In this paper, we provide an axiomatic approach to general premium principles giving rise to a decomposition into risk, as a generalization of the expected value, and deviation, as a generalization of the variance. We show that, for every premium principle, there exists a maximal risk measure capturing all risky components covered by the insurance prices. In a second step, we consider dual representations of convex risk measures consistent with the premium principle. In particular, we show that the convex conjugate of the aforementioned maximal risk measure coincides with the convex conjugate of the premium principle on the set of all finitely additive probability measures. In a last step, we consider insurance prices in the presence of a not neccesarily frictionless market, where insurance claims are traded. In this setup, we discuss premium principles that are consistent with hedging using securization products that are traded in the market.

High air pollution levels are associated with school absences. However, low level pollution impact on individual school absences are under-studied. We modelled PM2.5 and ozone concentrations at 36 schools from July 2015 to June 2018 using data from a dense, research grade regulatory sensor network. We determined exposures and daily absences at each school. We used generalized estimating equations model to retrospectively estimate rate ratios for association between outdoor pollutant concentrations and school absences. We estimated lost school revenue, productivity, and family economic burden. PM2.5 and ozone concentrations and absence rates vary across the School District. Pollution exposure were associated with as high a rate ratio of 1.02 absences per ug/m$^3$ and 1.01 per ppb increase for PM2.5 and ozone, respectively. Significantly, even PM2.5 and ozone exposure below regulatory standards (<12.1 ug/m$^3$ and <55 ppb) was associated with positive rate ratios of absences: 1.04 per ug/m$^3$ and 1.01 per ppb increase, respectively. Granular local measurements enabled demonstration of air pollution impacts that varied between schools undetectable with averaged pollution levels. Reducing pollution by 50% would save $452,000 per year districtwide. Pollution reduction benefits would be greatest in schools located in socioeconomically disadvantaged areas. Exposures to air pollution, even at low levels, are associated with increased school absences. Heterogeneity in exposure, disproportionately affecting socioeconomically disadvantaged schools, points to the need for fine resolution exposure estimation. The economic cost of absences associated with air pollution is substantial even excluding indirect costs such as hospital visits and medication. These findings may help inform decisions about recess during severe pollution events and regulatory considerations for localized pollution sources.

Because SARS-Cov-2 (COVID-19) statistics affect economic policies and political outcomes, governments have an incentive to control them. Manipulation may be less likely in democracies, which have checks to ensure transparency. We show that data on disease burden bear indicia of data modification by authoritarian governments relative to democratic governments. First, data on COVID-19 cases and deaths from authoritarian governments show significantly less variation from a 7 day moving average. Because governments have no reason to add noise to data, lower deviation is evidence that data may be massaged. Second, data on COVID-19 deaths from authoritarian governments do not follow Benford's law, which describes the distribution of leading digits of numbers. Deviations from this law are used to test for accounting fraud. Smoothing and adjustments to COVID-19 data may indicate other alterations to these data and a need to account for such alterations when tracking the disease.

In a market with stochastic interest rates, we consider an investor who can either (i) invest all if his money in a savings account or (ii) purchase zero-coupon bonds and invest the remainder of his wealth in a savings account. The indifference price of the bond is the price for which the investor could achieve the same expected utility under both scenarios. In an affine term structure setting, under the assumption that an investor has a utility function in either exponential or power form, we show that the indifference price of a zero-coupon bond is the root of an integral expression. As an example, we compute bond indifference prices and the corresponding indifference yield curves in the Vasicek setting and interpret the results.

We present general results on the univariate tail conditional expectation (TCE) and multivariate tail conditional expectation for location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal distributions, location-scale mixture of Student-$t$ distributions, location-scale mixture of Logistic distributions and location-scale mixture of Laplace distributions. We also consider portfolio risk decomposition with TCE for location-scale mixture of elliptical distributions.

Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in problems in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of Range-Value-at-Risk, which includes Value-at-Risk and Expected Shortfall as special cases, we establish new analytical bounds which we call convolution bounds. These bounds are easy to compute, and we show that they are sharp in many relevant cases. We pay a special attention to the problem of quantile aggregation, and the convolution bounds help us to identify approximations for the extremal dependence structure. The convolution bound enjoys several advantages, including interpretability, tractability and theoretical properties. To the best of our knowledge, there is no other theoretical result on quantile aggregation which is not covered by the convolution bounds, and thus the convolution bounds are genuinely the best one available. The results can be applied to compute bounds on the distribution of the sum of random variables. Some applications to operations research are discussed.

In this paper, we develop a deep neural network approach to solve a lifetime expected mortality-weighted utility-based model for optimal consumption in the decumulation phase of a defined contribution pension system. We formulate this problem as a multi-period finite-horizon stochastic control problem and train a deep neural network policy representing consumption decisions. The optimal consumption policy is determined by personal information about the retiree such as age, wealth, risk aversion and bequest motive, as well as a series of economic and financial variables including inflation rates and asset returns jointly simulated from a proposed seven-factor economic scenario generator calibrated from market data. We use the Australian pension system as an example, with consideration of the government-funded means-tested Age Pension and other practical aspects such as fund management fees. The key findings from our numerical tests are as follows. First, our deep neural network optimal consumption policy, which adapts to changes in market conditions, outperforms deterministic drawdown rules proposed in the literature. Moreover, the out-of-sample outperformance ratios increase as the number of training iterations increases, eventually reaching outperformance on all testing scenarios after less than 10 minutes of training. Second, a sensitivity analysis is performed to reveal how risk aversion and bequest motives change the consumption over a retiree's lifetime under this utility framework. Third, we provide the optimal consumption rate with different starting wealth balances. We observe that optimal consumption rates are not proportional to initial wealth due to the Age Pension payment. Forth, with the same initial wealth balance and utility parameter settings, the optimal consumption level is different between males and females due to gender differences in mortality.

Inspired by Stein's lemma, we consider the joint moments of $n$-dimensional elliptical distribution. We use two different methods to calculate the expectations $E[X_{1}^{2}f(\mathbf{X})]$ for any measurable function $f$ satisfying some regular conditions. Applying this result, we obtain recursion formulae for product moments of multivariate Gaussian random variables and multivariate elliptical random variables.

We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to:

--Write arbitrage as curvature of a principal fibre bundle.

--Parameterize arbitrage strategies by its holonomy.

--Give the Fundamental Theorem of Asset Pricing a differential homotopic characterization.

--Characterize Geometric Arbitrage Theory by five principles and show they they are consistent with the classical theory of stochastic finance.

--Derive for a closed market the equilibrium solution for market portfolio and dynamics in the cases where:

-->Arbitrage is allowed but minimized.

-->Arbitrage is not allowed.

--Prove that the no-free-lunch-with-vanishing-risk condition implies the zero curvature condition. The converse is in general not true and additionally requires the Novikov condition for the instantaneous Sharpe Ratio Dynamics to be satisfied.

In this paper we consider the following optimal stopping problem $$V^{\omega}_{{\rm A}}(s) = \sup_{\tau\in\mathcal{T}} \mathbb{E}_{s}[e^{-\int_0^\tau \omega(S_w) dw} g(S_\tau)],$$ where the process $S_t$ is a jump-diffusion process, $\mathcal{T}$ is a family of stopping times and $g$ and $\omega$ are fixed payoff function and discounting function, respectively. In a financial market context, if $g(s)=(K-s)^+$ or $g(s)=(s-K)^+$ and $\mathbb{E}$ is the expectation taken with respect to a martingale measure, $V^{\omega}_{{\rm A}}(s)$ describes the price of a perpetual American option with a discount rate depending on the value of the asset process $S_t$. If $\omega$ is a constant, the above problem produces the standard case of pricing perpetual American options. In the first part of this paper we find sufficient conditions for the convexity of the value function $V^{\omega}_{{\rm A}}(s)$. This allows us to determine the stopping region as a certain interval and hence we are able to identify the form of $V^{\omega}_{{\rm A}}(s)$. We also prove a put-call symmetry for American options with asset-dependent discounting. In the case when $S_t$ is a geometric L\'evy process we give exact expressions using the so-called omega scale functions introduced in Li and Palmowski (2018). We prove that the analysed value function satisfies HJB and we give sufficient conditions for the smooth fit property as well. Finally, we analyse few cases in detail performing extensive numerical analysis.

