In insurance mathematics optimal control problems over an infinite time horizon arise when computing risk measures. Their solutions correspond to solutions of deterministic semilinear (degenerate) elliptic partial differential equations. In this paper we propose a deep neural network algorithm for solving such partial differential equations in high dimensions. The algorithm is based on the correspondence of elliptic partial differential equations to backward stochastic differential equations with random terminal time.

Food insecurity is associated with increased risk for several health conditions and with increased national burden of chronic disease. Key determinants for household food insecurity are income and food costs. Forecasts show household disposable income for 2020 expected to fall and for 2021 to rise only slightly. Prices are forecast to rise. Thus, future increased food prices would be a significant driver of greater food insecurity. Structured expert judgement elicitation, a well-established method for quantifying uncertainty, using experts. In July 2020, each expert estimated the median, 5th percentile and 95th percentile quantiles of changes in price to April 2022 for ten food categories under three end-2020 settlement Brexit scenarios: A: full WTO terms; B: a moderately disruptive trade agreement (better than WTO); C: a minimally disruptive trade agreement. When combined in proportions for calculate Consumer Prices Index food basket costs, the median food price change under full WTO terms is expected to be +17.9% [90% credible interval:+5.2%, +35.1%]; with moderately disruptive trade agreement: +13.2% [+2.6%, +26.4%] and with a minimally disruptive trade agreement +9.3% [+0.8%, +21.9%]. The number of households experiencing food insecurity and its severity are likely to increase because of expected sizeable increases in median food prices in the months after Brexit, whereas low income group spending on food is unlikely to increase, and may be further eroded by other factors not considered here (e.g. COVID-19). Higher increases are more likely than lower rises and towards the upper limits, these would entail severe impacts. Research showing a low food budget leads to increasingly poor diet suggests that demand for health services in both the short and longer term is likely to increase due to the effects of food insecurity on the incidence and management of diet-sensitive conditions.

We address the modelling of commodities that are supposed to have positive price but, on account of a possible failure in the physical delivery mechanism, may turn out not to. This is done by explicitly incorporating a `delivery liability' option into the contract. As such it is a simple generalisation of the established Black model.

Hydraulic fracturing stimulates fracture swarm in reservoir formation though pressurized injection fluid. However restricted by the availability of formation data, the variability embraced by reservoir keeps uncertain, driving unstable gas recovery along with low resource efficiency, being responsible for resource scarcity, contaminated water, and injection-induced earthquake. Resource efficiency is qualified though new determined energy efficiency, a scale of recovery and associated environmental footprint. To maximize energy efficiency while minimize its' variation, we issue picked designs at reservoir conditions dependent optimal probabilities, assembling high efficiency portfolios and low risk portfolios for portfolio combination, which balance the variation and efficiency at optimal by adjusting the proportion of each portfolio. Relative to regular design for one well, the optimal portfolio combination applied in multiple wells receive remarkable variation reduction meanwhile substantial energy efficiency increase, in response to the call of more recovery per unit investment and less environment cost per unit nature gas extracted.

We study a discrete-time portfolio selection problem with partial information and maxi\-mum drawdown constraint. Drift uncertainty in the multidimensional framework is modeled by a prior probability distribution. In this Bayesian framework, we derive the dynamic programming equation using an appropriate change of measure, and obtain semi-explicit results in the Gaussian case. The latter case, with a CRRA utility function is completely solved numerically using recent deep learning techniques for stochastic optimal control problems. We emphasize the informative value of the learning strategy versus the non-learning one by providing empirical performance and sensitivity analysis with respect to the uncertainty of the drift. Furthermore, we show numerical evidence of the close relationship between the non-learning strategy and a no short-sale constrained Merton problem, by illustrating the convergence of the former towards the latter as the maximum drawdown constraint vanishes.

In this work we provide a simple setting that connects the structural modelling approach of Gai-Kapadia interbank networks with the mean-field approach to default contagion. To accomplish this we make two key contributions. First, we propose a dynamic default contagion model with endogenous early defaults for a finite set of banks, generalising the Gai-Kapadia framework. Second, we reformulate this system as a stochastic particle system leading to a limiting mean-field problem. We study the existence of these clearing systems and, for the mean-field problem, the continuity of the system response.

It is reported that financial news, especially financial events expressed in news, provide information to investors' long/short decisions and influence the movements of stock markets. Motivated by this, we leverage financial event streams to train a classification neural network that detects latent event-stock linkages and stock markets' systematic behaviours in the U.S. stock market. Our proposed pipeline includes (1) a combined event extraction method that utilizes Open Information Extraction and neural co-reference resolution, (2) a BERT/ALBERT enhanced representation of events, and (3) an extended hierarchical attention network that includes attentions on event, news and temporal levels. Our pipeline achieves significantly better accuracies and higher simulated annualized returns than state-of-the-art models when being applied to predicting Standard\&Poor 500, Dow Jones, Nasdaq indices and 10 individual stocks.

We show Bitcoin implied volatility on a 5 minute time horizon is modestly predictable from price, volatility momentum and alternative data including sentiment and engagement. Lagged Bitcoin index price and volatility movements contribute to the model alongside Google Trends with markets responding often several hours later. The code and datasets used in this paper can be found at https://github.com/Globe-Research/bitfear.

