This paper provides an overview of the finite difference method and its application to approximating financial partial differential equations (PDEs) in incomplete markets. In particular, we study German’s [6] stochastic volatility PDE derived from indifference pricing. In [6], it is shown that the first order- correction to derivatives valued by indifference pricing can be computed as a function involving the stochastic volatility PDE itself. In this paper, we present three explicit finite difference models to approximate the stochastic volatility PDE and compare the resulting valuations to those generated by an Euler- Maruyama Monte Carlo pricing algorithm. We also discuss the significance of boundary condition choice for explicit finite difference models.

This dissertation investigates the role of grammatical versus methodological influences in the production and perception of final devoicing in experimentally-elicited speech from Russian. It addresses the question of how the partial preservation of the phonological voicing contrast in word-final obstruents is affected by (i) task-independent factors that reflect phonological and lexical properties of stimuli words (underlying voicing, word length, lexical competition) and (ii) task-dependent biases that arise due to the nature of the experimental task performed by the speaker (availability of orthographic inputs, presence of minimal pairs among the stimuli). Results of a series of acoustic production and perceptual identification tasks reveal that task-dependent factors account for the presence of robust and perceptually salient differences in the parameter of phonetic voicing. Several types of stimuli items also show limited but statistically significant differences in closure/frication duration and release duration that are independent of the presence of orthography or inclusion of full minimal pairs among test items. Taken together, these findings indicate that non-grammatical factors can play a prominent biasing role in both production and perception of the voicing contrast in experimentally-elicited speech, such that certain voicing-dependent cues are maintained only in the presence of task-dependent pressures. However, not all incompletely neutralized differences between phonologically voiced versus voiceless final obstruents can be attributed to the effects of orthography or inclusion of minimal pairs among the stimuli. In the theoretical domain, these results are argued to favour a less restrictive definition of neutralization and a model of phonology that views devoicing as a loss of the primary acoustic cue to the underlying voicing contrast rather than complete identity of the [voiced] feature.

Foraging behaviour in Drosophila melanogaster larvae is influenced by natural allelic variation in the foraging (for) gene that encodes a cyclic GMP – dependent protein Kinase (PKG), such that rovers (forR) traverse greater distances while foraging than sitters (fors). Foraging behaviour is also influenced by natural allelic variation in the wings up A (wupA) gene that encodes the Troponin-I protein (TnI). Specifically, wupAlow allele suppresses the dominance of the forR allele, turning rovers into sitters. The dominance of the natural wupA alleles and their interactions with allelic combinations in for has not been characterized. I conducted various crosses and found that wupA alleles exhibit incomplete dominance. More importantly, I found that allelic combinations of wupA and for gave rise to a range in larval foraging behaviour. In this study, I propose that this gradient effect in foraging behaviour is due to variation in levels of PKG activity and TnI phosphorylation potential.

Foraging behaviour in Drosophila melanogaster larvae is influenced by natural allelic variation in the foraging (for) gene that encodes a cyclic GMP – dependent protein Kinase (PKG), such that rovers (forR) traverse greater distances while foraging than sitters (fors). Foraging behaviour is also influenced by natural allelic variation in the wings up A (wupA) gene that encodes the Troponin-I protein (TnI). Specifically, wupAlow allele suppresses the dominance of the forR allele, turning rovers into sitters. The dominance of the natural wupA alleles and their interactions with allelic combinations in for has not been characterized. I conducted various crosses and found that wupA alleles exhibit incomplete dominance. More importantly, I found that allelic combinations of wupA and for gave rise to a range in larval foraging behaviour. In this study, I propose that this gradient effect in foraging behaviour is due to variation in levels of PKG activity and TnI phosphorylation potential.

No description available.

Genetically identical cells and organisms growing in homogenous environmental conditions can show significant phenotypic variation. Furthermore, mutations often have consequences that vary among individuals (incomplete penetrance). Biochemical processes such as those involved in gene expression are subjected to fluctuations due to their inherent probabilistic nature. However, it is not clear how these fluctuations affect multicellular organisms carrying mutations and if stochastic variation in gene expression among individuals could confer any advantage to populations. We have investigated the consequences of stochastic gene expression using the nematode Caenorhabditis elegans as a model. Here we show that inter-individual stochastic variation in the induction of both specific and more general buffering systems combine to determine the outcome of inherited mutations in each individual. Also, we demonstrate that genetic and environmental robustness are coupled in C. elegans. Individuals with higher induction of stress response are more robust to the effect of mutations, however they incur a fitness cost, thus suggesting that variation at the population level could be beneficial in unpredictable environments. / Células y organismos genéticamente idénticos y creciendo en un ambiente homogéneo pueden mostrar diferencias en sus fenotipos. Además, una misma mutación puede afectar de un modo distinto a individuos de una misma población. Es sabido que los procesos bioquímicos responsables de la expresión de genes están sujetos a fluctuaciones debido a su inherentemente naturaleza probabilística. Sin embargo, el rol que juegan estas fluctuaciones en individuos portadores de mutaciones ha sido poco estudiado, así cómo si la expresión estocástica de genes puede conferir alguna ventaja al nivel poblacional. Para investigar las consecuencias de la expresión estocástica de genes usamos como modelo al nemátodo Caenorhabditis elegans. En este trabajo demostramos que existe variación entre individuos en la inducción de mecanismos (tanto gen-específicos como globales) que confieren robustez al desarrollo. En consecuencia, diferencias fenotípicas entre mutantes están determinadas por su variación. También, demostramos que la robustez a perturbaciones genéticos y ambientales están estrechamente ligadas en C. elegans. Individuos que inducen estocásticamente una mayor respuesta a stress, están fenotípicamente mejor protegidos al efecto de mutaciones pero incurren en un costo reproductivo importante. Eso sugiere, que variaciones estocásticas al nivel poblacional pueden ser benéficas cuando las poblaciones afrontan ambientes impredecibles.

