Learning Data-Driven Models of Non-Verbal Behaviors for Building Rapport Using an Intelligent Virtual Agent

There is a growing societal need to address the increasing prevalence of behavioral health issues, such as obesity, alcohol or drug use, and general lack of treatment adherence for a variety of health problems. The statistics, worldwide and in the USA, are daunting. Excessive alcohol use is the third leading preventable cause of death in the United States (with 79,000 deaths annually), and is responsible for a wide range of health and social problems. On the positive side though, these behavioral health issues (and associated possible diseases) can often be prevented with relatively simple lifestyle changes, such as losing weight with a diet and/or physical exercise, or learning how to reduce alcohol consumption. Medicine has therefore started to move toward finding ways of preventively promoting wellness, rather than solely treating already established illness. Evidence-based patient-centered Brief Motivational Interviewing (BMI) interven- tions have been found particularly effective in helping people find intrinsic motivation to change problem behaviors after short counseling sessions, and to maintain healthy lifestyles over the long-term. Lack of locally available personnel well-trained in BMI, however, often limits access to successful interventions for people in need. To fill this accessibility gap, Computer-Based Interventions (CBIs) have started to emerge. Success of the CBIs, however, critically relies on insuring engagement and retention of CBI users so that they remain motivated to use these systems and come back to use them over the long term as necessary. Because of their text-only interfaces, current CBIs can therefore only express limited empathy and rapport, which are the most important factors of health interventions. Fortunately, in the last decade, computer science research has progressed in the design of simulated human characters with anthropomorphic communicative abilities. Virtual characters interact using humans’ innate communication modalities, such as facial expressions, body language, speech, and natural language understanding. By advancing research in Artificial Intelligence (AI), we can improve the ability of artificial agents to help us solve CBI problems. To facilitate successful communication and social interaction between artificial agents and human partners, it is essential that aspects of human social behavior, especially empathy and rapport, be considered when designing human-computer interfaces. Hence, the goal of the present dissertation is to provide a computational model of rapport to enhance an artificial agent’s social behavior, and to provide an experimental tool for the psychological theories shaping the model. Parts of this thesis were already published in [LYL+12, AYL12, AL13, ALYR13, LAYR13, YALR13, ALY14].

A Study on the Correlation of Bivariate And Trivariate Normal Models

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.

Three essays on asset pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lvy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.

Contemporary aspects of dividends: Before and during the financial crisis

The number of dividend paying firms has been on the decline since the popularity of stock repurchases in the 1980s, and the recent financial crisis has brought about a wave of dividend reductions and omissions. This dissertation examined the U.S. firms and American Depository Receipts that are listed on the U.S. equity exchanges according to their dividend paying history in the previous twelve quarters. While accounting for the state of the economy, the firm’s size, profitability, earned equity, and growth opportunities, it determines whether or not the firm will pay a dividend in the next quarter. It also examined the likelihood of a dividend change. Further, returns of firms were examined according to their dividend paying history and the state of the economy using the Fama-French three-factor model. Using forward, backward, and step-wise selection logistic regressions, the results show that firms with a history of regular and uninterrupted dividend payments are likely to continue to pay dividends, while firms that do not have a history of regular dividend payments are not likely to begin to pay dividends or continue to do so. The results of a set of generalized polytomous logistic regressions imply that dividend paying firms are more likely to reduce dividend payments during economic expansions, as opposed to recessions. Also the analysis of returns using the Fama-French three factor model reveals that dividend paying firms are earning significant abnormal positive returns. As a special case, a similar analysis of dividend payment and dividend change was applied to American Depository Receipts that trade on the NYSE, NASDAQ, and AMEX exchanges and are issued by the Bank of New York Mellon. Returns of American Depository Receipts were examined using the Fama-French two-factor model for international firms. The results of the generalized polytomous logistic regression analyses indicate that dividend paying status and economic conditions are also important for dividend level change of American Depository Receipts, and Fama-French two-factor regressions alone do not adequately explain returns for these securities.

A study of stock market linkages between the US and frontier countries

My dissertation investigates the financial linkages and transmission of economic shocks between the US and the smallest emerging markets (frontier markets). The first chapter sets up an empirical model that examines the impact of US market returns and conditional volatility on the returns and conditional volatilities of twenty-one frontier markets. The model is estimated via maximum likelihood; utilizes the GARCH model of errors, and is applied to daily country data from the MSCI Barra. We find limited, but statistically significant exposure of Frontier markets to shocks from the US. Our results suggest that it is not the lagged US market returns that have impact; rather it is the expected US market returns that influence frontier market returns The second chapter sets up an empirical time-varying parameter (TVP) model to explore the time-variation in the impact of mean US returns on mean Frontier market returns. The model utilizes the Kalman filter algorithm as well as the GARCH model of errors and is applied to daily country data from the MSCI Barra. The TVP model detects statistically significant time-variation in the impact of US returns and low, but statistically and quantitatively important impact of US market conditional volatility. The third chapter studies the risk-return relationship in twenty Frontier country stock markets by setting up an international version of the intertemporal capital asset pricing model. The systematic risk in this model comes from covariance of Frontier market stock index returns with world returns. Both the systematic risk and risk premium are time-varying in our model. We also incorporate own country variances as additional determinants of Frontier country returns. Our results suggest statistically significant impact of both world and own country risk in explaining Frontier country returns. Time-variation in the world risk premium is also found to be statistically significant for most Frontier market returns. However, own country risk is found to be quantitatively more important.

Three Essays on Asset Pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lévy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.