How may exposure risks to SARS-CoV-2 be assessed quantitatively? The material metabolism approach of Industrial Ecology can be applied to the mass flows of these virions by their numbers, as a key step in the analysis of the current pandemic. Several transmission routes of SARS-2 from emission by a person to exposure of another person have been modelled and quantified. Start is a COVID-19 illness progression model specifying rising emissions by an infected person: the human virion factory. The first route covers closed spaces, with an emission, concentration, and decay model quantifying exposure. A next set of routes covers person-to-person contacts mostly in open spaces, modelling the spatial distribution of exhales towards inhalation. These models also cover incidental exposures, like coughs and sneezes, and exposure through objects. Routes through animal contacts, excrements, and food, have not been quantified. Potential exposures differ by six orders of magnitude. Closed rooms, even with reasonably (VR 2) to good (VR 5) ventilation, constitute the major exposure risks. Close person-to-person contacts of longer duration create two orders of magnitude lower exposure risks. Open spaces may create risks an order of magnitude lower again. Burst of larger droplets may cause a common cold but not viral pneumonia as the virions in such droplets cannot reach the alveoli. Fomites have not shown viable viruses in hospitals, let alone infections. Infection by animals might be possible, as by cats and ferrets kept as pets. These results indicate priority domains for individual and collective measures. The wide divergence in outcomes indicates robustness to most modelling and data improvements, hardly leading to major changes in relative exposure potentials. However, models and data can substantially be improved.

In this paper we review Bernstein and grid-type copulas for arbitrary dimensions and general grid resolutions in connection with discrete random vectors possessing uniform margins. We further suggest a pragmatic way to fit the dependence structure of multivariate data to Bernstein copulas via grid-type copulas and empirical contingency tables. Finally, we discuss a Monte Carlo study for the simulation and PML estimation for aggregate dependent losses form observed windstorm and flooding data.

The review introduces the history of cryptocurrencies, offering a description of the blockchain technology behind them. Differences between cryptocurrencies and the exchanges on which they are traded have been shown. The central part surveys the analysis of cryptocurrency price changes on various platforms. The statistical properties of the fluctuations in the cryptocurrency market have been compared to the traditional markets. With the help of the latest statistical physics methods the non-linear correlations and multiscale characteristics of the cryptocurrency market are analyzed. In the last part the co-evolution of the correlation structure among the 100 cryptocurrencies having the largest capitalization is retraced. The detailed topology of cryptocurrency network on the Binance platform from bitcoin perspective is also considered. Finally, an interesting observation on the Covid-19 pandemic impact on the cryptocurrency market is presented and discussed: recently we have witnessed a "phase transition" of the cryptocurrencies from being a hedge opportunity for the investors fleeing the traditional markets to become a part of the global market that is substantially coupled to the traditional financial instruments like the currencies, stocks, and commodities.

The main contribution is an extensive demonstration that structural self-organization in the cryptocurrency markets has caused the same to attain complexity characteristics that are nearly indistinguishable from the Forex market at the level of individual time-series. However, the cross-correlations between the exchange rates on cryptocurrency platforms differ from it. The cryptocurrency market is less synchronized and the information flows more slowly, which results in more frequent arbitrage opportunities. The methodology used in the review allows the latter to be detected, and lead-lag relationships to be discovered.

This paper studies the optimal dividend for a multi-line insurance group, in which each subsidiary runs a product line and is exposed to some external credit risk. The default contagion is considered such that one default event may increase the default probabilities of all surviving subsidiaries. The total dividend problem for the insurance group is investigated and we find that the optimal dividend strategy is still of the barrier type. Furthermore, we show that the optimal barrier of each subsidiary is modulated by the default state. That is, how many and which subsidiaries have defaulted will determine the dividend threshold of each surviving subsidiary. These conclusions are based on the analysis of the associated recursive system of Hamilton-Jacobi-Bellman variational inequalities (HJBVIs). The existence of the classical solution is established and the verification theorem is proved. In the case of two subsidiaries, the value function and optimal barriers are given in analytical forms, allowing us to conclude that the optimal barrier of one subsidiary decreases if the other subsidiary defaults.

Are policies implemented in individual states to prevent pandemic deaths effective when there is no policy coordination by the federal government? We answer this question by developing a stochastic extension of a SIRD epidemiological model for a country composed of multiple states. Our model allows for interstate mobility. We consider three policies: mask mandates, stay-at-home orders, and interstate travel bans. We fit our model to daily U.S. state-level COVID-19 death counts and exploit our estimates to produce various policy counterfactuals. While the restrictions imposed by some states inhibited a significant number of virus deaths, we find that more than two-thirds of U.S. COVID-19 deaths could have been prevented by late September 2020 had the federal government imposed federal mandates as early as some of the earliest states did. Our results highlight the need for a coordination-aimed approach by a federal government for the successful containment of a pandemic.

We study the effects on economic activity of a pure temporary change in government debt and the relationship between the debt multiplier and the level of debt in an overlapping generations framework. The debt multiplier is positive but quite small during normal times while it is much larger during crises. Moreover, it increases with the steady state level of debt. Hence, the call for fiscal consolidation during recessions seems ill-advised. Finally, a rise in the steady state debt-to-GDP level increases the steady state real interest rate providing more room for manoeuvre to monetary policy to fight deflationary shocks.