Photocopy of typescript. / Digitized by Kansas Correctional Industries

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 254-255. / by Chau-Chyun Chen. / Sc.D.

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 35). / Traffic simulation is an important aspect of understanding how people move throughout various road systems. It can provide insight into the design of city streets and how well they can handle certain traffic patterns. There are various simulators available, ranging from free tools such as TRANSIMS to commercial implementations such as TransCAD. The available tools provide complex, large scale and very detailed simulation capabilities. The Virtual City Testbed addresses aspects that are not available in these tools. Primarily, the test bed provides the ability for interaction with the traffic system in real time. Instead of basing the simulation solely on automated vehicle models, we allow for human participants to interact with individual cars via a remote simulation client. Thus we are able to inject realistic human input into our simulation. A second feature provided by our simulation is the ability to disrupt a simulation in progress. A disruption usually involves disabling access to a set of streets which forces the traffic to adapt as it moves around the road system. This yields a way to study the way traffic motion changes within a road system under the presence of unexpected events such as natural disasters or other real life disruptions. Ultimately, we provide a test bed for studying traffic under varying environmental conditions. / by Oleg I. Kozhushnyan. / M.Eng.

In this thesis, we analyze the computational problem of estimating financial risk in nested Monte Carlo simulation. An outer simulation is used to generate financial scenarios, and an inner simulation is used to estimate future portfolio values in each scenario. Mean squared error (MSE) for standard nested simulation converges at the rate $k^{-2/3}$, where $k$ is the computational budget. In the first part of this thesis, we focus on one risk measure, the probability of a large loss, and we propose a new algorithm to estimate this risk. Our algorithm sequentially allocates computational effort in the inner simulation based on marginal changes in the risk estimator in each scenario. Theoretical results are given to show that the risk estimator has an asymptotic MSE of order $k^{-4/5+\epsilon}$, for all positive $\epsilon$, that is faster compared to the conventional uniform inner sampling approach. Numerical results consistent with the theory are presented. In the second part of this thesis, we introduce a regression-based nested Monte Carlo simulation method for risk estimation. The proposed regression method combines information from different risk factor realizations to provide a better estimate of the portfolio loss function. The MSE of the regression method converges at the rate $k^{-1}$ until reaching an asymptotic bias level which depends on the magnitude of the regression error. Numerical results consistent with our theoretical analysis are provided and numerical comparisons with other methods are also given. In the third part of this thesis, we propose a method based on weighted regression. Similar to the unweighted regression method, the MSE of the weighted regression method converges at the rate $k^{-1}$ until reaching an asymptotic bias level, which depends on the size of the regression error. However, the weighted approach further reduces MSE by emphasizing scenarios that are more important to the calculation of the risk measure. We find a globally optimal weighting strategy for general risk measures in an idealized setting. For applications, we propose and test a practically implementable two-pass method, where the first pass uses an unweighted regression and the second pass uses weights based on the first pass.

Complex nonlinear dynamic models with an intractable likelihood or moments are increasingly common in economics. A popular approach to estimating these models is to match informative sample moments with simulated moments from a fully parameterized model using SMM or Indirect Inference. This dissertation consists of three chapters exploring different aspects of such simulation-based estimation methods. The following chapters are presented in the order in which they were written during my thesis. Chapter 1, written with Serena Ng, provides an overview of existing frequentist and Bayesian simulation-based estimators. These estimators are seemingly computationally similar in the sense that they all make use of simulations from the model in order to do the estimation. To better understand the relationship between these estimators, this chapters introduces a Reverse Sampler which expresses the Bayesian posterior moments as a weighted average of frequentist estimates. As such, it highlights a deeper connection between the two class of estimators beyond the simulation aspect. This Reverse Sampler also allows us to compare the higher-order bias properties of these estimators. We find that while all estimators have an automatic bias correction property (Gourieroux et al., 1993) the Bayesian estimator introduces two additional biases. The first is due to computing a posterior mean rather than the mode. The second is due to the prior, which penalizes the estimates in a particular direction. Chapter 2, also written with Serena Ng, proves that the Reverse Sampler described above targets the desired Approximate Bayesian Computation (ABC) posterior distribution. The idea relies on a change of variable argument: the frequentist optimization step implies a non-linear transformation. As a result, the unweighted draws follow a distribution that depends on the likelihood that comes from the simulations, and a Jacobian term that arises from the non-linear transformation. Hence, solving the frequentist estimation problem multiple times, with different numerical seeds, leads to an optimization-based importance sampler where the weights depend on the prior and the volume of the Jacobian of the non-linear transformation. In models where optimization is relatively fast, this Reverse Sampler is shown to compare favourably to existing ABC-MCMC or ABC-SMC sampling methods. Chapter 3, relaxes the parametric assumptions on the distribution of the shocks in simulation-based estimation. It extends the existing SMM literature, where even though the choice of moments is flexible and potentially nonparametric, the model itself is assumed to be fully parametric. The large sample theory in this chapter allows for both time-series and short-panels which are the two most common data types found in empirical applications. Using a flexible sieve density reduces the sensitivity of estimates and counterfactuals to an ad hoc choice of distribution such as the Gaussian density. Compared to existing work on sieve estimation, the Sieve-SMM estimator involves dynamically generated data which implies non-standard bias and dependence properties. First, the dynamics imply an accumulation of the bias resulting in a larger nonparametric approximation error than in static models. To ensure that it does not accumulate too much, a set decay conditions on the data generating process are given and the resulting bias is derived. Second, by construction, the dependence properties of the simulated data vary with the parameter values so that standard empirical process results, which rely on a coupling argument, do not apply in this setting. This non-standard dependent empirical process is handled through an inequality built by adapting results from the existing literature. The results hold for bounded empirical processes under a geometric ergodicity condition. This is illustrated in the paper with Monte-Carlo simulations and two empirical applications.

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / Microfiche copy available in Archives and Engineering. / Bibliography: leaves 270-272. / M.S.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

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