Research articles for the 2021-01-04

A Stochastic Investment Model for Actuarial Use in South Africa
Şule Şahin,Shaun Levitan

In this paper, we propose a stochastic investment model for actuarial use in South Africa by modelling price inflation rates, share dividends, long term and short-term interest rates for the period 1960-2018 and inflation-linked bonds for the period 2000-2018. Possible bi-directional relations between the economic series have been considered, the parameters and their confidence intervals have been estimated recursively to examine their stability and the model validation has been tested. The model is designed to provide long-term forecasts that should find application in long-term modelling for institutions such as pension funds and life insurance companies in South Africa

A Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria
Yu-Jui Huang,Zhou Zhou

This paper studies a nonzero-sum Dynkin game in discrete time under non-exponential discounting. For both players, there are two levels of game-theoretic reasoning intertwined. First, each player looks for an intra-personal equilibrium among her current and future selves, so as to resolve time inconsistency triggered by non-exponential discounting. Next, given the other player's chosen stopping policy, each player selects a best response among her intra-personal equilibria. A resulting inter-personal equilibrium is then a Nash equilibrium between the two players, each of whom is restricted to her intra-personal equilibria. Under appropriate conditions, we show that an inter-personal equilibrium exists, based on concrete iterative procedures along with Zorn's lemma. To illustrate our theoretic results, we investigate the negotiation between two firms, deriving inter-personal equilibria explicitly. In particular, it shows that coercive power in negotiation depends crucially on the impatience levels of the two firms.

Analysis and Design of Markets for Tradable MobilityCredit Schemes
Siyu Chen,Ravi Seshadri,Carlos Lima Azevedo,Arun P. Akkinepally,Renming Liu,Andrea Araldo,Yu Jiang,Moshe E. Ben-Akiva

Tradable mobility credit (TMC) schemes are an approach to travel demand management that have received significant attention in the transportation domain in recent years as a promising means to mitigate the adverse environmental, economic and social effects of urban traffic congestion. In TMC schemes, a regulator provides an initial endowment of mobility credits (or tokens) to all potential travelers. In order to use the transportation system, travelers need to spend a certain amount of tokens (tariff) that could vary with their choice of mode, route, departure time etc. The tokens can be bought and sold in a market that is managed by and operated by a regulator at a price that is dynamically determined by the demand and supply of tokens. This paper proposes and analyzes alternative market models for a TMC system (focusing on market design aspects such as allocation/expiration of credits, rules governing trading, transaction costs, regulator intervention, price dynamics), and develops a methodology to explicitly model the disaggregate behavior of individuals within the market. Extensive simulation experiments are conducted within a departure time context for the morning commute problem to compare the performance of the alternative designs relative to congestion pricing and a no control scenario. The simulation experiments employ a day to day assignment framework wherein transportation demand is modeled using a logit-mixture model and supply is modeled using a standard bottleneck model. The paper addresses a growing and imminent need to develop methodologies to realistically model TMCs that are suited for real-world deployments and can help us better understand the performance of these systems and the impact in particular, of market dynamics.

Bankruptcy prediction using disclosure text features
Sridhar Ravula

A public firm's bankruptcy prediction is an important financial research problem because of the security price downside risks. Traditional methods rely on accounting metrics that suffer from shortcomings like window dressing and retrospective focus. While disclosure text-based metrics overcome some of these issues, current methods excessively focus on disclosure tone and sentiment. There is a requirement to relate meaningful signals in the disclosure text to financial outcomes and quantify the disclosure text data. This work proposes a new distress dictionary based on the sentences used by managers in explaining financial status. It demonstrates the significant differences in linguistic features between bankrupt and non-bankrupt firms. Further, using a large sample of 500 bankrupt firms, it builds predictive models and compares the performance against two dictionaries used in financial text analysis. This research shows that the proposed stress dictionary captures unique information from disclosures and the predictive models based on its features have the highest accuracy.

Better Bunching, Nicer Notching
Marinho Bertanha,Andrew H. McCallum,Nathan Seegert

We study the bunching identification strategy for an elasticity parameter that summarizes agents' response to changes in slope (kink) or intercept (notch) of a schedule of incentives. A notch identifies the elasticity but a kink does not, when the distribution of agents is fully flexible. We propose new non-parametric and semi-parametric identification assumptions on the distribution of agents that are weaker than assumptions currently made in the literature. We revisit the original empirical application of the bunching estimator and find that our weaker identification assumptions result in meaningfully different estimates. We provide the Stata package "bunching" to implement our procedures.

