In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal investment plan, and derive necessary and sufficient conditions for optimality. This allows us to construct the optimal policy in terms of the solution to a stochastic backward equation under the worst-case scenario. In a time-homogeneous setting - where risk is driven by a geometric Brownian motion and Knightian uncertainty is realized through a so-called "k-ignorance" - we are able to provide the explicit form of the optimal irreversible investment plan.

Do boundedly rational players learn to choose equilibrium strategies as they play a game repeatedly? A large literature in behavioral game theory has proposed and experimentally tested various learning algorithms, but a comparative analysis of their equilibrium convergence properties is lacking. In this paper we analyze Experience-Weighted Attraction (EWA), which generalizes fictitious play, best reply dynamics, reinforcement learning and also replicator dynamics. We provide a comprehensive analytical characterization of the asymptotic behavior of EWA learning in $2\times 2$ games. We recover some well-known results in the limiting cases in which EWA reduces to the learning rules that it generalizes, but also obtain new results for other parameterizations. For example, we show that in coordination games EWA may only converge to the Pareto-efficient equilibrium, never reaching the Pareto-inefficient one; that in Prisoner Dilemma games it may converge to fixed points of mutual cooperation; and that in Matching Pennies games it may fail to converge to any fixed point, following instead limit cycles or chaos.

In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme being a generalization of the classical Crank-Nicolson scheme. The proposed method has $2-\alpha$ order of accuracy with respect to time where $\alpha\in(0,1)$ is the subdiffusion parameter, and $2$ with respect to space. Further, we provide the stability and convergence analysis. Finally, we present some numerical results.

The multi-factor model is a widely used model in quantitative investment. The success of a multi-factor model is largely determined by the effectiveness of the alpha factors used in the model. This paper proposes a new evolutionary algorithm called AutoAlpha to automatically generate effective formulaic alphas from massive stock datasets. Specifically, first we discover an inherent pattern of the formulaic alphas and propose a hierarchical structure to quickly locate the promising part of space for search. Then we propose a new Quality Diversity search based on the Principal Component Analysis (PCA-QD) to guide the search away from the well-explored space for more desirable results. Next, we utilize the warm start method and the replacement method to prevent the premature convergence problem. Based on the formulaic alphas we discover, we propose an ensemble learning-to-rank model for generating the portfolio. The backtests in the Chinese stock market and the comparisons with several baselines further demonstrate the effectiveness of AutoAlpha in mining formulaic alphas for quantitative trading.

We designed a machine learning algorithm that identifies patterns between ESG profiles and financial performances for companies in a large investment universe. The algorithm consists of regularly updated sets of rules that map regions into the high-dimensional space of ESG features to excess return predictions. The final aggregated predictions are transformed into scores which allow us to design simple strategies that screen the investment universe for stocks with positive scores. By linking the ESG features with financial performances in a non-linear way, our strategy based upon our machine learning algorithm turns out to be an efficient stock picking tool, which outperforms classic strategies that screen stocks according to their ESG ratings, as the popular best-in-class approach. Our paper brings new ideas in the growing field of financial literature that investigates the links between ESG behavior and the economy. We show indeed that there is clearly some form of alpha in the ESG profile of a company, but that this alpha can be accessed only with powerful, non-linear techniques such as machine learning.

A large body of research documents that the 2010 dependent coverage mandate of the Affordable Care Act was responsible for significantly increasing health insurance coverage among young adults. No prior research has examined whether sexual minority young adults also benefitted from the dependent coverage mandate, despite previous studies showing lower health insurance coverage among sexual minorities and the fact that their higher likelihood of strained relationships with their parents might predict a lower ability to use parental coverage. Our estimates from the American Community Surveys using difference-in-differences and event study models show that men in same-sex couples age 21-25 were significantly more likely to have any health insurance after 2010 compared to the associated change for slightly older 27 to 31-year-old men in same-sex couples. This increase is concentrated among employer-sponsored insurance, and it is robust to permutations of time periods and age groups. Effects for women in same-sex couples and men in different-sex couples are smaller than the associated effects for men in same-sex couples. These findings confirm the broad effects of expanded dependent coverage and suggest that eliminating the federal dependent mandate could reduce health insurance coverage among young adult sexual minorities in same-sex couples.

