We consider Karush-Kuhn-Tucker (KKT) systems, which depend on a parameter. Our contribution concerns with the existence of solution of the directionally perturbed KKT system, approximating the given primal-dual base solution. To our knowledge, we give the first explicit result of this kind in...

We consider a linear two-stage stochastic program. Whereas optimization in the traditional setting is based solely on expectation, we include risk measures reflecting dispersions of the random objective. Presenting the mean-risk models, we aim to extend existing results for the expectation-based...

We analyze the connection between the optimal solutions of minimum time and fixed final time optimal control problems. We discuss some controllability conditions which guarantee the equivalence of the two problems. In fact, under such conditions, not only does an optimal control...

In this paper we consider the pricing of point-to-point bandwidth leasing contracts and options. The underlying asset of these contracts is a point-to-point telecommunications connection. Due to the network structure the network capacity prices depend nonlinearly on each other. A leasing...

We consider multiple simple recourse (MSR) models, both continuous and integer versions, which generalize the corresponding simple recourse (SR) models by allowing for a refined penalty cost structure for individual shortages and surpluses. It will be shown that (convex approximations of) such...

In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction...

We develop an algorithm to compute optimal policies for Markov decision processes subject to constraints that result from some observability restrictions on the process. We assume that the state of the Markov process is unobservable. There is an observable process related to the unobservable...

Upper and lower bounds are studied for the solutions of Markov renewal equations. Some of their special cases are derived under specific marginal conditons and in an alternating environment. The method to construct the bounds is also explained in detail. At the end, these bounds are applied to a...

We present tools and guidelines for investigating Lipschitz continuity of the value functions in MDP’s, using the Hausdorff metric and the Kantorovich metric for measuring the influence of the constraint set and the transition law, respectively. The methods are explained by examples....

Some new results which generalize the Hahn-Banach theorem from scalar or vector-valued case to set-valued case are obtained. The existence of the Borwein-strong subgradient and Yang-weak subgradient for set-valued maps are also proven. We present a new Lagrange multiplier theorem and a new...