Bilateral incomplete-information negotiations of multiple issues present a difficult yet common negotiation problem that is complicated to solve from a mechanism design perspective. Unlike multilateral situations, where the individual aspirations of multiple agents can potentially be used against one another to achieve socially desirable outcomes, bilateral negotiations only involve two agents; this makes the negotiations appear to be a zero-sum game pitting agent against agent. While this is essentially true, the gain of one agent is the loss of the other, with multiple issues, it is not unusual that issues are valued asymmetrically such that agents can gain on issues important to them but suffer losses on issues of less importance. Being able to make trade-offs amongst the issues to take advantage of this asymmetry allows both agents to experience overall benefit. The major complication is negotiating under the uncertainty of incomplete information, where agents do not know each other's preferences and neither agent wants to be taken advantage of by revealing its private information to the other agent, or by being too generous in its negotiating. This leaves agents stumbling in the dark trying to find appropriate trade-offs amongst issues. In this work, we introduce the Bilateral Automated Mediation (BAM) framework. The BAM framework is aimed at helping agents alleviate the difficulties of negotiating under uncertainty by formulating a negotiation environment that is suitable for creating agreements that benefit both agents jointly. Our mediator is a composition of many different negotiation ideas and methods put together in a novel third-party framework that guides agents through the agreement space of the negotiation, but instead of arbitrating a final agreement, it allows the agents themselves to ratify the final agreement.

Bilateral incomplete-information negotiations of multiple issues present a difficult yet common negotiation problem that is complicated to solve from a mechanism design perspective. Unlike multilateral situations, where the individual aspirations of multiple agents can potentially be used against one another to achieve socially desirable outcomes, bilateral negotiations only involve two agents; this makes the negotiations appear to be a zero-sum game pitting agent against agent. While this is essentially true, the gain of one agent is the loss of the other, with multiple issues, it is not unusual that issues are valued asymmetrically such that agents can gain on issues important to them but suffer losses on issues of less importance. Being able to make trade-offs amongst the issues to take advantage of this asymmetry allows both agents to experience overall benefit. The major complication is negotiating under the uncertainty of incomplete information, where agents do not know each other's preferences and neither agent wants to be taken advantage of by revealing its private information to the other agent, or by being too generous in its negotiating. This leaves agents stumbling in the dark trying to find appropriate trade-offs amongst issues. In this work, we introduce the Bilateral Automated Mediation (BAM) framework. The BAM framework is aimed at helping agents alleviate the difficulties of negotiating under uncertainty by formulating a negotiation environment that is suitable for creating agreements that benefit both agents jointly. Our mediator is a composition of many different negotiation ideas and methods put together in a novel third-party framework that guides agents through the agreement space of the negotiation, but instead of arbitrating a final agreement, it allows the agents themselves to ratify the final agreement.

<p>In most machine learning approaches, it is usually assumed that data are complete. When data are partially missing due to various reasons, for example, the failure of a subset of sensors, image corruption or inadequate medical measurements, many learning methods designed for complete data cannot be directly applied. In this dissertation we treat two kinds of problems with incomplete data using non-parametric Bayesian approaches: classification with incomplete features and analysis of low-rank matrices with missing entries.</p><p>Incomplete data in classification problems are handled by assuming input features to be generated from a mixture-of-experts model, with each individual expert (classifier) defined by a local Gaussian in feature space. With a linear classifier associated with each Gaussian component, nonlinear classification boundaries are achievable without the introduction of kernels. Within the proposed model, the number of components is theoretically ``infinite'' as defined by a Dirichlet process construction, with the actual number of mixture components (experts) needed inferred based upon the data under test. With a higher-level DP we further extend the classifier for analysis of multiple related tasks (multi-task learning), where model components may be shared across tasks. Available data could be augmented by this way of information transfer even when tasks are only similar in some local regions of feature space, which is particularly critical for cases with scarce incomplete training samples from each task. The proposed algorithms are implemented using efficient variational Bayesian inference and robust performance is demonstrated on synthetic data, benchmark data sets, and real data with natural missing values.</p><p>Another scenario of interest is to complete a data matrix with entries missing. The recovery of missing matrix entries is not possible without additional assumptions on the matrix under test, and here we employ the common assumption that the matrix is low-rank. Unlike methods with a preset fixed rank, we propose a non-parametric Bayesian alternative based on the singular value decomposition (SVD), where missing entries are handled naturally, and the number of underlying factors is imposed to be small and inferred in the light of observed entries. Although we assume missing at random, the proposed model is generalized to incorporate auxiliary information including missingness features. We also make a first attempt in the matrix-completion community to acquire new entries actively. By introducing a probit link function, we are able to handle counting matrices with the decomposed low-rank matrices latent. The basic model and its extensions are validated on</p><p>synthetic data, a movie-rating benchmark and a new data set presented for the first time.</p> / Dissertation

We present two option pricing models, both different from the classical Black-Scholes-Merton model. The first model, suggested by Heston, considers the case where the asset price volatility is stochastic. For this model we study the asset price process and give in detail the derivation of the European call option price process. The second model, suggested by Brody-Hughston-Macrina, describes the observation of certain information about the claim perturbed by a noise represented by a Brownian bridge. Here we also study in detail the properties of this noisy information process and give the derivations of both asset price dynamics and the European call option price process.