Optimal and near-optimal () inventory policies for Levy demand processes
Optimal and Near-Optimal (s,S) Inventory Policies for Levy Demand Processes
A Levy jump process is a continuous-time, real-valued stochastic process which has independent and stationary increments, with no Brownian component. We study some of the fundamental properties of Levy jump processes and develop (s,S) inventory models for them. Of particular interest to us is the gamma-distributed Levy process, in which the demand that occurs in a fixed period of time has a gamma distribution. We study the relevant properties of these processes, and we develop a quadratically convergent...
Optimal bound for the discrepancies of lacunary sequences
The law of the iterated logarithm for discrepancies of lacunary sequences is studied. An optimal bound is given under a very mild Diophantine type condition.
Optimal choice problem with backward solicitation
Optimal closing of a pair trade with a model containing jumps
A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely used investment strategy in the financial industry. Recently, Ekström, Lindberg, and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is modelled by an Ornstein-Uhlenbeck process. In the present work the model is generalized to also include jumps. More precisely, we assume that the difference between the assets is an...
Optimal contracts in continuous-time models.
Optimal control and performance analysis of an queue with batches of negative customers
We consider a Markov decision process for an queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different...
Optimal control and performance analysis of an MX/M/1 queue with batches of negative customers
We consider a Markov decision process for an MX/M/1 queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different...
Optimal control by means switchings
Optimal control characteristics of a queueing system with batch services
Optimal control for a BMAP/G/1 queue with two service modes.
Optimal control for a BMAP/SM/1 queue with MAP-input of disasters and two operation modes
A single-server queueing system with a batch markovian arrival process (BMAP) and MAP-input of disasters causing all customers to leave the system instantaneously is considered. The system has two operation modes, which depend on the current queue length. The embedded and arbitrary time stationary queue length distribution has been derived and the optimal control threshold strategy has been determined.
Optimal control for a BMAP/SM/1 queue with MAP-input of disasters and two operation modes
A single-server queueing system with a batch Markovian arrival process (BMAP) and MAP-input of disasters causing all customers to leave the system instantaneously is considered. The system has two operation modes, which depend on the current queue length. The embedded and arbitrary time stationary queue length distribution has been derived and the optimal control threshold strategy has been determined.
Optimal control of a batch service queueing system with bounded waiting time
Optimal control of a stochastic heat equation with boundary-noise and boundary-control
We are concerned with the optimal control of a nonlinear stochastic heat equation on a bounded real interval with Neumann boundary conditions. The specificity here is that both the control and the noise act on the boundary. We start by reformulating the state equation as an infinite dimensional stochastic evolution equation. The first main result of the paper is the proof of existence and uniqueness of a mild solution for the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The C1 regularity...
Optimal filtering for bilinear system states and its application to terpolymerization process identification.
Optimal hysteretic control for a queue with two operation modes.
Optimal linear filtering of general multidimensional Gaussian processes and its application to Laplace transforms of quadratic functionals.
Optimal mean-variance bounds on order statistics from families determined by star ordering
We present optimal upper bounds for expectations of order statistics from i.i.d. samples with a common distribution function belonging to the restricted family of probability measures that either precede or follow a given one in the star ordering. The bounds for families with monotone failure density and rate on the average are specified. The results are obtained by projecting functions onto convex cones of Hilbert spaces.
Optimal nonlinear transformations of random variables
In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....