Recently, Ross (2015) derived a theorem, namely the "Recovery Theorem", that allows for the recovery of the pricing kernel and real-world asset distribution, under particular assumptions, from a forward-looking risk neutral distribution. However, recovering the real-world distribution involves solving two ill-posed problems. In this paper, we introduce and test the accuracy of a regularised multivariate mixture distribution to recover the real-world distribution. In addition, we show that this method improves the estimation accuracy of the real-world distribution. Furthermore, we carry out an empirical study, using weekly South African Top40 option trade data, to show that the recovered distribution is in line with economic theory.

This paper shows that expected uncertainty should be included as a key determinant in the derivation of the natural probability distribution of assets because it contains information that goes beyond information contained in state prices. I redefine the contingent state prices derived in the Recovery Theorem model using a multivariate Markov chain. I employ a mixture transition distribution where the proposed states depend on the level of the S&P 500 index and on the expected uncertainty derived from option prices. Controlling for uncertainty is critical because the transition path between states depends on the propensity of an underlying asset to vary. The multivariate RT produces forecast results far superior to the univariate RT.

This dissertation is concerned with Ross' (2011) Recovery Theorem. It is generally held that a forward-looking probability distribution is unobtainable from derivative prices, because the market's risk-preferences are conceptually inextricable from the implied real-world distribution. Ross' result recovers this distribution without making the strong preference assumptions assumed necessary under the conventional paradigm. This dissertation aims to give the reader a thorough understanding of Ross Recovery, both from a theoretical and practical point of view. This starts with a formal delineation of the model and proof of the central result, motivated by the informal nature of Ross' working paper. This dissertation relaxes one of Ross' assumptions and arrives at the equivalent conclusion. This is followed by a critique of the model and assumptions. An a priori discussion only goes so far, but potentially problematic assumptions are identified, chief amongst which being time additive preferences of a representative agent. Attention is then turned to practical application of the theorem. The author identifies a number of obstacles to applying the result { some of which are somewhat atypical and have not been directly addressed in the literature { and suggests potential solutions. A salient obstacle is calibrating a state price matrix. This leads to an implementation of Ross Recovery on the FTSE/JSE Top40. The suggested approach is found to be workable, though certainly not the final word on the matter. A testing framework for the model is discussed and the dissertation is concluded with a consideration of the findings and the theorem's applicability.

This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount factor (SDF) is a positive semi-martingale multiplicative functional of X. A key result is the uniqueness theorem for a positive eigenfunction of the pricing operator such that X is recurrent under a new probability measure associated with this eigenfunction (recurrent eigenfunction). As economic applications, we prove uniqueness of the Hansen and Scheinkman (2009) factorization of the Markovian SDF corresponding to the recurrent eigenfunction, extend the Recovery Theorem of Ross (2015) from discrete time, finite state irreducible Markov chains to recurrent BRPs, and obtain the long maturity asymptotics of the pricing operator. When an asset pricing model is specified by given risk-neutral probabilities together with a short rate function of the Markovian state, we give sufficient conditions for existence of a recurrent eigenfunction and provide explicit examples in a number of important financial models, including affine and quadratic diffusion models and an affine model with jumps. These examples show that the recurrence assumption, in addition to fixing uniqueness, rules out unstable economic dynamics, such as the short rate asymptotically going to infinity or to a zero lower bound trap without possibility of escaping.

This volume contains the latest in the series of ICAPR proceedings on the state-of-the-art of different facets of pattern recognition. These conferences have already carved out a unique position among events attended by the pattern recognition community. The contributions tackle open problems in the classic fields of image and video processing, document analysis and multimedia object retrieval as well as more advanced topics in biometrics speech and signal analysis. Many of the papers focus both on theory and application driven basic research pattern recognition.

Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Focussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.