Real Options using Markov Chains: an application to Production Capacity Decisions

In this work we address investment decisions using real options. A standard numerical approach for valuing real options is dynamic programming. The basic idea is to establish a discrete-valued lattice of possible future values of the underlying stochastic variable (demand in our case). For most approaches in the literature, the stochastic variable is assumed normally distributed and then approximated by a binomial distribution, resulting in a binomial lattice. In this work, we investigate the use of a sparse Markov chain to model such variable. The Markov approach is expected to perform better since it does not assume any type of distribution for the demand variation, the probability of a variation on the demand value is dependent on the current demand value and thus, no longer constant, and it generalizes the binomial lattice since the latter can be modelled as a Markov chain. We developed a stochastic dynamic programming model that has been implemented both on binomial and Markov models. A numerical example of a production capacity choice problem has been solved and the results obtained show that the investment decisions are different and, as expected the Markov chain approach leads to a better investment policy.Flexible Capacity Investments, Real Options, Markov Chains, Dynamic Programming

A decision support system for TV self-promotion scheduling

This paper describes a Decision Support System (DSS) that aims to plan and maintain the weekly self-promotion space for an over the air TV station. The self-promotion plan requires the assignment of several self-promotion advertisements to a given set of available time slots over a pre-specified planning period. The DSS consists of a data base, a statistic module, an optimization module, and a user interface. The input data is provided by the TV station and by an external audiometry company, which collects daily audience information. The statistical module provides estimates based on the data received from the audiometry company. The optimization module uses a genetic algorithm that can find good solutions quickly. The interface reports the solution and corresponding metrics and can also be used by the decision makers to manually change solutions and input data. Here, we report mainly on the optimization module, which uses a genetic algorithm (GA) to obtain solutions of good quality for realistic sized problem instances in a reasonable amount of time. The GA solution quality is assessed using the optimal solutions obtained by using a branch-and-bound based algorithm to solve instances of small size, for which optimality gaps below 1% are obtained.This research had the support of COMPETE-FEDERPORTUGAL2020-POCI-NORTE2020-FCT funding via grants POCI-01-0145-FEDER 031447 and 031821, NORTE-01-0145-FEDER-000020, and PTDC-EEI-AUT-2933-2014|16858–TOCCATA

Two-Dimensional Scaling Limits via Marked Nonsimple Loops

We postulate the existence of a natural Poissonian marking of the double (touching) points of SLE(6) and hence of the related continuum nonsimple loop process that describes macroscopic cluster boundaries in 2D critical percolation. We explain how these marked loops should yield continuum versions of near-critical percolation, dynamical percolation, minimal spanning trees and related plane filling curves, and invasion percolation. We show that this yields for some of the continuum objects a conformal covariance property that generalizes the conformal invariance of critical systems. It is an open problem to rigorously construct the continuum objects and to prove that they are indeed the scaling limits of the corresponding lattice objects.Comment: 25 pages, 5 figure

Optimal investment timing using Markov jump price processes

In this work, we address an investment problem where the investment can either be made immediately or postponed to a later time, in the hope that market conditions become more favourable. In our case, uncertainty is introduced through market price. When the investment is undertaken, a fixed sunk cost must be paid and a series of cash flows are to be received. Therefore, we are faced with an irreversible investment. Real options analysis provides an adequate framework for this type of problems by recognizing these two characteristics, uncertainty and irreversibility, explicitly. We describe algorithmic solutions for this type of problems by modelling market prices evolution by Markov jump processes.Irreversible investment, optimal stopping, dynamic programming, Markov jump processes

The Brownian Web: Characterization and Convergence

The Brownian Web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in ${\mathbb R}\times{\mathbb R}$. We extend the earlier work of Arratia and of T\'oth and Werner by providing characterization and convergence results for the BW distribution, including convergence of the system of all coalescing random walkssktop/brownian web/finale/arXiv submits/bweb.tex to the BW under diffusive space-time scaling. We also provide characterization and convergence results for the Double Brownian Web, which combines the BW with its dual process of coalescing Brownian motions moving backwards in time, with forward and backward paths ``reflecting'' off each other. For the BW, deterministic space-time points are almost surely of ``type'' $(0,1)$ -- {\em zero} paths into the point from the past and exactly {\em one} path out of the point to the future; we determine the Hausdorff dimension for all types that actually occur: dimension 2 for type $(0,1)$, 3/2 for $(1,1)$ and $(0,2)$, 1 for $(1,2)$, and 0 for $(2,1)$ and $(0,3)$.Comment: 52 pages with 4 figure

A decision support system for planning promotion time slots

We report on the development of a Decision Support System (DSS) to plan the best assignment for the weekly promotion space of a TV station. Each product to promote has a given target audience that is best reached at specific time periods during the week. The DSS aims to maximize the total viewing for each product within its target audience while fulfilling a set of constraints defined by the user. The purpose of this paper is to describe the development and successful implementation of a heuristic-based scheduling software system that has been developed for a major Portuguese TV station.Fundação para a Ciência e a Tecnologia (FCT)- FCT/POCI 2010/FEDER, Projecto POCTI/MAT/61842/2004Estação de Televisão SI

Non-Equilibrium Modeling of the Fe XVII 3C/3D ratio for an Intense X-ray Free Electron Laser

We present a review of two methods used to model recent LCLS experimental results for the 3C/3D line intensity ratio of Fe XVII (Bernitt et al. 2012), the time-dependent collisional-radiative method and the density-matrix approach. These are described and applied to a two-level atomic system excited by an X-ray free electron laser. A range of pulse parameters is explored and the effects on the predicted Fe XVII 3C and 3D line intensity ratio are calculated. In order to investigate the behavior of the predicted line intensity ratio, a particular pair of A-values for the 3C and 3D transitions was chosen (2.22 $\times$ 10$^{13}$ s$^{-1}$ and 6.02 $\times$ 10$^{12}$ s$^{-1}$ for the 3C and 3D, respectively), but our conclusions are independent of the precise values. We also reaffirm the conclusions from Oreshkina et al.(2014, 2015): the non-linear effects in the density matrix are important and the reduction in the Fe XVII 3C/3D line intensity ratio is sensitive to the laser pulse parameters, namely pulse duration, pulse intensity, and laser bandwidth. It is also shown that for both models the lowering of the 3C/3D line intensity ratio below the expected time-independent oscillator strength ratio has a significant contribution due to the emission from the plasma after the laser pulse has left the plasma volume. Laser intensities above $\sim 1\times 10^{12}$ W/cm$^{2}$ are required for a reduction in the 3C/3D line intensity ratio below the expected time independent oscillator strength ratio

Building innovation networks: the process of partner selection by young knowledge intensive firms

This paper addresses the selection of partners in innovation networks. It builds on the existing literature to develop an integrative framework that encompasses the main factors identified as influencing selection of partners by young knowledge-intensive firms. It considers that both persistence and novelty are present in the network building process, and so integrates several explanations advanced by the literature: social capital, imprinting and inertia for tie persistence; network embeddedness and proximity for new tie selection. Using a rare event logit model, we estimate the likelihood of selecting an innovation partner using data about the partnerships established by young Portuguese biotechnology firms, purposefully collected through questionnaire-based face-to-face interviews, complemented with documentary information. The results uncover different network building strategies in terms of partner selection to access the different types of resource needed for innovation and highlight the advantages of adopting an integrated framework.FC