We introduce a new system of stochastic differential equations which models dependence of market beta and unsystematic risk upon size, measured by market capitalization. We fit our model using size deciles data from Kenneth French's data library. This model is somewhat similar to generalized volatility-stabilized models in (Pal, 2011; Pickova, 2013). The novelty of our work is twofold. First, we take into account the difference between price and total returns (in other words, between market size and wealth processes). Second, we work with actual market data. We study the long-term properties of this system of equations, and reproduce observed linearity of the capital distribution curve. Our model has two modifications: for price returns and for equity premium. Somewhat surprisingly, they exhibit the same fit, with very similar coefficients. In the Appendix, we analyze size-based real-world index funds.

The second fundamental theorem of asset pricing characterizes completeness of a financial market by uniqueness of prices of financial claims. The associated super- and sub-hedging dualities give upper and lower bounds of the no-arbitrage interval. In this article we provide conditional versions of these results in discrete time.

The main tool we use are consistency properties of dynamic non-linear expectations, which we apply to the super- and sub-hedging prices. The obtained results extend existing results in the literature, where the conditional setting is in most cases considered only on finite probability spaces. Using non-linear expectations we also provide a new perspective on the optional decomposition theorem.

A new procedure is presented for the objective comparison and evaluation of default definitions. This allows the lender to find a default threshold at which the financial loss of a loan portfolio is minimised, in accordance with Basel II. Alternative delinquency measures, other than simply measuring payments in arrears, can also be evaluated using this optimisation procedure. Furthermore, a simulation study is performed in testing the procedure from `first principles' across a wide range of credit risk scenarios. Specifically, three probabilistic techniques are used to generate cash flows, while the parameters of each are varied, as part of the simulation study. The results show that loss minima can exist for a select range of credit risk profiles, which suggests that the loss optimisation of default thresholds can become a viable practice. The default decision is therefore framed anew as an optimisation problem in choosing a default threshold that is neither too early nor too late in loan life. These results also challenges current practices wherein default is pragmatically defined as `90 days past due', with little objective evidence for its overall suitability or financial impact, at least beyond flawed roll rate analyses or a regulator's decree.

In this work, we develop a multi-factor approximation for Stochastic Volterra Equations with Lipschitz coefficients and kernels of completely monotone type that may be singular. Our approach consists in truncating and then discretizing the integral defining the kernel, which corresponds to a classical Stochastic Differential Equation. We prove strong convergence results for this approximation. For the particular rough kernel case with Hurst parameter lying in $(0,1/2)$, we propose various discretization procedures and give their precise rates of convergence. We illustrate the efficiency of our approximation schemes with numerical tests for the rough Bergomi model.

We study deep learning-based schemes for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). First we show how to improve the performances of the proposed scheme in [W. E and J. Han and A. Jentzen, Commun. Math. Stat., 5 (2017), pp.349-380] regarding computational time by using a single neural network architecture instead of the stacked deep neural networks. Furthermore, those schemes can be stuck in poor local minima or diverges, especially for a complex solution structure and longer terminal time. To solve this problem, we investigate to reformulate the problem by including local losses and exploit the Long Short Term Memory (LSTM) networks which are a type of recurrent neural networks (RNN). Finally, in order to study numerical convergence and thus illustrate the improved performances with the proposed methods, we provide numerical results for several 100-dimensional nonlinear BSDEs including nonlinear pricing problems in finance.

We propose a novel deep learning architecture suitable for the prediction of investor interest for a given asset in a given time frame. This architecture performs both investor clustering and modelling at the same time. We first verify its superior performance on a synthetic scenario inspired by real data and then apply it to two real-world databases, a publicly available dataset about the position of investors in Spanish stock market and proprietary data from BNP Paribas Corporate and Institutional Banking.

Does the ability to protect an asset from unsecured creditors affect its price? This paper identifies the impact of bankruptcy protection on house prices using 139 changes in homestead exemptions. Large increases in the homestead exemption raised house prices 3% before 2005. Smaller exemption increases, to adjust for inflation, did not affect house prices. The effect disappeared after BAPCPA, a 2005 federal law designed to prevent bankruptcy abuse. The effect was bigger in inelastic locations.

