The carbon footprint of Bitcoin has drawn wide attention, but Bitcoin's long-term impact on the climate remains uncertain. Here we present a framework to overcome uncertainties in previous estimates and project Bitcoin's electricity consumption and carbon footprint in the long term. If we assume Bitcoin's market capitalization grows in line with the one of gold, we find that the annual electricity consumption of Bitcoin may increase from 60 to 400 TWh between 2020 and 2100. The future carbon footprint of Bitcoin strongly depends on the decarbonization pathway of the electricity sector. If the electricity sector achieves carbon neutrality by 2050, Bitcoin's carbon footprint has peaked already. However, in the business-as-usual scenario, emissions sum up to 2 gigatons until 2100, an amount comparable to 7% of global emissions in 2019. The Bitcoin price spike at the end of 2020 shows, however, that progressive development of market capitalization could yield an electricity consumption of more than 100 TWh already in 2021, and lead to cumulative emissions of over 5 gigatons by 2100. Therefore, we also discuss policy instruments to reduce Bitcoin's future carbon footprint.

We study the expression rates of deep neural networks (DNNs for short) for option prices written on baskets of $d$ risky assets, whose log-returns are modelled by a multivariate L\'evy process with general correlation structure of jumps. We establish sufficient conditions on the characteristic triplet of the L\'evy process $X$ that ensure $\varepsilon$ error of DNN expressed option prices with DNNs of size that grows polynomially with respect to $\mathcal{O}(\varepsilon^{-1})$, and with constants implied in $\mathcal{O}(\cdot)$ which grow polynomially with respect $d$, thereby overcoming the curse of dimensionality and justifying the use of DNNs in financial modelling of large baskets in markets with jumps.

In addition, we exploit parabolic smoothing of Kolmogorov partial integrodifferential equations for certain multivariate L\'evy processes to present alternative architectures of ReLU DNNs that provide $\varepsilon$ expression error in DNN size $\mathcal{O}(|\log(\varepsilon)|^a)$ with exponent $a \sim d$, however, with constants implied in $\mathcal{O}(\cdot)$ growing exponentially with respect to $d$. Under stronger, dimension-uniform non-degeneracy conditions on the L\'evy symbol, we obtain algebraic expression rates of option prices in exponential L\'evy models which are free from the curse of dimensionality. In this case the ReLU DNN expression rates of prices depend on certain sparsity conditions on the characteristic L\'evy triplet. We indicate several consequences and possible extensions of the present results.

The allocation of venture capital is one of the primary factors determining who takes products to market, which startups succeed or fail, and as such who gets to participate in the shaping of our collective economy. While gender diversity contributes to startup success, most funding is allocated to male-only entrepreneurial teams. In the wake of COVID-19, 2020 is seeing a notable decline in funding to female and mixed-gender teams, giving raise to an urgent need to study and correct the longstanding gender bias in startup funding allocation. We conduct an in-depth data analysis of over 48,000 companies on Crunchbase, comparing funding allocation based on the gender composition of founding teams. Detailed findings across diverse industries and geographies are presented. Further, we construct machine learning models to predict whether startups will reach an equity round, revealing the surprising finding that the CEO's gender is the primary determining factor for attaining funding. Policy implications for this pressing issue are discussed.

We present an overview of the broad class of financial models in which the prices of assets are L\'evy-Ito processes driven by an $n$-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is associated with an $n$-dimensional L\'evy process. Each model consists of a pricing kernel, a money market account, and one or more risky assets. We show how the excess rate of return above the interest rate can be calculated for risky assets in such models, thus showing the relationship between risk and return when asset prices have jumps. The framework is applied to a variety of asset classes, allowing one to construct new models as well as interesting generalizations of familiar models.

This article outlines our point of view regarding the applicability, state-of-the-art, and potential of quantum computing for problems in finance. We provide an introduction to quantum computing as well as a survey on problem classes in finance that are computationally challenging classically and for which quantum computing algorithms are promising. In the main part, we describe in detail quantum algorithms for specific applications arising in financial services, such as those involving simulation, optimization, and machine learning problems. In addition, we include demonstrations of quantum algorithms on IBM Quantum back-ends and discuss the potential benefits of quantum algorithms for problems in financial services. We conclude with a summary of technical challenges and future prospects.

Cross-border Electric Interconnection towards renewables is a promising solution for electric sector under the UN 2030 sustainable development goals which is widely promoted in emerging economies. This paper comprehensively investigates state of art in renewable resources and cross-border electric interconnection in South America. Based on the raw data collected from typical countries, a long-term scenario forecast methodology is applied to estimate key indicators of electric sector in target years, comparing the prospects of active promoting cross-border Interconnections Towards Renewables (ITR) scenario with Business as Usual (BAU) scenario in South America region. Key indicators including peak load, installed capacity, investment, and generation cost are forecasted and comparative analyzed by year 2035 and 2050. The comparative data analysis shows that by promoting cross-border interconnection towards renewables in South America, renewable resources can be highly utilized for energy supply, energy matrix can be optimized balanced, economics can be obviously driven and generation cost can be greatly reduced.