Fixed income has received far less attention than equity portfolio optimisation since Markowitz' original work of 1952, partly as a result of the need to model rates and credit risk. We argue that the shape of the efficient frontier is mainly controlled by linear constraints, with the standard deviation relatively unimportant, and propose a two-factor model for its time evolution.

We provide a data-driven analysis of how investor expectations about economic growth and stock market returns changed during the February-March 2020 stock market crash induced by the COVID-19 pandemic. We surveyed wealthy retail investors who are clients of Vanguard in mid-February 2020, around the all-time stock market high, and then again on March 11 and 12, after the stock market had collapsed by over 20%. The average investor turned more pessimistic about the short-run performance of both stock markets and the economy. Investors also perceived higher probability of both further extreme stock market declines and large declines in short-run real economic activity. In contrast, investors' expectations about the long run remained largely unchanged, and if anything improved. Disagreement among investors about economic and stock market outcomes also increased substantially. Our analysis is an input in both the design of the ongoing economic policy response and in further advancing economic theories.

This paper addresses the joint calibration problem of SPX options and VIX options or futures. We show that the problem can be formulated as a semimartingale optimal transport problem under a finite number of discrete constraints, in the spirit of [arXiv:1906.06478]. We introduce a PDE formulation along with its dual counterpart. The optimal processes can then be represented via the solutions of Hamilton-Jacobi-Bellman equations arising from the dual formulation. A numerical example shows that the model can be accurately calibrated to the SPX European options and the VIX futures simultaneously.

We first revisit the problem of kernel estimation of spot volatility in a general continuous It\^o semimartingale model in the absence of microstructure noise, and prove a Central Limit Theorem with optimal convergence rate, which is an extension of Figueroa and Li (2020) as we allow for a general two-sided kernel function. Next, to handle the microstructure noise of ultra high-frequency observations, we present a new type of pre-averaging/kernel estimator for spot volatility under the presence of additive microstructure noise. We prove Central Limit Theorems for the estimation error with an optimal rate and study the problems of optimal bandwidth and kernel selection. As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator is minimal for exponential or Laplace kernels, hence, justifying the need of working with unbounded kernels as proposed in this work. Feasible implementation of the proposed estimators with optimal bandwidth is also developed. Monte Carlo experiments confirm the superior performance of the devised method.

This study examines whether the efficiency of cryptocurrency markets (Bitcoin and Ethereum) evolve over time based on Lo's (2004) adaptive market hypothesis (AMH). In particular, we measure the degree of market efficiency using a generalized least squares-based time-varying model that does not depend on sample size, unlike previous studies that used conventional methods. The empirical results show that (1) the degree of market efficiency varies with time in the markets, (2) the degree of market efficiency varies with time, (2) Bitcoin's market efficiency level is higher than that of Ethereum over most periods, and (3) a market with high market liquidity has been evolving. We conclude that the results support the AMH for the most established cryptocurrency market.

SREC markets are a relatively novel market-based system to incentivize the production of energy from solar means. A regulator imposes a floor on the amount of energy each regulated firm must generate from solar power in a given period and provides them with certificates for each generated MWh. Firms offset these certificates against the floor and pay a penalty for any lacking certificates. Certificates are tradable assets, allowing firms to purchase/sell them freely. In this work, we formulate a stochastic control problem for generating and trading in SREC markets from a regulated firm's perspective. We account for generation and trading costs, the impact both have on SREC prices, provide a characterization of the optimal strategy, and develop a numerical algorithm to solve this control problem. Through numerical experiments, we explore how a firm who acts optimally behaves under various conditions. We find that an optimal firm's generation and trading behaviour can be separated into various regimes, based on the marginal benefit of obtaining an additional SREC, and validate our theoretical characterization of the optimal strategy. We also conduct parameter sensitivity experiments and conduct comparisons of the optimal strategy to other candidate strategies.