This study examines the influence of grandchildren's gender on grandparents' voting behavior using independently collected individual-level data. The survey was conducted immediately after the House of Councilors election in Japan. I observed that individuals with a granddaughter were more likely to vote for female candidates by around 10 % than those without. However, having a daughter did not affect the parents' voting behavior. Furthermore, having a son or a grandson did not influence grandparents' voting behavior. This implies that grandparents voted for their granddaughter's future benefit because granddaughters may be too young vote in a male-dominated and aging society.

In many businesses, and particularly in finance, the behavior of a client might drastically change over time. It is consequently crucial for recommender systems used in such environments to be able to adapt to these changes. In this study, we propose a novel collaborative filtering algorithm that captures the temporal context of a user-item interaction through the users' and items' recent interaction histories to provide dynamic recommendations. The algorithm, designed with issues specific to the financial world in mind, uses a custom neural network architecture that tackles the non-stationarity of users' and items' behaviors. The performance and properties of the algorithm are monitored in a series of experiments on a G10 bond request for quotation proprietary database from BNP Paribas Corporate and Institutional Banking.

Various parametric volatility models for financial data have been developed to incorporate high-frequency realized volatilities and better capture market dynamics. However, because high-frequency trading data are not available during the close-to-open period, the volatility models often ignore volatility information over the close-to-open period and thus may suffer from loss of important information relevant to market dynamics. In this paper, to account for whole-day market dynamics, we propose an overnight volatility model based on It\^o diffusions to accommodate two different instantaneous volatility processes for the open-to-close and close-to-open periods. We develop a weighted least squares method to estimate model parameters for two different periods and investigate its asymptotic properties. We conduct a simulation study to check the finite sample performance of the proposed model and method. Finally, we apply the proposed approaches to real trading data.

Studying the micro-trading behaviors before stock price jumps is an important problem for financial regulations and investment decisions. In this study, we provide a new framework to study pre-jump trading behaviors based on multivariate time series analysis. Different from the existing literature, our methodology takes into account the temporal information embedded in the trading-related attributes and can better evaluate and compare the abnormality levels of different attributes. Moreover, it can explore the joint informativeness of the attributes as well as select a subset of highly informative but minimally redundant attributes to analyze the homogeneous and idiosyncratic patterns in the pre-jump trades of individual stocks. In addition, our analysis involves a set of technical indicators to describe micro-trading behaviors. To illustrate the viability of the proposed methodology, an application case is conducted based on the level-2 data of 189 constituent stocks of the China Security Index 300. The individual and joint informativeness levels of the attributes in predicting price jumps are evaluated and compared. To this end, our experiment provides a set of jump indicators that can represent the pre-jump trading behaviors in the Chinese stock market and have detected some stocks with extremely abnormal pre-jump trades.

This paper studies whether and how differently projected information about the impact of the Covid-19 pandemic affects individuals' prosocial behavior and expectations on future outcomes. We conducted an online experiment with British participants (N=961) when the UK introduced its first lockdown and the outbreak was on its growing stage. Participants were primed with either the environmental or economic consequences (i.e., negative primes), or the environmental or economic benefits (i.e., positive primes) of the pandemic, or with neutral information. We measured priming effects on an incentivized take-and-give dictator game and on participants' expectations about future environmental quality and economic growth. Our results show that primes affect participants' expectations, but not their prosociality. In particular, participants primed with environmental consequences hold a more pessimistic view on future environmental quality, while those primed with economic benefits are more optimistic about future economic growth. Instead, the positive environmental prime and the negative economic prime do not influence expectations. Our results offer insights into how information affects behavior and expectations during the Covid-19 pandemic.

Urban scaling analysis, the study of how aggregated urban features vary with the population of an urban area, provides a promising framework for discovering commonalities across cities and uncovering dynamics shared by cities across time and space. Here, we use the urban scaling framework to study an important, but under-explored feature in this community - income inequality. We propose a new method to study the scaling of income distributions by analyzing total income scaling in population percentiles. We show that income in the least wealthy decile (10%) scales close to linearly with city population, while income in the most wealthy decile scale with a significantly superlinear exponent. In contrast to the superlinear scaling of total income with city population, this decile scaling illustrates that the benefits of larger cities are increasingly unequally distributed. For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase. We repeat our analysis after adjusting income by housing cost, and find similar results. We then further analyze the shapes of income distributions. First, we find that mean, variance, skewness, and kurtosis of income distributions all increase with city size. Second, the Kullback-Leibler divergence between a city's income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population. As most urban scaling theories consider densifying interactions within cities as the fundamental process leading to the superlinear increase of many features, our results suggest this effect is only seen in the upper deciles of the cities. Our finding encourages future work to consider heterogeneous models of interactions to form a more coherent understanding of urban scaling.