In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a point estimate and confidence intervals. Finally, it constructs an approximate dynamic hedging strategy. We test the approach on different specifications of a Bermudan max-call option. In all cases it produces highly accurate prices and dynamic hedging strategies with small replication errors.

One of the major characteristics of financial time series is that they contain a large amount of non-stationary noise, which is challenging for deep neural networks. People normally use various features to address this problem. However, the performance of these features depends on the choice of hyper-parameters. In this paper, we propose to use neural networks to represent these indicators and train a large network constructed of smaller networks as feature layers to fine-tune the prior knowledge represented by the indicators. During back propagation, prior knowledge is transferred from human logic to machine logic via gradient descent. Prior knowledge is the deep belief of neural network and teaches the network to not be affected by non-stationary noise. Moreover, co-distillation is applied to distill the structure into a much smaller size to reduce redundant features and the risk of overfitting. In addition, the decisions of the smaller networks in terms of gradient descent are more robust and cautious than those of large networks. In numerical experiments, we find that our algorithm is faster and more accurate than traditional methods on real financial datasets. We also conduct experiments to verify and comprehend the method.

Many Stated Preference studies conducted in developing countries provide a low willingness to pay (WTP) for a wide range of goods and services. However, recent studies in these countries indicate that this may partly be a result of the choice of payment vehicle, not the preference for the good. Thus, low WTP may not indicate a low welfare effect for public projects in developing countries. We argue that in a setting where 1) there is imperfect substitutability between money and other measures of wealth (e.g. labor), and 2) institutions are perceived to be corrupt, including payment vehicles that are currently available to the individual and less pron to corruption may be needed to obtain valid welfare estimates. Otherwise, we risk underestimating the welfare benefit of projects. We demonstrate this through a rural household contingent valuation (CV) survey designed to elicit the value of access to reliable irrigation water in Ethiopia. Of the total average annual WTP for access to reliable irrigation service, cash contribution comprises only 24.41 %. The implication is that socially desirable projects might be rejected based on cost-benefit analysis as a result of welfare gain underestimation due to mismatch of payment vehicles choice in valuation study.

In a world increasingly dominated by AI applications, an understudied aspect is the carbon and social footprint of these power-hungry algorithms that require copious computation and a trove of data for training and prediction. While profitable in the short-term, these practices are unsustainable and socially extractive from both a data-use and energy-use perspective. This work proposes an ESG-inspired framework combining socio-technical measures to build eco-socially responsible AI systems. The framework has four pillars: compute-efficient machine learning, federated learning, data sovereignty, and a LEEDesque certificate.

Compute-efficient machine learning is the use of compressed network architectures that show marginal decreases in accuracy. Federated learning augments the first pillar's impact through the use of techniques that distribute computational loads across idle capacity on devices. This is paired with the third pillar of data sovereignty to ensure the privacy of user data via techniques like use-based privacy and differential privacy. The final pillar ties all these factors together and certifies products and services in a standardized manner on their environmental and social impacts, allowing consumers to align their purchase with their values.

An important theme is how to maximize the cooperation of employees when dealing with crisis measures taken by the company. Therefore, to find out what kind of employees have cooperated with the company's measures in the current corona (COVID-19) crisis, and what effect the cooperation has had to these employees/companies to get hints for preparing for the next crisis, the pass analysis was carried out using awareness data obtained from a questionnaire survey conducted on 2,973 employees of Japanese companies in China. The results showed that employees with higher social capital and resilience were more supportive of the company's measures against corona and that employees who were more supportive of corona measures were less likely to leave their jobs. However, regarding fatigue and anxiety about the corona felt by employees, it was shown that it not only works to support cooperation in corona countermeasures but also enhances the turnover intention. This means that just by raising the anxiety of employees, even if a company achieves the short-term goal of having them cooperate with the company's countermeasures against corona, it may not reach the longer-term goal by making them increase their intention to leave. It is important for employees to be aware of the crisis and to fear it properly. But more than that, it should be possible for the company to help employees stay resilient, build good relationships with them, and increase their social capital to make them support crisis measurement of the company most effectively while keeping their turnover intention low.

