We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an exponential, giving rise to long memory effects. In comparison with other available methods present in the literature, our procedure does not rely on subjective evaluations and is computationally inexpensive. The underlying basic idea is to use a suitable factor model to analyse the residual memory after sequentially removing more and more components, and stopping the process when the maximum amount of memory has been accounted for by the retained components. We validate our methodology on both synthetic and real financial data, and find in all cases a clear and computationally superior answer entirely compatible with available heuristic criteria, such as cumulative variance and cross-validation.

Paid crowdsourcing platforms suffer from low-quality work and unfair rejections, but paradoxically, most workers and requesters have high reputation scores. These inflated scores, which make high-quality work and workers difficult to find, stem from social pressure to avoid giving negative feedback. We introduce Boomerang, a reputation system for crowdsourcing that elicits more accurate feedback by rebounding the consequences of feedback directly back onto the person who gave it. With Boomerang, requesters find that their highly-rated workers gain earliest access to their future tasks, and workers find tasks from their highly-rated requesters at the top of their task feed. Field experiments verify that Boomerang causes both workers and requesters to provide feedback that is more closely aligned with their private opinions. Inspired by a game-theoretic notion of incentive-compatibility, Boomerang opens opportunities for interaction design to incentivize honest reporting over strategic dishonesty.

Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable $\mathbf{x}$ and a dependent variable $\mathbf{y}$ by modeling their conditional probability $p(\mathbf{y}|\mathbf{x})$. The paper develops best practices for conditional density estimation for finance applications with neural networks, grounded on mathematical insights and empirical evaluations. In particular, we introduce a noise regularization and data normalization scheme, alleviating problems with over-fitting, initialization and hyper-parameter sensitivity of such estimators. We compare our proposed methodology with popular semi- and non-parametric density estimators, underpin its effectiveness in various benchmarks on simulated and Euro Stoxx 50 data and show its superior performance. Our methodology allows to obtain high-quality estimators for statistical expectations of higher moments, quantiles and non-linear return transformations, with very little assumptions about the return dynamic.

Optimization methods are used to determine equilibria of investment in cryptocurrencies. The basic assumptions involve existence of a core group (the "wealthy") that fears the loss of substantial assets through government seizure. Speculators constitute another group that tends to introduce volatility and risk for the wealthy. The wealthy must divide their assets between the home currency and the cryptocurrency, while the government decides on the probability of seizing a fraction the assets of this group. Under the assumption that each group exhibits risk aversion through a utility function, we establish the existence and uniqueness of Nash equilibrium. Also examined is the more realistic optimization problem in which the government policy cannot be reversed, while the wealthy can adjust their allocation in reaction to the government's designation of probability. The methodology leads to an understanding the equilibrium market capitalization of cryptocurrencies.

Transportation Network Companies (TNCs) are changing the transportation ecosystem, but micro-decisions of drivers and users need to be better understood to assess the system-level impacts of TNCs. In this regard, we contribute to the literature by estimating a) individuals' preferences of being a rider, a driver, or a non-user of TNC services; b) preferences of ridehailing users for ridepooling; c) TNC drivers' choice to switch to vehicles with better fuel economy, and also d) the drivers' decision to buy, rent or lease new vehicles with driving for TNCs being a major consideration. Elicitation of drivers' preferences using a unique sample (N=11,902) of the U.S. population residing in TNC-served areas is the key feature of this study. The statistical analysis indicates that ridehailing services are mainly attracting personal vehicle users as riders, without substantially affecting demand for transit. Moreover, around 10% of ridehailing users reported postponing the purchase of a new car due to the availability of TNC services. The model estimation results indicate that the likelihood of being a TNC user increases with the increase in age for someone younger than 44 years, but the pattern is reversed post 44 years. This change in direction of the marginal effect of age is insightful as the previous studies have reported a negative association. We also find that postgraduate drivers who live in metropolitan regions are more likely to switch to fuel-efficient vehicles. These findings would inform transportation planners and TNCs in developing policies to improve the fuel economy of the fleet.

