper. Mathematics Subject Classif...

This is the second article in the series opened by the paper [4]. Jacobi curves were defined, computed, and studied in that paper for regular extremals of smooth control systems. Here we do the same for singular extremals. The last section contains a feedback classification and normal forms of generic single–input affine in control systems on a 3-dimensional manifold.