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Optimal position targeting with stochastic linear-quadratic costs

Stefan Ankirchner, Thomas Kruse (2015)

Banach Center Publications

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 sequential multiple hypothesis testing in presence of control variables

Andrey Novikov (2009)

Kybernetika

Suppose that at any stage of a statistical experiment a control variable X that affects the distribution of the observed data Y at this stage can be used. The distribution of Y depends on some unknown parameter θ , and we consider the problem of testing multiple hypotheses H 1 : θ = θ 1 , H 2 : θ = θ 2 , ... , H k : θ = θ k allowing the data to be controlled by X , in the following sequential context. The experiment starts with assigning a value X 1 to the control variable and observing Y 1 as a response. After some analysis, another value X 2 for...

Optimal solutions to stochastic differential inclusions

Mariusz Michta (2002)

Applicationes Mathematicae

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

Rolando Cavazos-Cadena, Raúl Montes-de-Oca (2000)

Applicationes Mathematicae

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 with advanced information flow: selected examples

Yaozhong Hu, Bernt Øksendal (2008)

Banach Center Publications

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 ℱ t + δ , where ℱ s 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.

Optimality of the replicating strategy for American options

Marek Kociński (1999)

Applicationes Mathematicae

The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox-Ross-Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an optimal replicating strategy that is not optimal in the global sense.

Optimization of Discrete-Time, Stochastic Systems

Papageorgiou, Nikolaos (1995)

Serdica Mathematical Journal

* This research was supported by a grant from the Greek Ministry of Industry and Technology.In this paper we study discrete-time, finite horizon stochastic systems with multivalued dynamics and obtain a necessary and sufficient condition for optimality using the dynamic programming method. Then we examine a nonlinear stochastic discrete-time system with feedback control constraints and for it, we derive a necessary and sufficient condition for optimality which we then use to establish the existence...

Optimization schemes for wireless sensor network localization

Ewa Niewiadomska-Szynkiewicz, Michał Marks (2009)

International Journal of Applied Mathematics and Computer Science

Many applications of wireless sensor networks (WSN) require information about the geographical location of each sensor node. Self-organization and localization capabilities are one of the most important requirements in sensor networks. This paper provides an overview of centralized distance-based algorithms for estimating the positions of nodes in a sensor network. We discuss and compare three approaches: semidefinite programming, simulated annealing and two-phase stochastic optimization-a hybrid...

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