COVID-19 spreading in financial networks: A semiparametric matrix regression model
Billio Monica,Casarin Roberto,Costola Michele,Iacopini Matteo

Network models represent a useful tool to describe the complex set of financial relationships among heterogeneous firms in the system. In this paper, we propose a new semiparametric model for temporal multilayer causal networks with both intra- and inter-layer connectivity. A Bayesian model with a hierarchical mixture prior distribution is assumed to capture heterogeneity in the response of the network edges to a set of risk factors including the European COVID-19 cases. We measure the financial connectedness arising from the interactions between two layers defined by stock returns and volatilities. In the empirical analysis, we study the topology of the network before and after the spreading of the COVID-19 disease.

Convergence rates of large-time sensitivities with the Hansen--Scheinkman decomposition
Hyungbin Park

This paper investigates the large-time asymptotic behavior of the sensitivities of cash flows. In quantitative finance, the price of a cash flow is expressed in terms of a pricing operator of a Markov diffusion process. We study the extent to which the pricing operator is affected by small changes of the underlying Markov diffusion. The main idea is a partial differential equation (PDE) representation of the pricing operator by incorporating the Hansen--Scheinkman decomposition method. The sensitivities of the cash flows and their large-time convergence rates can be represented via simple expressions in terms of eigenvalues and eigenfunctions of the pricing operator. Furthermore, compared to the work of Park (Finance Stoch. 4:773-825, 2018), more detailed convergence rates are provided. In addition, we discuss the application of our results to three practical problems: utility maximization, entropic risk measures, and bond prices. Finally, as examples, explicit results for several market models such as the Cox--Ingersoll--Ross (CIR) model, 3/2 model and constant elasticity of variance (CEV) model are presented.

Credit Crunch: The Role of Household Lending Capacity in the Dutch Housing Boom and Bust 1995-2018
Menno Schellekens,Taha Yasseri

What causes house prices to rise and fall? Economists identify household access to credit as a crucial factor. "Loan-to-Value" and "Debt-to-GDP" ratios are the standard measures for credit access. However, these measures fail to explain the depth of the Dutch housing bust after the 2009 Financial Crisis. This work is the first to model household lending capacity based on the formulas that Dutch banks use in the mortgage application process. We compare the ability of regression models to forecast housing prices when different measures of credit access are utilised. We show that our measure of household lending capacity is a forward-looking, highly predictive variable that outperforms `Loan-to-Value' and debt ratios in forecasting the Dutch crisis. Sharp declines in lending capacity foreshadow the market deceleration.

Deep reinforcement learning for portfolio management
Gang Huang,Xiaohua Zhou,Qingyang Song

The objective of this paper is to verify that current cutting-edge artificial intelligence technology, deep reinforcement learning, can be applied to portfolio management. We improve on the existing Deep Reinforcement Learning Portfolio model and make many innovations. Unlike many previous studies on discrete trading signals in portfolio management, we make the agent to short in a continuous action space, design an arbitrage mechanism based on Arbitrage Pricing Theory,and redesign the activation function for acquiring action vectors, in addition, we redesign neural networks for reinforcement learning with reference to deep neural networks that process image data. In experiments, we use our model in several randomly selected portfolios which include CSI300 that represents the market's rate of return and the randomly selected constituents of CSI500. The experimental results show that no matter what stocks we select in our portfolios, we can almost get a higher return than the market itself. That is to say, we can defeat market by using deep reinforcement learning.

Design and analysis of momentum trading strategies
Richard J. Martin

We give a complete description of the third-moment (skewness) characteristics of both linear and nonlinear momentum trading strategies, the latter being understood as transformations of a normalised moving-average filter (EMA). We explain in detail why the skewness is generally positive and has a term structure.

This paper is a synthesis of two papers published by the author in RISK in 2012, with some updates and comments.