The threat of the new coronavirus (COVID-19) is increasing. Regarding the difference in the infection rate observed in each region, in addition to studies seeking the cause due to differences in the social distance (population density), there is an increasing trend toward studies seeking the cause due to differences in social capital. However, studies have not yet been conducted on whether social capital could influence the infection rate even if it controls the effect of population density. Therefore, in this paper, we analyzed the relationship between infection rate, population density, and social capital using statistical data for each prefecture. Statistical analysis showed that social capital not only correlates with infection rates and population densities but still has a negative correlation with infection rates controlling for the effects of population density. Besides, controlling the relationship between variables by mean age showed that social capital had a greater correlation with infection rate than population density. In other words, social capital mediates the correlation between population density and infection rates. This means that social distance alone is not enough to deter coronavirus infection, and social capital needs to be recharged.

This paper critically reviews the research on the impact of immigration on employment and wages of natives in wealthy countries--where "natives" includes previous immigrants and their descendants. While written for a non-technical audience, the paper engages with technical issues and probes one particularly intense scholarly debate in an appendix. While the available evidence is not definitive, it paints a consistent picture. Industrial economies can generally absorb migrants quickly, in part because capital is mobile and flexible, in part because immigrants are consumers as well as producers. Thus, long-term average impacts are probably zero at worst. And the long-term may come quickly, especially if migration inflows are predictable to investors. Possibly, skilled immigration boosts productivity and wages for many others. Around the averages, there are distributional effects. Among low-income "native" workers, the ones who stand to lose the most are those who most closely resemble new arrivals, in being immigrants themselves, being low-skill, being less assimilated, and, potentially, undocumented. But native workers and earlier immigrants tend to benefit from the arrival of workers different from them, who complement more than compete with them in production. Thus skilled immigration can offset the effects of low-skill immigration on natives and earlier immigrants.

This paper reviews the research on the impacts of alcohol taxation outcomes such as heavy drinking and mortality. Where data availability permits, reviewed studies are replicated and reanalyzed. Despite weaknesses in the majority of studies, and despite seeming disagreements among the more credible one--ones based on natural experiments--we can be reasonably confident that taxing alcohol reduces drinking in general and problem drinking in particular. The larger and cleaner the underlying natural experiment, the more apt a study is to detect impacts on drinking. Estimates from the highest-powered study settings, such as in Alaska in 2002 and Finland in 2004, suggest an elasticity of mortality with respect to price of -1 to -3. A 10% price increase in the US would, according to this estimate, save 2,000-6,000 lives and 48,000-130,000 years of life each year.

This paper reviews the research on the impacts of incarceration on crime. Where data availability permits, reviewed studies are replicated and reanalyzed. Among three dozen studies I reviewed, I obtained or reconstructed the data and code for eight. Replication and reanalysis revealed significant methodological concerns in seven and led to major reinterpretations of four. I estimate that, at typical policy margins in the United States today, decarceration has zero net impact on crime outside of prison. That estimate is uncertain, but at least as much evidence suggests that decarceration reduces crime as increases it. The crux of the matter is that tougher sentences hardly deter crime, and that while imprisoning people temporarily stops them from committing crime outside prison walls, it also tends to increase their criminality after release. As a result, "tough-on-crime" initiatives can reduce crime in the short run but cause offsetting harm in the long run. A cost-benefit analysis finds that even under a devil's advocate reading of this evidence, in which incarceration does reduce crime in U.S., it is unlikely to increase aggregate welfare.