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 ...

In this paper we consider the problem of minimizing a quadratic functional for a discretetime linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and sufficient conditions for the existence of the optimal control can be formulated as matrix inequalities in frequency domain. Furthermore, we show that if the opt...

The problem of sampled-data (SD) based adaptive linear quadratic (LQ) optimal control is considered for linear stochastic continuous-time systems with unknown parameters and disturbances. To overcome the difficulties caused by the unknown parameters and incompleteness of the state information, and to probe into the influence of sample size on system performance, a cost-biased parameter estimato...

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

Contrary to the models of deterministic life cycle saving, we take it for granted that uncertainty of one’s future is the essential problem of saving decisions. However, unlike the stochastic life cycle models, we capture this crucial uncertainty by a non-Bayesian scenario-based satisficing approach. Decision makers first form aspirations for a few relevant scenarios, and then search for saving...

An aggregation technique for constraints with values in Hilbert spaces is suggested. The technique allows to replace the original optimization problem by a sequence of subproblems having scalar or finite-dimensional constraints. Applications to optimal control, games and stochastic programming are discussed in detail.

In this paper, we revisit and clarify the celebrated machine maintenance and sale age model of Kamien and Schwartz (KS) involving a machine subject to failure. KS formulate and solve the problem as a deterministic optimal control problem with the probability of the machine failure as the state variable. Thus, they obtain deterministic optimal maintenance and sale date. We study two underlying s...