In this paper, we propose a new threshold-kernel jump-detection method for jump-diffusion processes, which iteratively applies thresholding and kernel methods in an approximately optimal way to achieve improved finite-sample performance. We use the expected number of jump misclassifications as the objective function to optimally select the threshold parameter of the jump detection scheme. We prove that the objective function is quasi-convex and obtain a new second-order infill approximation of the optimal threshold in closed form. The approximate optimal threshold depends not only on the spot volatility, but also the jump intensity and the value of the jump density at the origin. Estimation methods for these quantities are then developed, where the spot volatility is estimated by a kernel estimator with thresholding and the value of the jump density at the origin is estimated by a density kernel estimator applied to those increments deemed to contain jumps by the chosen thresholding criterion. Due to the interdependency between the model parameters and the approximate optimal estimators built to estimate them, a type of iterative fixed-point algorithm is developed to implement them. Simulation studies for a prototypical stochastic volatility model show that it is not only feasible to implement the higher-order local optimal threshold scheme but also that this is superior to those based only on the first order approximation and/or on average values of the parameters over the estimation time period.

Maximising dividends is one classical stability criterion in actuarial risk theory. Motivated by the fact that dividends are paid periodically in real life, $\textit{periodic}$ dividend strategies were recently introduced (Albrecher, Gerber and Shiu, 2011). In this paper, we incorporate fixed transaction costs into the model and study the optimal periodic dividend strategy with fixed transaction costs for spectrally negative L\'evy processes.

The value function of a periodic $(b_u,b_l)$ strategy is calculated by means of exiting identities and It\^o's excusion when the surplus process is of unbounded variation. We show that a sufficient condition for optimality is that the L\'evy measure admits a density which is completely monotonic. Under such assumptions, a periodic $(b_u,b_l)$ strategy is confirmed to be optimal.

Results are illustrated.

In this paper, we propose a novel numerical method for Path-Dependent Partial Differential Equations (PPDEs). These equations firstly appeared in the seminal work of Dupire [2009], where the functional It\^o calculus was developed to deal with path-dependent financial derivatives contracts. More specificaly, we generalize the Deep Galerking Method (DGM) of Sirignano and Spiliopoulos [2018] to deal with these equations. The method, which we call Path-Dependent DGM (PDGM), consists of using a combination of feed-forward and Long Short-Term Memory architectures to model the solution of the PPDE. We then analyze several numerical examples, many from the Financial Mathematics literature, that show the capabilities of the method under very different situations.

This research develops a Machine Learning approach able to predict labor shortages for occupations. We compile a unique dataset that incorporates both Labor Demand and Labor Supply occupational data in Australia from 2012 to 2018. This includes data from 1.3 million job advertisements (ads) and 20 official labor force measures. We use these data as explanatory variables and leverage the XGBoost classifier to predict yearly labor shortage classifications for 132 standardized occupations. The models we construct achieve macro-F1 average performance scores of up to 86 per cent. However, the more significant findings concern the class of features which are most predictive of labor shortage changes. Our results show that job ads data were the most predictive features for predicting year-to-year labor shortage changes for occupations. These findings are significant because they highlight the predictive value of job ads data when they are used as proxies for Labor Demand, and incorporated into labor market prediction models. This research provides a robust framework for predicting labor shortages, and their changes, and has the potential to assist policy-makers and businesses responsible for preparing labor markets for the future of work.

We model sectoral production by cascading binary compounding processes. The sequence of processes is discovered in a self-similar hierarchical structure stylized in the economy-wide networks of production. Nested substitution elasticities and Hicks-neutral productivity growth are measured such that the general equilibrium feedbacks between all sectoral unit cost functions replicate the transformation of networks observed as a set of two temporally distant input-output coefficient matrices. We examine this system of unit cost functions to determine how idiosyncratic sectoral productivity shocks propagate into aggregate macroeconomic fluctuations in light of potential network transformation. Additionally, we study how sectoral productivity increments propagate into the dynamic general equilibrium, thereby allowing network transformation and ultimately producing social benefits.

