While researchers increasingly use deep neural networks (DNN) to analyze individual choices, overfitting and interpretability issues remain as obstacles in theory and practice. By using statistical learning theory, this study presents a framework to examine the tradeoff between estimation and approximation errors, and between prediction and interpretation losses. It operationalizes the DNN interpretability in the choice analysis by formulating the metrics of interpretation loss as the difference between true and estimated choice probability functions. This study also uses the statistical learning theory to upper bound the estimation error of both prediction and interpretation losses in DNN, shedding light on why DNN does not have the overfitting issue. Three scenarios are then simulated to compare DNN to binary logit model (BNL). We found that DNN outperforms BNL in terms of both prediction and interpretation for most of the scenarios, and larger sample size unleashes the predictive power of DNN but not BNL. DNN is also used to analyze the choice of trip purposes and travel modes based on the National Household Travel Survey 2017 (NHTS2017) dataset. These experiments indicate that DNN can be used for choice analysis beyond the current practice of demand forecasting because it has the inherent utility interpretation, the flexibility of accommodating various information formats, and the power of automatically learning utility specification. DNN is both more predictive and interpretable than BNL unless the modelers have complete knowledge about the choice task, and the sample size is small. Overall, statistical learning theory can be a foundation for future studies in the non-asymptotic data regime or using high-dimensional statistical models in choice analysis, and the experiments show the feasibility and effectiveness of DNN for its wide applications to policy and behavioral analysis.

Whereas deep neural network (DNN) is increasingly applied to choice analysis, it is challenging to reconcile domain-specific behavioral knowledge with generic-purpose DNN, to improve DNN's interpretability and predictive power, and to identify effective regularization methods for specific tasks. This study designs a particular DNN architecture with alternative-specific utility functions (ASU-DNN) by using prior behavioral knowledge. Unlike a fully connected DNN (F-DNN), which computes the utility value of an alternative k by using the attributes of all the alternatives, ASU-DNN computes it by using only k's own attributes. Theoretically, ASU-DNN can dramatically reduce the estimation error of F-DNN because of its lighter architecture and sparser connectivity. Empirically, ASU-DNN has 2-3% higher prediction accuracy than F-DNN over the whole hyperparameter space in a private dataset that we collected in Singapore and a public dataset in R mlogit package. The alternative-specific connectivity constraint, as a domain-knowledge-based regularization method, is more effective than the most popular generic-purpose explicit and implicit regularization methods and architectural hyperparameters. ASU-DNN is also more interpretable because it provides a more regular substitution pattern of travel mode choices than F-DNN does. The comparison between ASU-DNN and F-DNN can also aid in testing the behavioral knowledge. Our results reveal that individuals are more likely to compute utility by using an alternative's own attributes, supporting the long-standing practice in choice modeling. Overall, this study demonstrates that prior behavioral knowledge could be used to guide the architecture design of DNN, to function as an effective domain-knowledge-based regularization method, and to improve both the interpretability and predictive power of DNN in choice analysis.

While deep neural networks (DNNs) have been increasingly applied to choice analysis showing high predictive power, it is unclear to what extent researchers can interpret economic information from DNNs. This paper demonstrates that DNNs can provide economic information as complete as classical discrete choice models (DCMs). The economic information includes choice predictions, choice probabilities, market shares, substitution patterns of alternatives, social welfare, probability derivatives, elasticities, marginal rates of substitution (MRS), and heterogeneous values of time (VOT). Unlike DCMs, DNNs can automatically learn the utility function and reveal behavioral patterns that are not prespecified by domain experts. However, the economic information obtained from DNNs can be unreliable because of the three challenges associated with the automatic learning capacity: high sensitivity to hyperparameters, model non-identification, and local irregularity. To demonstrate the strength and challenges of DNNs, we estimated the DNNs using a stated preference survey, extracted the full list of economic information from the DNNs, and compared them with those from the DCMs. We found that the economic information either aggregated over trainings or population is more reliable than the disaggregate information of the individual observations or trainings, and that even simple hyperparameter searching can significantly improve the reliability of the economic information extracted from the DNNs. Future studies should investigate other regularizations and DNN architectures, better optimization algorithms, and robust DNN training methods to address DNNs' three challenges, to provide more reliable economic information from DNN-based choice models.

We discuss a possible solution to an unintended consequence of having grades, certificates, rankings and other diversions in the act of transferring knowledge; and zoom in specifically to the topic of having grades, on a curve. We conduct a thought experiment, taking a chapter (and some more?) from the financial markets, (where we trade pollution and what not?), to create a marketplace, where we can trade our grade, similar in structure to the interest rate swap. We connect this to broader problems that are creeping up, unintentionally, due to artificial labels we are attaching, to ourselves. The policy and philosophical implications of our arguments are to suggest that all trophies that we collect (including certificates, grades, medals etc.) should be viewed as personal equity or private equity (borrowing another widely used term in finance) and we should not use them to determine the outcomes in any selection criteria except have a cutoff point: either for jobs, higher studies, or, financial scholarships, other than for entertainment or spectator sports. We suggest alternate methods for grading and performance assessment and put forth tests for teaching and learning similar to the Turing Test for intelligence.

