# Research articles for the 2020-12-16

A Khasminskii Type Averaging Principle for Non-autonomous Slow-fast Stochastic Differential Equations and an Application to a Local Stochastic Volatility Model
Filippo de Feo
arXiv

In this work we study the averaging principle for non-autonomous slow-fast systems of stochastic differential equations. In particular in the first part we generalize Khasminskii's averaging principle to the non-autonomous case, assuming the sublinearity, the Lipschitzianity and the Holder's continuity in time of the coefficients, an ergodic hypothesis and an $\mathcal{L}^2$-bound of the fast component. In this setting we prove the weak convergence of the slow component to the solution of the averaged equation. Moreover we provide a suitable dissipativity condition under which the ergodic hypothesis and the $\mathcal{L}^2$-bound of the fast component, which are implicit conditions, are satisfied.

In the second part we propose a financial application of this result: we apply the theory developed to a slow-fast local stochastic volatility model. First we prove the weak convergence of the model to a local volatility one. Then under a risk neutral measure we show that the prices of the derivatives, possibly path-dependent, converge to the ones calculated using the limit model.

A Threshold for Quantum Advantage in Derivative Pricing
Shouvanik Chakrabarti,Rajiv Krishnakumar,Guglielmo Mazzola,Nikitas Stamatopoulos,Stefan Woerner,William J. Zeng
arXiv

We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual Redemption Forward (TARF) derivatives as benchmark use cases. We uncover blocking challenges in known approaches and introduce a new method for quantum derivative pricing - the re-parameterization method - that avoids them. This method combines pre-trained variational circuits with fault-tolerant quantum computing to dramatically reduce resource requirements. We find that the benchmark use cases we examine require 7.5k logical qubits and a T-depth of 46 million and thus estimate that quantum advantage would require a logical clock speed of 10Mhz. While the resource requirements given here are out of reach of current systems, we hope they will provide a roadmap for further improvements in algorithms, implementations, and planned hardware architectures.

Development of cloud, digital technologies and the introduction of chip technologies
arXiv

Hardly any other area of research has recently attracted as much attention as machine learning (ML) through the rapid advances in artificial intelligence (AI). This publication provides a short introduction to practical concepts and methods of machine learning, problems and emerging research questions, as well as an overview of the participants, an overview of the application areas and the socio-economic framework conditions of the research.

In expert circles, ML is used as a key technology for modern artificial intelligence techniques, which is why AI and ML are often used interchangeably, especially in an economic context. Machine learning and, in particular, deep learning (DL) opens up entirely new possibilities in automatic language processing, image analysis, medical diagnostics, process management and customer management. One of the important aspects in this article is chipization. Due to the rapid development of digitalization, the number of applications will continue to grow as digital technologies advance. In the future, machines will more and more provide results that are important for decision making. To this end, it is important to ensure the safety, reliability and sufficient traceability of automated decision-making processes from the technological side. At the same time, it is necessary to ensure that ML applications are compatible with legal issues such as responsibility and liability for algorithmic decisions, as well as technically feasible. Its formulation and regulatory implementation is an important and complex issue that requires an interdisciplinary approach. Last but not least, public acceptance is critical to the continued diffusion of machine learning processes in applications. This requires widespread public discussion and the involvement of various social groups.

Disentangling the socio-ecological drivers behind illegal fishing in a small-scale fishery managed by a TURF system
Silvia de Juan,Maria Dulce Subida,Andres Ospina-Alvarez,Ainara Aguilar,Miriam Fernandez
arXiv

A substantial increase in illegal extraction of the benthic resources in central Chile is likely driven by an interplay of numerous socio-economic local factors that threatens the success of the fisheries management areas (MA) system. To assess this problem, the exploitation state of a commercially important benthic resource (i.e., keyhole limpet) in the MAs was related with socio-economic drivers of the small-scale fisheries. The potential drivers of illegal extraction included rebound effect of fishing effort displacement by MAs, level of enforcement, distance to surveillance authorities, wave exposure and land-based access to the MA, and alternative economic activities in the fishing village. The exploitation state of limpets was assessed by the proportion of the catch that is below the minimum legal size, with high proportions indicating a poor state, and by the relative median size of limpets fished within the MAs in comparison with neighbouring OA areas, with larger relative sizes in the MA indicating a good state. A Bayesian-Belief Network approach was adopted to assess the effects of potential drivers of illegal fishing on the status of the benthic resource in the MAs. Results evidenced the absence of a direct link between the level of enforcement and the status of the resource, with other socio-economic (e.g., alternative economic activities in the village) and context variables (e.g., fishing effort or distance to surveillance authorities) playing important roles. Scenario analysis explored variables that are susceptible to be managed, evidencing that BBN is a powerful approach to explore the role of multiple external drivers, and their impact on marine resources, in complex small-scale fisheries.