Duality for optimal consumption under no unbounded profit with bounded risk
Michael Monoyios

We give a definitive treatment of duality for optimal consumption over the infinite horizon, in a semimartingale incomplete market satisfying no unbounded profit with bounded risk (NUPBR). Rather than base the dual domain on (local) martingale deflators, we use a class of supermartingale deflators such that deflated wealth plus cumulative deflated consumption is a supermartingale for all admissible consumption plans. This yields a strong duality, because the enlarged dual domain of processes dominated by deflators is naturally closed, without invoking its closure. In this way we automatically reach the bipolar of the set of deflators. We complete this picture by proving that the set of processes dominated by local martingale deflators is dense in our dual domain, confirming that we have identified the natural dual space. In addition to the optimal consumption and deflator, we characterise the optimal wealth process. At the optimum, deflated wealth is a supermartingale and a potential, while deflated wealth plus cumulative deflated consumption is a uniformly integrable martingale. This is the natural generalisation of the corresponding feature in the terminal wealth problem, where deflated wealth at the optimum is a uniformly integrable martingale. We use no constructions involving equivalent local martingale measures. This is natural, given that such measures typically do not exist over the infinite horizon and that we are working under NUPBR, which does not require their existence. The structure of the duality proof reveals an interesting feature compared with the terminal wealth problem. There, the dual domain is $L^{1}$-bounded, but here the primal domain has this property, and hence many steps in the duality proof show a marked reversal of roles for the primal and dual domains, compared with the proofs of Kramkov and Schachermayer.

Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19
Nick James

This paper uses new and recently introduced methodologies to study the similarity in the dynamics and behaviours of cryptocurrencies and equities surrounding the COVID-19 pandemic. We study two collections; 45 cryptocurrencies and 72 equities, both independently and in conjunction. First, we examine the evolution of cryptocurrency and equity market dynamics, with a particular focus on their change during the COVID-19 pandemic. We demonstrate markedly more similar dynamics during times of crisis. Next, we apply recently introduced methods to contrast trajectories, erratic behaviours, and extreme values among the two multivariate time series. Finally, we introduce a new framework for determining the persistence of market anomalies over time. Surprisingly, we find that although cryptocurrencies exhibit stronger collective dynamics and correlation in all market conditions, equities behave more similarly in their trajectories, extremes, and show greater persistence in anomalies over time.

Estimation of Tempered Stable L\'{e}vy Models of Infinite Variation
José E. Figueroa-López,Ruoting Gong,Yuchen Han

In this paper we propose a new method for the estimation of a semiparametric tempered stable L\'{e}vy model. The estimation procedure combines iteratively an approximate semiparametric method of moment estimator, Truncated Realized Quadratic Variations (TRQV), and a newly found small-time high-order approximation for the optimal threshold of the TRQV of tempered stable processes. The method is tested via simulations to estimate the volatility and the Blumenthal-Getoor index of the generalized CGMY model as well as the integrated volatility of a Heston type model with CGMY jumps. The method outperforms other efficient alternatives proposed in the literature.

Exploring the Impact of COVID-19 in the Sustainability of Airbnb Business Model
Rim Krouk,Fernando Almeida

Society is undergoing many transformations and faces economic crises, environmental, social, and public health issues. At the same time, the Internet, mobile communications, cloud technologies, and social networks are growing rapidly and fostering the digitalization processes of business and society. It is in this context that the shared economy has assumed itself as a new social and economic system based on the sharing of resources and has allowed the emergence of innovative businesses like Airbnb. However, COVID-19 has challenged this business model in the face of restrictions imposed in the tourism sector. Its consequences are not exclusively short-term and may also call into question the sustainability of Airbnb. In this sense, this study aims to explore the sustainability of the Airbnb business model considering two theories which advocate that hosts can cover the short-term financial effects, while another defends a paradigm shift in the demand for long-term accommodations to ensure greater stability for hosts.

Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options
Andrew Papanicolaou

This article explores the relationship between the SPX and VIX options markets. High-strike VIX call options are used to hedge tail risk in the SPX, which means that SPX options are a reflection of the extreme-strike asymptotics of VIX options, and vice versa. This relationship can be quantified using moment formulas in a model-free way. Comparisons are made between VIX and SPX implied volatilities along with various examples of stochastic volatility models.

Forward indifference valuation and hedging of basis risk under partial information
Mahan Tahvildari

We study the hedging and valuation of European and American claims on a non-traded asset $Y$, when a traded stock $S$ is available for hedging, with $S$ and $Y$ following correlated geometric Brownian motions. This is an incomplete market, often called a basis risk model. The market agent's risk preferences are modelled using a so-called forward performance process (forward utility), which is a time-decreasing utility of exponential type. Moreover, the market agent (investor) does not know with certainty the values of the asset price drifts. This market setting with drift parameter uncertainty is the partial information scenario. We discuss the stochastic control problem obtained by setting up the hedging portfolio and derive the optimal hedging strategy. Furthermore, a (dual) forward indifference price representation of the claim and its PDE are obtained. With these results, the residual risk process representing the basis risk (hedging error), pay-off decompositions and asymptotic expansions of the indifference price in the European case are derived. We develop the analogous stochastic control and stopping problem with an American claim and obtain the corresponding forward indifference price valuation formula.