A novel procedure is presented for the objective comparison and evaluation of a bank's decision rules in optimising the timing of loan recovery. This procedure is based on finding a delinquency threshold at which the financial loss of a loan portfolio (or segment therein) is minimised. Our procedure is an expert system that incorporates the time value of money, costs, and the fundamental trade-off between accumulating arrears versus forsaking future interest revenue. Moreover, the procedure can be used with different delinquency measures (other than payments in arrears), thereby allowing an indirect comparison of these measures. We demonstrate the system across a range of credit risk scenarios and portfolio compositions. The computational results show that threshold optima can exist across all reasonable values of both the payment probability (default risk) and the loss rate (loan collateral). In addition, the procedure reacts positively to portfolios afflicted by either systematic defaults (such as during an economic downturn) or episodic delinquency (i.e., cycles of curing and re-defaulting). In optimising a portfolio's recovery decision, our procedure can better inform the quantitative aspects of a bank's collection policy than relying on arbitrary discretion alone.

We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition sharpens and improves on previous results. We connect the condition, and hence the problem of existence and uniqueness of asset prices, with the recent literature on stochastic discount factor decompositions. Finally, we discuss computation of the test value associated with our condition, providing a Monte Carlo method that is naturally parallelizable.

Recently, to account for low-frequency market dynamics, several volatility models, employing high-frequency financial data, have been developed. However, in financial markets, we often observe that financial volatility processes depend on economic states, so they have a state heterogeneous structure. In this paper, to study state heterogeneous market dynamics based on high-frequency data, we introduce a novel volatility model based on a continuous Ito diffusion process whose intraday instantaneous volatility process evolves depending on the exogenous state variable, as well as its integrated volatility. We call it the state heterogeneous GARCH-Ito (SG-Ito) model. We suggest a quasi-likelihood estimation procedure with the realized volatility proxy and establish its asymptotic behaviors. Moreover, to test the low-frequency state heterogeneity, we develop a Wald test-type hypothesis testing procedure. The results of empirical studies suggest the existence of leverage, investor attention, market illiquidity, stock market comovement, and post-holiday effect in S&P 500 index volatility.

I propose a new conceptual framework to disentangle the impacts of weather and climate on economic activity and growth: A stochastic frontier model with climate in the production frontier and weather shocks as a source of inefficiency. I test it on a sample of 160 countries over the period 1950-2014. Temperature and rainfall determine production possibilities in both rich and poor countries; positively in cold countries and negatively in hot ones. Weather anomalies reduce inefficiency in rich countries but increase inefficiency in poor and hot countries; and more so in countries with low weather variability. The climate effect is larger that the weather effect.

Reaching the 2030 targets for the EU primary energy use (PE) and CO2eq emissions (CE) requires an accurate assessment of how different technologies perform on these two fronts. In this regard, the focus in academia is increasingly shifting from traditional technologies to electricity consuming alternatives. Calculating and comparing their performance with respect to traditional technologies requires conversion factors (CFs) like a primary energy factor and a CO2eq intensity. These reflect the PE and CE associated with each unit of electricity consumed. Previous work has shown that the calculation and use of CFs is a contentious and multifaceted issue. However, this has mostly remained a theoretical discussion. A stock-taking of how CFs are actually calculated and used in academic literature has so far been missing, impeding insight into what the contemporary trends and challenges are. Therefore, we structurally review 65 publications across six methodological aspects. We find that 72% of the publications consider only a single country, 86% apply a purely retrospective perspective, 54% apply a yearly temporal resolution, 65% apply a purely operational (instead of a life-cycle) perspective, 91% make use of average (rather than marginal) CFs, and 75% ignore electricity imports from surrounding countries. We conclude that there is a strong need in the literature for a publicly available, transparently calculated dataset of CFs, which avoids the shortcomings found in the literature. This would enable more accurate and transparent PE and CE calculations, and support the development of new building energy performance assessment methods and smart grid algorithms.