We develop and implement methods for determining whether introducing new securities or relaxing investment constraints improves the investment opportunity set for prospect investors. We formulate a new testing procedure for prospect spanning for two nested portfolio sets based on subsampling and Linear Programming. In an application, we use the prospect spanning framework to evaluate whether well-known anomalies are spanned by standard factors. We find that of the strategies considered, many expand the opportunity set of the prospect type investors, thus have real economic value for them. In-sample and out-of-sample results prove remarkably consistent in identifying genuine anomalies for prospect investors.

We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a plugin estimator based on empirical measures and show it is consistent but lacks suitable robustness. To address this we propose novel estimators which use a larger set of martingale measures defined through a tradeoff between the radius of Wasserstein balls around the empirical measure and the allowed norm of martingale densities. We establish consistency and robustness of these estimators and argue that they offer a superior performance relative to the plugin estimator. We generalise the results by replacing the superhedging criterion with acceptance relative to a risk measure. We further extend our study, in part, to the case of markets with traded options, to a multiperiod setting and to settings with model uncertainty. We also study convergence rates of estimators and convergence of superhedging strategies.

The manipulation of LIBOR by a group of banks became one of the major blows to the remaining confidence in financial industry. Yet, despite an enormous amount of popular literature on the subject, rigorous time-series studies are few. In my paper, I discuss the following hypothesis. Namely, if we should assume for a statistical null, the quotes, which were submitted by the member banks were true, the deviations from the LIBOR should have been entirely random because they were determined by idiosyncratic conditions by the member banks. This hypothesis can be statistically verified. Serial correlations of the rates, which cannot be explained by the differences in credit qualities of the member banks or the domicile Governments, were subjected to correlation tests. A new econometric method--the analysis of the Wigner-Ville function borrowed from quantum mechanics and signal processing--is used and explained for the statistical interpretation of regression residuals.

The stock market of China experienced an abrupt crash in 2015 and evaporated over one third of the market value. Given its associations with fear and fine-resolutions in frequency, the illiquidity of stocks may offer a promising perspective of understanding and even signaling the market crash. In this study, by connecting stocks that mutually explain illiquidity fluctuations, a illiquidity network is established to model the market. It is found that as compared to non-crash days, the market is more densely connected on crash days due to heavier but more homogeneous illiquidity dependencies that facilitate abrupt collapses. Critical socks in the illiquidity network, in particular the ones in sector of finance are targeted for inspection because of their crucial roles in taking over and passing on the losing of illiquidity. The cascading failures of stocks in market crash is profiled as disseminating from small degrees to high degrees that usually locate in the core of the illiquidity network and then back to the periphery. And by counting the days with random failures in previous five days, an early single is implemented to successfully warn more than half crash days, especially those consecutive ones at early phase. Our results would help market practitioners like regulators detect and prevent risk of crash in advance.

Traditional data sources for the analysis of housing markets show several limitations, that recently started to be overcome using data coming from housing sales advertisements (ads) websites. In this paper, using a large dataset of ads in Italy, we provide the first comprehensive analysis of the problems and potential of these data. The main problem is that multiple ads ("duplicates") can correspond to the same housing unit. We show that this issue is mainly caused by sellers' attempt to increase visibility of their listings. Duplicates lead to misrepresentation of the volume and composition of housing supply, but this bias can be corrected by identifying duplicates with machine learning tools. We then focus on the potential of these data. We show that the timeliness, granularity, and online nature of these data allow monitoring of housing demand, supply and liquidity, and that the (asking) prices posted on the website can be more informative than transaction prices.

In finance, durations between successive transactions are usually modeled by the autoregressive conditional duration model based on a continuous distribution omitting zero values. Zero or close-to-zero durations can be caused by either split transactions or independent transactions. We propose a discrete model allowing for excessive zero values based on the zero-inflated negative binomial distribution with score dynamics. This model allows to distinguish between the processes generating split and standard transactions. We use the existing theory on score models to establish the invertibility of the score filter and verify that sufficient conditions hold for the consistency and asymptotic normality of the maximum likelihood of the model parameters. In an empirical study of DJIA stocks, we find that split transactions cause on average 63% of close-to-zero values. Furthermore, the loss of decimal places in the proposed approach is less severe than incorrect treatment of close-to-zero values in continuous models.