Governmental incentives for green bonds investment
Bastien Baldacci,Dylan Possamaï

Motivated by the recent studies on the green bond market, we build a model in which an investor trades on a portfolio of green and conventional bonds, both issued by the same governmental entity. The government provides incentives to the bondholder in order to increase the amount invested in green bonds. These incentives are, optimally, indexed on the prices of the bonds, their quadratic variation and covariation. We show numerically on a set of French governmental bonds that our methodology outperforms the current tax-incentives systems in terms of green investments. Moreover, it is robust to model specification for bond prices and can be applied to a large portfolio of bonds using classical optimisation methods.

Mind the wealth gap: a new allocation method to match micro and macro statistics for household wealth
Michele Cantarella,Andrea Neri,Maria Giovanna Ranalli

The financial and economic crisis recently experienced by many European countries has increased demand for timely, coherent and consistent distributional information for the household sector. In the Euro area, most of the NCBs collect such information through income and wealth surveys, which are often used to inform their decisions. These surveys, however, can often suffer from biases, usually caused by non-response and under-reporting behaviours, leading to a mismatch with macroeconomic aggregates. In this paper, we develop a novel allocation method which combines information from a power law (Pareto) model and imputation procedures so to address these issues simultaneously, when only limited external information is available. We provide two important contributions: first, we adjust the weights of observed survey households for non-response bias, then, we correct for measurement error. Finally, we produce distributional indicators for four Euro-Area countries.

Model-free price bounds under dynamic option trading
Ariel Neufeld,Julian Sester

In this paper we extend discrete time semi-static trading strategies by also allowing for dynamic trading in a finite amount of options, and we study the consequences for the model-independent super-replication prices of exotic derivatives. These include duality results as well as a precise characterization of pricing rules for the dynamically tradable options triggering an improvement of the price bounds for exotic derivatives in comparison with the conventional price bounds obtained through the martingale optimal transport approach.

Predicting the Performance of a Future United Kingdom Grid and Wind Fleet When Providing Power to a Fleet of Battery Electric Vehicles
Anthony D Stephens,David R Walwyn

Sales of new petrol and diesel passenger vehicles may not be permitted in the United Kingdom (UK) post-2030. Should this happen, it is likely that vehicles presently powered by hydrocarbons will be progressively replaced by Battery Electric Vehicles (BEVs). This paper describes the use of mathematical modelling, drawing on real time records of the UK electricity grid, to investigate the likely performance of the grid when supplying power to a fleet of up to 35 million BEVs. The model highlights the importance of understanding how the grid will cope when powering a BEV fleet under conditions similar to those experienced during an extended wind lull during the 3rd week of January 2017. Allowing a two-way flow of electricity between the BEVs and the grid, known as the vehicle-to-grid (V2G) configuration, turns out to be of key importance in minimising the need for additional gas turbine generation or energy storage during wind lulls. This study has shown that with the use of V2G, it should be possible to provide power to about 15 million BEVs with the gas turbine capacity currently available. Without V2G, it is likely that the current capacity of the gas turbines and associated gas infrastructure might be overwhelmed by even a relatively small BEV fleet. Since it is anticipated that 80% of BEV owners will be able to park the vehicles at their residences, widespread V2G will enable both the powering of residences when supply from the grid is constrained and the charging of BEVs when supply is in excess. The model shows that this configuration will maintain a constant load on the grid and avoid the use of either expensive alternative storage or hydrogen obtained by reforming methane. There should be no insuperable problem in providing power to the 20% of BEV owners who do not have parking at their residences; their power could come directly from the grid.

Pricing spread option with liquidity adjustments
Kevin Shuai Zhang,Traian Pirvu

We study the pricing and hedging of European spread options on correlated assets when, in contrast to the standard framework and consistent with imperfect liquidity markets, the trading in the stock market has a direct impact on stocks prices. We consider a partial-impact and a full-impact model in which the price impact is caused by every trading strategy in the market. The generalized Black-Scholes pricing partial differential equations (PDEs) are obtained and analysed. We perform a numerical analysis to exhibit the illiquidity effect on the replication strategy of the European spread option. Compared to the Black-Scholes model or a partial impact model, the trader in the full impact model buys more stock to replicate the option, and this leads to a higher option price.