Mid-price movement prediction based on limit order book (LOB) data is a challenging task due to the complexity and dynamics of the LOB. So far, there have been very limited attempts for extracting relevant features based on LOB data. In this paper, we address this problem by designing a new set of handcrafted features and performing an extensive experimental evaluation on both liquid and illiquid stocks. More specifically, we implement a new set of econometrical features that capture statistical properties of the underlying securities for the task of mid-price prediction. Moreover, we develop a new experimental protocol for online learning that treats the task as a multi-objective optimization problem and predicts i) the direction of the next price movement and ii) the number of order book events that occur until the change takes place. In order to predict the mid-price movement, the features are fed into nine different deep learning models based on multi-layer perceptrons (MLP), convolutional neural networks (CNN) and long short-term memory (LSTM) neural networks. The performance of the proposed method is then evaluated on liquid and illiquid stocks, which are based on TotalView-ITCH US and Nordic stocks, respectively. For some stocks, results suggest that the correct choice of a feature set and a model can lead to the successful prediction of how long it takes to have a stock price movement.

I derive practical formulas for optimal arrangements between sophisticated stock market investors (namely, continuous-time Kelly gamblers) and the brokers who lend them cash for leveraged bets on a high Sharpe asset (i.e. the market portfolio). Rather than, say, the broker posting a monopoly price for margin loans, the gambler agrees to use a greater quantity of margin debt than he otherwise would in exchange for an interest rate that is lower than the broker would otherwise post. The gambler thereby attains a higher asymptotic capital growth rate and the broker enjoys a greater rate of intermediation profit than would obtain under non-cooperation. If the threat point represents a vicious breakdown of negotiations (resulting in zero margin loans), then we get an elegant rule of thumb: $r_L^*=(3/4)r+(1/4)(\nu-\sigma^2/2)$, where $r$ is the broker's cost of funds, $\nu$ is the compound-annual growth rate of the market index, and $\sigma$ is the annual volatility. We show that, regardless of the particular threat point, the gambler will negotiate to size his bets as if he himself could borrow at the broker's call rate.

Most products are produced and sold by supply chain networks, where an interconnected network of producers and intermediaries set prices to maximize their profits. I show that there exists a unique equilibrium in a price-setting game on a network. The key distortion reducing both total profits and social welfare is multiple-marginalization, which is magnified by strategic interactions. Individual profits are proportional to influentiality, which is a new measure of network centrality defined by the equilibrium characterization. The results emphasize the importance of the network structure when considering policy questions such as mergers or trade tariffs.

I present evidence incorporating costly thought solves three puzzles in the retirement literature. The first puzzle is, given incentives, the extent of bunching of labour market exits at legislated state pension ages (SPA) seems incompatible with rational expectations. Adding to the evidence for this puzzle, I include an empirical analysis focusing on whether liquidity constraints can explain this bunching and find they cannot. The nature of this puzzle is clarified by exploring a life-cycle model with rational agents that matches aggregate profiles. This model succeeds in matching aggregates by overestimating the impact of the SPA on poorer individuals whilst underestimating its impact on wealthier people. The second puzzle is people are often mistaken about their own pension provisions. Concerning the second puzzle, I incorporate rational inattention to the SPA into the aforementioned life-cycle model, allowing for mistaken beliefs. To the best of my knowledge, this paper is the first not only to incorporate rational inattention into a life-cycle model but also to assess a rationally inattentive model against non-experimental individual choice data. This facilitates another important contribution: discipling the cost of attention with subjective belief data. Preliminary results indicate rational inattention improves the aggregate fit and better matches the response of participation to the SPA across the wealth distribution, hence offering a resolution to the first puzzle. The third puzzle is despite actuarially advantageous options to defer receipt of pension benefits, take up is extremely low. An extension of the model generates an explanation of this last puzzle: the actuarial calculations implying deferral is preferable ignore the utility cost of tracking your pension which can be avoided by claiming. These puzzles are researched in the context of the reform to the UK female SPA.

We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$ under random linear transformations. This allows us to compute probabilities of a variety of tail events, which classical multivariate regularly varying models would report to be asymptotically negligible. We illustrate our findings with applications to risk assessment in financial systems and reinsurance markets under a bipartite network structure.