The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Arbitrage-free regularization, geometric learning, and non-Euclidean filtering in finance

This thesis brings together elements of differential geometry, machine learning, and pathwise stochastic analysis to answer problems in mathematical finance. The overarching theme is the development of new stochastic machine learning algorithms which incorporate arbitrage-free and geometric features into their estimation procedures in order to give more accurate forecasts and preserve the geometric and financial structure in the data. This thesis is divided into three part. The first part introduces the non-Euclidean upgrading (NEU) meta-algorithm which builds the universal reconfiguration and universal approximation properties into any objective learning algorithm. These properties state that a procedure can reproduce any dataset exactly and approximate any function to arbitrary precision, respectively. This is done through an unsupervised learning procedure which identifies a geometry optimizing the relationship between a dataset and the objective learning algorithm used to explain it. The effectiveness of this procedure is supported both theoretically and numerically. The numerical implementations find that NEU-ordinary least squares outperforms leading regularized regression algorithms and that NEU-PCA explains more variance with one NEU-principal component than PCA does with four classical principal components. The second part of the thesis introduces a computationally efficient characterization of intrinsic conditional expectation for Cartan-Hadamard manifolds. This alternative characterization provides an explicit way of computing non-Euclidean conditional expectation by using geometric transformations of specific Euclidean conditional expectations. This reduces many non-convex intrinsic estimation problems to transformations of well studied Euclidean conditional expectations. As a consequence, computationally tractable non-Euclidean filtering equations are derived and used to successfully forecast efficient portfolios by exploiting their geometry. The third and final part of this thesis introduces a flexible modeling framework and a stochastic learning methodology for incorporating arbitrage-free features into many asset price models. The procedure works by minimally deforming the structure of a model until the objective measure acts as a martingale measure for that model. Reformulations of classical no-arbitrage results such as NFLVR, the minimal martingale measure, and the arbitrage-free Nelson-Siegel correction of the Nelson-Siegel model are all derived as solutions to specific arbitrage-free regularization problems. The flexibility and generality of this framework allows classical no-arbitrage pricing theory to be extended to models that admit arbitrage opportunities but are deformable into arbitrage-free models. Numerical implications are investigated in each of the three parts making up this thesis

Applications of robust optimal control to decision making in the presence of uncertainty

This thesis is concerned with robustness of decision making in financial economics. Feedback control models developed in engineering are applied to three separate though linked problems in order to examine the role and impact of robustness in the creation and application of decision rules. Three problems are examined using robust optimal control techniques to evaluate the impact of robustness and stability in financial economic models. The first problem examines the use of linear models of robust optimal control in the pricing of castastrophe based derivatives and finds its relative performance to be superior to the popular jump diffusion and stochastic volatility models in the pricing of these emerging instruments. The novelty of the approach arises from the examination of the impact of robustness and stability of the pricing solution. The second problem involves robustness and stability of hedging. An alternative method of creating hedging rules is developed. The method is based on robust control Lyapunov functions that are simple, robust and stable in operation, yet in practice are not so conservative that they eliminate all trading gains. The third problem involves the development of robust control policies for managing risk, using non-linear robust optimal control techniques to provide clear evidence of superior performance of robust models when compared with existing VAR and EVT approaches to risk management. The novelty in the approach arises from the development of a simple and powerful risk management metric

Science handbook

2005 handbook for the faculty of Scienc

Science handbook

2005 handbook for the faculty of Scienc