Robust Analysis of Stock Price Time Series Using CNN and LSTM-Based Deep Learning Models
Sidra Mehtab,Jaydip Sen,Subhasis Dasgupta

Prediction of stock price and stock price movement patterns has always been a critical area of research. While the well-known efficient market hypothesis rules out any possibility of accurate prediction of stock prices, there are formal propositions in the literature demonstrating accurate modeling of the predictive systems that can enable us to predict stock prices with a very high level of accuracy. In this paper, we present a suite of deep learning-based regression models that yields a very high level of accuracy in stock price prediction. To build our predictive models, we use the historical stock price data of a well-known company listed in the National Stock Exchange (NSE) of India during the period December 31, 2012 to January 9, 2015. The stock prices are recorded at five minutes intervals of time during each working day in a week. Using these extremely granular stock price data, we build four convolutional neural network (CNN) and five long- and short-term memory (LSTM)-based deep learning models for accurate forecasting of the future stock prices. We provide detailed results on the forecasting accuracies of all our proposed models based on their execution time and their root mean square error (RMSE) values.

Simplified stochastic calculus with applications in Economics and Finance
Aleš Černý,Johannes Ruf

The paper introduces a simple way of recording and manipulating general stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically present). The calculus is fail-safe in that, under minimal assumptions, all informal calculations yield mathematically well-defined stochastic processes. The calculus is also intuitive as it allows the user to pretend all jumps are of compound Poisson type. The new calculus is very effective when it comes to computing drifts and expected values that possibly involve a change of measure. Such drift calculations yield, for example, partial integro-differential equations, Hamilton-Jacobi-Bellman equations, Feynman-Kac formulae, or exponential moments needed in numerous applications. We provide several illustrations of the new technique, among them a novel result on the Margrabe option to exchange one defaultable asset for another.

Super-App Behavioral Patterns in Credit Risk Models: Financial, Statistical and Regulatory Implications
Luisa Roa,Alejandro Correa-Bahnsen,Gabriel Suarez,Fernando Cortés-Tejada,María A. Luque,Cristián Bravo

In this paper we present the impact of alternative data that originates from an app-based marketplace, in contrast to traditional bureau data, upon credit scoring models. These alternative data sources have shown themselves to be immensely powerful in predicting borrower behavior in segments traditionally underserved by banks and financial institutions. Our results, validated across two countries, show that these new sources of data are particularly useful for predicting financial behavior in low-wealth and young individuals, who are also the most likely to engage with alternative lenders. Furthermore, using the TreeSHAP method for Stochastic Gradient Boosting interpretation, our results also revealed interesting non-linear trends in the variables originating from the app, which would not normally be available to traditional banks. Our results represent an opportunity for technology companies to disrupt traditional banking by correctly identifying alternative data sources and handling this new information properly. At the same time alternative data must be carefully validated to overcome regulatory hurdles across diverse jurisdictions.

The 2020 Global Stock Market Crash: Endogenous or Exogenous?
Ruiqiang Song,Min Shu,Wei Zhu

Starting on February 20, 2020, the global stock markets began to suffer the worst decline since the Great Recession in 2008, and the COVID-19 has been widely blamed on the stock market crashes. In this study, we applied the log-periodic power law singularity (LPPLS) methodology based on multilevel time series to unravel the underlying mechanisms of the 2020 global stock market crash by analyzing the trajectories of 10 major stock market indexes from both developed and emergent stock markets, including the S&P 500, DJIA, NASDAQ, FTSE, DAX, NIKKEI, CSI 300, HSI, BSESN, and BOVESPA. In order to effectively distinguish between endogenous crash and exogenous crash, we proposed using the LPPLS confidence indicator as a classification proxy. The results show that the apparent LPPLS bubble patterns of the super-exponential increase, corrected by the accelerating logarithm-periodic oscillations, have indeed presented in the price trajectories of the seven indexes: S&P 500, DJIA, NASDAQ, DAX, CSI 300, BSESN, and BOVESPA, indicating that the large positive bubbles have formed endogenously prior to the 2020 stock market crash, and the subsequent crashes for the seven indexes are endogenous, stemming from the increasingly systemic instability of the stock markets, while the well-known external shocks such as the COVID-19 pandemic etc. only acted as sparks during the 2020 global stock market crash. In contrast, the obvious signatures of the LPPLS model have not been observed in the price trajectories of the three remaining indexes: FTSE, NIKKEI, and HSI, signifying that the crashes in these three indexes are exogenous, stemming from external shocks. The novel classification method of crash types proposed in this study can also be used to analyze regime changes of any price trajectories in global financial markets.