Economic dimension of crimes against cultural-historical and archaeological heritage (EN)
Shteryo Nozharov
arXiv

The publication is one of the first studies of its kind, devoted to the economic dimension of crimes against cultural and archaeological heritage. Lack of research in this area is largely due to irregular global prevalence vague definition of economic value of the damage these crimes cause to the society at national and global level, to present and future generations. The author uses classical models of Becker and Freeman, by modifying and complementing them with the tools of economics of culture based on the values of non-use. The model tries to determine the opportunity costs of this type of crime in several scenarios and based on this to determine the extent of their limitation at an affordable cost to society and raising public benefits of conservation of World and National Heritage.

Estimating real-world probabilities: A forward-looking behavioral framework
Ricardo Crisóstomo
arXiv

We show that disentangling sentiment-induced biases from fundamental expectations significantly improves the accuracy and consistency of probabilistic forecasts. Using data from 1994 to 2017, we analyze 15 stochastic models and risk-preference combinations and in all possible cases a simple behavioral transformation delivers substantial forecast gains. Our results are robust across different evaluation methods, risk-preference hypotheses and sentiment calibrations, demonstrating that behavioral effects can be effectively used to forecast asset prices. Further analyses confirm that our real-world densities outperform densities recalibrated to avoid past mistakes and improve predictive models where risk aversion is dynamically estimated from option prices.

Exploring Narrative Economics: An Agent-Based-Modeling Platform that Integrates Automated Traders with Opinion Dynamics
Kenneth Lomas,Dave Cliff
arXiv

In seeking to explain aspects of real-world economies that defy easy understanding when analysed via conventional means, Nobel Laureate Robert Shiller has since 2017 introduced and developed the idea of Narrative Economics, where observable economic factors such as the dynamics of prices in asset markets are explained largely as a consequence of the narratives (i.e., the stories) heard, told, and believed by participants in those markets. Shiller argues that otherwise irrational and difficult-to-explain behaviors, such as investors participating in highly volatile cryptocurrency markets, are best explained and understood in narrative terms: people invest because they believe, because they have a heartfelt opinions, about the future prospects of the asset, and they tell to themselves and others stories (narratives) about those beliefs and opinions. In this paper we describe what is, to the best of our knowledge, the first ever agent-based modelling platform that allows for the study of issues in narrative economics. We have created this by integrating and synthesizing research in two previously separate fields: opinion dynamics (OD), and agent-based computational economics (ACE) in the form of minimally-intelligent trader-agents operating in accurately modelled financial markets. We show here for the first time how long-established models in OD and in ACE can be brought together to enable the experimental study of issues in narrative economics, and we present initial results from our system. The program-code for our simulation platform has been released as freely-available open-source software on GitHub, to enable other researchers to replicate and extend our work

Model of cunning agents
Mateusz Denys
arXiv

A numerical agent-based spin model of financial markets, based on the Potts model from statistical mechanics, with a novel interpretation of the spin variable (as regards financial-market models) is presented. In this model, a value of the spin variable is only the agent's opinion concerning current market situation, which he communicates to his nearest neighbors. Instead, the agent's action (i.e., buying, selling, or staying inactive) is connected with a change of the spin variable. Hence, the agents can be considered as cunning in this model. That is, these agents encourage their neighbors to buy stocks if the agents have an opportunity to sell them, and the agents encourage their neighbors to sell stocks if the agents have a reversed opportunity. Predictions of the model are in good agreement with empirical data from various real-life financial markets. The model reproduces the shape of the usual and absolute-value autocorrelation function of returns as well as the distribution of times between superthreshold losses.

Optimal contracts under adverse selection for staple goods: efficiency of in-kind insurance
Clémence Alasseur,Corinne Chaton,Emma Hubert
arXiv

An income loss can have a negative impact on households, forcing them to reduce their consumption of some staple goods. This can lead to health issues and, consequently, generate significant costs for society. We suggest that consumers can, to prevent these negative consequences, buy insurance to secure sufficient consumption of a staple good if they lose part of their income. We develop a two-period/two-good principal-agent problem with adverse selection and endogenous reservation utility to model insurance with in-kind benefits. This model allows us to obtain semi-explicit solutions for the insurance contract and is applied to the context of fuel poverty. For this application, our model allows to conclude that, even in the least efficient scenario from the households point of view, i.e., when the insurance is provided by a monopoly, this mechanism decreases significantly the risk of fuel poverty of households by ensuring them a sufficient consumption of energy. The effectiveness of in-kind insurance is highlighted through a comparison with income insurance, but our results nevertheless underline the need to regulate such insurance market.

Towards robust and speculation-reduction real estate pricing models based on a data-driven strategy