We utilize a fundamentally different model of trading costs to look at the effect of the opening of the Hong Kong Shanghai Connect that links the stock exchanges in the two cities, arguably the biggest event in international business and finance since Christopher Columbus set sail for India. We design a novel methodology that compensates for the lack of data on trading costs in China. We estimate trading costs across similar positions on the dual listed set of securities in Hong Kong and China, hoping to provide useful pieces of information to help scale 'The Great Wall of Chinese Securities Trading Costs'. We then compare actual and estimated trading costs on a sample of real orders across the Hong Kong securities in the dual listed pair to establish the accuracy of our measurements. The primary question we seek to address is 'Which market would be better to trade to gain exposure to the same (or similar) set of securities or sectors?' We find that trading costs on Shanghai, which might have been lower than Hong Kong, might have become higher leading up to the Connect. What remains to be seen is whether this increase in trading costs is a temporary equilibrium due to the frenzy to gain exposure to Chinese securities or whether this phenomenon will persist once the two markets start becoming more and more tightly coupled. It would be interesting to see if this pioneering policy will lead to securities exchanges across the globe linking up one another, creating a trade anything, anywhere and anytime marketplace. Looking beyond mere trading costs, such studies can be used to gather some evidence on what effect the mode of governance and other aspects of life in one country have on another country, once they start joining up their financial markets.

Quantitative finance has had a long tradition of a bottom-up approach to complex systems inference via multi-agent systems (MAS). These statistical tools are based on modelling agents, which trade via a centralised order book to emulate complex and diverse market phenomena. Nevertheless, the issue of agent learning in MAS, which is crucial to price formation and hence to all market activity, has not yet fully benefited from the recent progress of artificial intelligence, and namely reinforcement learning. In order to address this, we present here a next-generation MAS stock market simulator, in which each agent learns to trade autonomously via reinforcement learning. We calibrate it to real market data from the London Stock Exchange over the years 2007 to 2018, and use it to highlight the beneficial impact of agent suboptimal learning on market stability.

We design three continuous-time models in finite horizon of a commodity price, whose dynamics can be affected by the actions of a representative risk--neutral producer and a representative risk-neutral trader. Depending on the model, the producer can control the drift and/or the volatility of the price whereas the trader can at most affect the volatility. The producer can affect the volatility in two ways: either by randomizing her production rate or, as the trader, using other means such as spreading false information. Moreover, the producer contracts at time zero a fixed position in a European convex derivative with the trader. The trader can be price-taker, as in the first two models, or she can also affect the volatility of the commodity price, as in the third model. We solve all three models semi-explicitly and give closed-form expressions of the derivative price over a small time horizon, preventing arbitrage opportunities to arise. We find that when the trader is price-taker, the producer can always compensate the loss in expected production profit generated by an increase of volatility by a gain in the derivative position by driving the price at maturity to a suitable level. Finally, in case the trader is active, the model takes the form of a nonzero-sum linear-quadratic stochastic differential game and we find that when the production rate is already at its optimal stationary level, there is an amount of derivative position that makes both players better off when entering the game.

The equity risk premium puzzle is that the return on equities has far exceeded the average return on short-term risk-free debt and cannot be explained by conventional representative-agent consumption based equilibrium models. We review a few attempts done over the years to explain this anomaly: 1. Inclusion of highly unlikely events with low probability (Ugly state along with Good and Bad), or market crashes / Black Swans. 2. Slow moving habit, or time-varying subsistence level, added to the basic power utility function. 3. A separation of the inter-temporal elasticity of substitution and risk aversion, combined with long run risks which captures time varying economic uncertainty. We explore whether a fusion of the above approaches supplemented with better methods to handle the below reservations would provide a more realistic and yet tractable framework to tackle the various conundrums in the social sciences: 1. Unlimited ability of individuals to invest as compared to their ability to consume. 2. Lack of an objective measuring stick of value 3. Unintended consequences due to the dynamic nature of social systems 4. Relaxation of the transversality condition to avoid the formation of asset price bubbles 5. How durable is durable? Accounting for durable goods since nothing lasts forever The world we live in produces fascinating phenomenon despite (or perhaps, due to) being a hotchpotch of varying doses of the above elements. The rationale for a unified theory is that beauty can emerge from chaos since the best test for a stew is its taste. Many long standing puzzles seem to have been resolved using different techniques. The various explanations need to stand the test of time before acceptance; but then unexpected outcomes set in and new puzzles emerge. As real analysis and limits tell us: We are getting Closer and Closer; Yet it seems we are still Far Far Away...

This paper presents an optimal allocation problem in a financial market with one risk-free and one risky asset, when the market is driven by a stochastic market price of risk. We solve the problem in continuous time, for an investor with a Constant Relative Risk Aversion (CRRA) utility, under two scenarios: when the market price of risk is observable (the {\em full information case}), and when it is not (the {\em partial information case}). The corresponding market models are complete in the partial information case and incomplete in the other case, hence the two scenarios exhibit rather different features. We study how the access to more accurate information on the market price of risk affects the optimal strategies and we determine the maximal price that the investor would be willing to pay to get such information. In particular, we examine two cases of additional information, when an exact observation of the market price of risk is available either at time $0$ only (the {\em initial information case}), or during the whole investment period (the {\em dynamic information case}).