The OxyContin Reformulation Revisited: New Evidence From Improved Definitions of Markets and Substitutes
Shiyu Zhang,Daniel Guth

The opioid epidemic began with prescription pain relievers. In 2010 Purdue Pharma reformulated OxyContin to make it more difficult to abuse. OxyContin misuse fell dramatically, and concurrently heroin deaths began to rise. Previous research overlooked generic oxycodone and argued that the reformulation induced OxyContin users to switch directly to heroin. Using a novel and fine-grained source of all oxycodone sales from 2006-2014, we show that the reformulation led users to substitute from OxyContin to generic oxycodone, and the reformulation had no overall impact on opioid or heroin mortality. In fact, generic oxycodone, instead of OxyContin, was the driving factor in the transition to heroin. Finally, we show that by omitting generic oxycodone we recover the results of the literature. These findings highlight the important role generic oxycodone played in the opioid epidemic and the limited effectiveness of a partial supply-side intervention.

The Value Added of Machine Learning to Causal Inference: Evidence from Revisited Studies
Anna Baiardi,Andrea A. Naghi

A new and rapidly growing econometric literature is making advances in the problem of using machine learning methods for causal inference questions. Yet, the empirical economics literature has not started to fully exploit the strengths of these modern methods. We revisit influential empirical studies with causal machine learning methods and identify several advantages of using these techniques. We show that these advantages and their implications are empirically relevant and that the use of these methods can improve the credibility of causal analysis.

Using attention to model long-term dependencies in occupancy behavior
Max Kleinebrahm,Jacopo Torriti,Russell McKenna,Armin Ardone,Wolf Fichtner

Models simulating household energy demand based on different occupant and household types and their behavioral patterns have received increasing attention over the last years due the need to better understand fundamental characteristics that shape the demand side. Most of the models described in the literature are based on Time Use Survey data and Markov chains. Due to the nature of the underlying data and the Markov property, it is not sufficiently possible to consider day to day dependencies in occupant behavior. An accurate mapping of day to day dependencies is of increasing importance for accurately reproducing mobility patterns and therefore for assessing the charging flexibility of electric vehicles. This study bridges the gap between energy related activity modelling and novel machine learning approaches with the objective to better incorporate findings from the field of social practice theory in the simulation of occupancy behavior. Weekly mobility data are merged with daily time use survey data by using attention based models. In a first step an autoregressive model is presented, which generates synthetic weekly mobility schedules of individual occupants and thereby captures day to day dependencies in mobility behavior. In a second step, an imputation model is presented, which enriches the weekly mobility schedules with detailed information about energy relevant at home activities. The weekly activity profiles build the basis for modelling consistent electricity, heat and mobility demand profiles of households. Furthermore, the approach presented forms the basis for providing data on socio-demographically differentiated occupant behavior to the general public.

What does the consumer know about the environmental damage caused by the disposable cup and the need to replace it
Guillermo José Navarro del Toro

The objective of this work was to know the amount and frequency with which the people of Arandas in the Altos de Jalisco region use disposable cups and then know how willing they are to use edible cups made with natural gelatin. In this regard, it is worth commenting that these can not only be nutritious for those who consume them (since gelatin is a fortifying nutrient created from the skin and bone of pigs and cows), but they could also be degraded in a few days or be ingested by animals. To collect the information, a survey consisting of six questions was used, which was applied to 31 people by telephone and another 345 personally (in both cases they were applied to young people and adults). The results show that the residents of that town considerably use plastic cups in the different events that take place each week, which are more numerous during the patron saint festivities or at the end of the year. Even so, these people would be willing to change these habits, although for this, measures must be taken that do not affect the companies in that area, which work mainly with plastics and generate a high percentage of jobs.

When Risks and Uncertainties Collide: Mathematical Finance for Arbitrage Markets in a Quantum Mechanical View
Simone Farinelli,Hideyuki Takada

Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the instantaneous arbitrage capability generated by the market itself. The asset and market portfolio dynamics have a quantum mechanical description, which is constructed by quantizing the deterministic version of the stochastic Lagrangian system describing a market allowing for arbitrage. Results, obtained by solving the Schroedinger equation, coincide with those obtained by solving the stochastic Euler Lagrange equations derived by a variational principle and providing therefore consistency.