Epidemic Compartmental Models and Their Insurance Applications

Our society’s efforts to fight pandemics rely heavily on our ability to understand, model and predict the transmission dynamics of infectious diseases. Compartmental models are among the most commonly used mathematical tools to explain reported infections and deaths. This chapter offers a brief overview of basic compartmental models as well as several actuarial applications, ranging from product design and reserving of epidemic insurance, to the projection of healthcare demand and the allocation of scarce resources. The intent is to bridge classical epidemiological models with actuarial and financial applications that provide healthcare coverage and utilise limited healthcare resources during pandemics.

The Legal maxims of Maʾālāt and its Contemporary Application on Financial Transactions

Our religion with its wisdom and jurisprudence; it is wise for Muslims to look at their future and what their actions and behavior will lead to - after benefiting from the experiences of the past and the experiences of the present - by anticipating it and challenging it and preparing for it with what it needs of sciences and arts that guarantee them a sublime human meeting, as Abdulqadir Al-Kilani said. Hence our interest in the outcomes and their fundamentalist rules and contemporary financial applications. As for the study’s goal, it is to employ our Islamic fundamental, intentional, jurisprudential and intellectual knowledge in a jurisprudential adaptation of the most prominent contemporary transactions. Therefore, the research problem is: What is the role of the rules of fate in the jurisprudential view of contemporary transactions. The research method is inductive, analytical, and deductive method. By extrapolating the legal texts established to consider the outcomes and then analyzing those texts to derive appropriate provisions for contemporary financial transactions. The most prominent results: First: that Islam prepared man to consider the fates and freed him from the obstacles of superstition, pessimism, volatility, and astrology. Second: The rules of fate aim to consider the legal rulings related to the true tomorrow and the possible actions of the taxpayers based on the past, understanding the reality and anticipating the future according to the possible capacity. Third: The Holy Qur’an was concerned with the cosmic and social norms as harbingers of the fates and the meanings of their perception, as it was concerned with time in all its parts, past, present and future, so that the Muslim would be on the basis of his order in his movement, his residence, its causes, and its consequences.

Transformations of Telegraph Processes and Their Financial Applications

In this paper, we consider non-linear transformations of classical telegraph process. The main results consist of deriving a general partial differential Equation (PDE) for the probability density (pdf) of the transformed telegraph process, and then presenting the limiting PDE under Kac’s conditions, which may be interpreted as the equation for a diffusion process on a circle. This general case includes, for example, classical cases, such as limiting diffusion and geometric Brownian motion under some specifications of non-linear transformations (i.e., linear, exponential, etc.). We also give three applications of non-linear transformed telegraph process in finance: (1) application of classical telegraph process in the case of balance, (2) application of classical telegraph process in the case of dis-balance, and (3) application of asymmetric telegraph process. For these three cases, we present European call and put option prices. The novelty of the paper consists of new results for non-linear transformed classical telegraph process, new models for stock prices based on transformed telegraph process, and new applications of these models to option pricing.

How Fast Does the Clock of Finance Run?—A Time-Definition Enforcing Stationarity and Quantifying Overnight Duration

A definition of time based on the assumption of scale invariance may enhance and simplify the analysis of historical series with cyclically recurrent patterns and seasonalities. By enforcing simple-scaling and stationarity of the distributions of returns, we identify a successful protocol of time definition in finance, functional from tens of minutes to a few days. Within this time definition, the significant reduction of cyclostationary effects allows analyzing the structure of the stochastic process underlying the series on the basis of statistical sampling sliding along the whole time series. At the same time, the duration of periods in which markets remain inactive is properly quantified by the novel clock, and the corresponding returns (e.g., overnight or weekend) can be consistently taken into account for financial applications. The method is applied to the S&P500 index recorded at a 1 min frequency between September 1985 and June 2013.

How to gauge investor behavior? A comparison of online investor sentiment measures

Given the increasing interest in and the growing number of publicly available methods to estimate investor sentiment from social media platforms, researchers and practitioners alike are facing one crucial question – which is best to gauge investor sentiment? We compare the performance of daily investor sentiment measures estimated from Twitter and StockTwits short messages by publicly available dictionary and machine learning based methods for a large sample of stocks. To determine their relevance for financial applications, these investor sentiment measures are compared by their effects on the cross-section of stocks (i) within a Fama and MacBeth (J Polit Econ 81:607–636, 1973) regression framework applied to a measure of retail investors’ order imbalances and (ii) by their ability to forecast abnormal returns in a model-free portfolio sorting exercise. Interestingly, we find that investor sentiment measures based on finance-specific dictionaries do not only have a greater impact on retail investors’ order imbalances than measures based on machine learning approaches, but also perform very well compared to the latter in our asset pricing application.

Long-term, Short-term and Sudden Event: Trading Volume Movement Prediction with Graph-based Multi-view Modeling

Trading volume movement prediction is the key in a variety of financial applications. Despite its importance, there is few research on this topic because of its requirement for comprehensive understanding of information from different sources. For instance, the relation between multiple stocks, recent transaction data and suddenly released events are all essential for understanding trading market. However, most of the previous methods only take the fluctuation information of the past few weeks into consideration, thus yielding poor performance. To handle this issue, we propose a graph-based approach that can incorporate multi-view information, i.e., long-term stock trend, short-term fluctuation and sudden events information jointly into a temporal heterogeneous graph. Besides, our method is equipped with deep canonical analysis to highlight the correlations between different perspectives of fluctuation for better prediction. Experiment results show that our method outperforms strong baselines by a large margin.

Mean-Reverting 4/2 Principal Components Model. Financial Applications

In this paper, we propose a new multivariate mean-reverting model incorporating state-of-the art 4/2 stochastic volatility and a convenient principal component stochastic volatility (PCSV) decomposition for the stochastic covariance. We find a quasi closed-form characteristic function and propose analytic approximations, which aid in the pricing of derivatives and calculation of risk measures. Parameters are estimated on three bivariate series, using a two-stage methodology involving method of moments and least squares. Moreover, a scaling factor is added for extra degrees of freedom to match data features. As an application, we consider investment strategies for a portfolio with two risky assets and a risk-free cash account. We calculate value-at-risk (VaR) values at a 95% risk level using both simulation-based and distribution-based methods. A comparison of these VaR values supports the effectiveness of our approximations and the potential for higher dimensions.