|
on Computational Economics |
|
Issue of 2015‒05‒09
six papers chosen by |
| By: | Mehdad, E. (Tilburg University, School of Economics and Management) |
| Abstract: | Simulation is a popular tool for analyzing complex systems. However, simulation models are often difficult to build and require significant time to run. We often need to invest much money and time to use a simulation model of a complex system. To benefit more from a simulation investment, we may use the simulation input/output data to build a metamodel (model of the simulation model). This metamodel may adequately approximate the original simulation model, but is simpler to build and run. Though there are many types of metamodels, we focus on Kriging (or Gaussian process) models. The advantage of Kriging is that it not only predicts the simulation output but also quantifies the prediction uncertainty. We may use the Kriging metamodel to guide the search for the global optimum of the simulation model. A popular method for the global optimization of deterministic simulation is so-called efficient global optimization (EGO) and its expected improvement (EI). EGO uses a Kriging metamodel to calculate EI, and balances exploitation (local search) and exploration (global search) when searching for the optimal input combination for the simulation model. In this dissertation, we investigate several methodological questions about Kriging metamodels and their use in EGO for deterministic and random simulation models. In Chapter 2, we study multivariate Kriging versus univariate Kriging for simulation models with multiple responses. In Chapter 3, we focus on two related questions: (1) How to select the next combination to be simulated when searching for the global optimum? (2) How to derive confidence intervals for outputs of input combinations not yet simulated? In Chapter 4, we study Kriging metamodels that are required to be either convex or monotonic. In Chapter 5, we introduce intrinsic Kriging as a metamodel of deterministic and random simulation models. In Chapter 6, we study the use of intrinsic Kriging as a new metamodel in global optimization of deterministic and random simulations. |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiutis:5b5c276a-fe68-4ce9-b8a8-1482662f8e1d&r=cmp |
| By: | Bell, Peter N |
| Abstract: | Exploration is a costly activity that helps a business improve their understanding of a potential mineral deposit. Yet, even with strong exploration results, the business faces uncertainty over the value of the mine. I model this situation as a game of chance. The game starts by giving an agent an asset with random value and ends when the agent chooses to accept the random value or reject it and receive zero instead. The agent can pay to learn more about the asset’s value as many times as they like before they end the game, but no amount of exploration will remove all uncertainty. I provide a decision rule for the agent based on an interval estimate for the asset value and analyze performance of the decision rule in a simulation experiment. |
| Keywords: | Mineral exploration, game theory, learning, simulation. |
| JEL: | C02 C44 C63 C70 D83 Q39 |
| Date: | 2015–02–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:62159&r=cmp |
| By: | Lorenza Campagnolo (Fondazione Eni Enrico Mattei and Centro Euro-Mediterraneo sui Cambiamenti Climatici); Fabio Eboli (Fondazione Eni Enrico Mattei and Centro Euro-Mediterraneo sui Cambiamenti Climatici) |
| Keywords: | Material Productivity, Resource Efficiency, Sustainable Development Indicators, Computable General Equilibrium |
| JEL: | C68 D58 L61 O13 |
| Date: | 2015–04 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2015.36&r=cmp |
| By: | Bell, Peter N |
| Abstract: | Consider an agent who holds a stock, but is allowed to buy and hold some quantity of at-the-money put options on the stock. Such an agent must decide the optimal use of financial derivatives under trade restrictions. This paper uses simulation to compare the optimal quantity when the agent maximizes mean-variance utility or Value at Risk over wealth at option expiry. The optimal quantity is larger than the stock holding under mean-variance utility and precisely the same under value at risk. The options do not remove all variation in returns but still benefit the agent. |
| Keywords: | Portfolio optimization; put option; trade restrictions; simulation. |
| JEL: | C00 C15 C63 G11 G22 |
| Date: | 2014–10–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:62155&r=cmp |
| By: | Desmond J. Higham |
| Abstract: | Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizing with a numerical method and applying standard Monte Carlo. His multilevel Monte Carlo method offers an order of speed up given by the inverse of epsilon, where epsilon is the required accuracy. So computations can run 100 times more quickly when two digits of accuracy are required. The multilevel philosophy has since been adopted by a range of researchers and a wealth of practically significant results has arisen, most of which have yet to make their way into the expository literature. In this work, we give a brief, accessible, introduction to multilevel Monte Carlo and summarize recent results applicable to the task of option evaluation. |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1505.00965&r=cmp |
| By: | Baştürk N.; Grassi S.; Hoogerheide L.; Opschoor A.; Dijk H.K. van (GSBE) |
| Abstract: | This paper presents the R package MitISEM mixture of t by importance sampling weighted expectation maximization which provides an automatic and flexible two-stage method to approximate a non-elliptical target density kernel - typically a posterior density kernel - using an adaptive mixture of Student-t densities as approximating density. In the first stage a mixture of Student-t densities is fitted to the target using an expectation maximization EM algorithm where each step of the optimization procedure is weighted using importance sampling. In the second stage this mixture density is a candidate density for efficient and robust application of importance sampling or the Metropolis-Hastings MH method to estimate properties of the target distribution. The package enables Bayesian inference and prediction on model parameters and probabilities, in particular, for models where densities have multi-modal or other non-elliptical shapes like curved ridges. These shapes occur in research topics in several scientific fields. For instance, analysis of DNA data in bioinformatics, obtaining loans in the banking sector by heterogeneous groups in financial economics and analysis of educations effect on earned income in labor economics. The package MitISEM provides also an extended algorithm, sequential MitISEM, which substantially decreases computation time when the target density has to be approximated for increasing data samples. This occurs when the posterior or predictive density is updated with new observations and/or when one computes model probabilities using predictive likelihoods. We illustrate the MitISEM algorithm using three canonical statistical and econometric models that are characterized by several types of non-elliptical posterior shapes and that describe well-known data patterns in econometrics and finance. We show that MH using the candidate density obtained by MitISEM outperforms, in terms of numerical efficiency, MH using a simpler candidate, as well as the Gibbs sampler. The MitISEM approach is also used for Bayesian model comparison using predictive likelihoods. |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2015011&r=cmp |