We propose a method based on continuous time Markov chain approximation to compute the distribution of Parisian stopping times and price Parisian options under general one-dimensional Markov processes. We prove the convergence of the method under a general setting and obtain sharp estimate of the convergence rate for diffusion models. Our theoretical analysis reveals how to design the grid of the CTMC to achieve faster convergence. Numerical experiments are conducted to demonstrate the accuracy and efficiency of our method for both diffusion and jump models. To show the versality of our approach, we develop extensions for multi-sided Parisian stopping times, the joint distribution of Parisian stopping times and first passage times, Parisian bonds and for more sophisticated models like regime-switching and stochastic volatility models.

We propose a general family of piecewise hyperbolic absolute risk aversion (PHARA) utility, including many non-standard utilities as examples. A typical application is the composition of an HARA preference and a piecewise linear payoff in hedge fund management. We derive a unified closed-form formula of the optimal portfolio, which is a four-term division. The formula has clear economic meanings, reflecting the behavior of risk aversion, risk seeking, loss aversion and first-order risk aversion. One main finding is that risk-taking behaviors are greatly increased by non-concavity and reduced by non-differentiability.

Biofouling of ships causes major environmental and economic consequences all over the world. In addition, biofouling management of ship hulls causes both social, environmental and economic risks that should all be considered reaching well-balanced decisions. In addition, each case is unique and thus optimal management strategy must be considered case-specifically. We produced a novel decision support tool using Bayesian networks to promote the comprehensive understanding about the complex biofouling management issue in the Baltic Sea and to identify potential management options and their consequences. The tool compares the biofouling management strategies in relation to NIS (non-indigenous species) introduction risk, eco-toxicological risk due to biocidal coating, carbon dioxide emissions resulting from fuel consumption and costs related to fuel consumption, in-water cleaning and coating. According to the results, the optimal biofouling management strategy would consist of a biocidal-free coating with regular in-water cleaning and with devices collecting the material. However, the best biocidal-free coating type and the optimal in-water cleaning interval varies and depends e.g. on the operational profile of the ship. The decision support tool can increase the multi-perspective understanding about the issue and support the implementation of the optimal biofouling management strategies in the Baltic Sea.

A positive correlation between exposure and counterparty credit risk gives rise to the so-called Wrong-Way Risk (WWR). Even after a decade of the financial crisis, addressing WWR in both sound and tractable ways remains challenging. Academicians have proposed arbitrage-free set-ups through copula methods but those are computationally expensive and hard to use in practice. Resampling methods are proposed by the industry but they lack mathematical foundations. The purpose of this article is to bridge this gap between the approaches used by academicians and industry. To this end, we propose a stochastic correlation approach to asses WWR. The methods based on constant correlation to model the dependency between exposure and counterparty credit risk assume a linear dependency, thus fail to capture the tail dependence. Using a stochastic correlation we move further away from the Gaussian copula and can capture the tail risk. This effect is reflected in the results where the impact of stochastic correlation on calculated CVA is substantial when compared to the case when a high constant correlation is assumed between exposure and credit. Given the uncertainty inherent to CVA, the proposed method is believed to provide a promising way to model WWR.

The foreign exchange market has taken an important role in the global financial market. While foreign exchange trading brings high-yield opportunities to investors, it also brings certain risks. Since the establishment of the foreign exchange market in the 20th century, foreign exchange rate forecasting has become a hot issue studied by scholars from all over the world. Due to the complexity and number of factors affecting the foreign exchange market, technical analysis cannot respond to administrative intervention or unexpected events. Our team chose several pairs of foreign currency historical data and derived technical indicators from 2005 to 2021 as the dataset and established different machine learning models for event-driven price prediction for oversold scenario.

This paper attempts to analyse policymaking in the field of Intellectual Property (IP) as an instrument of economic growth across the Global North and South. It begins by studying the links between economic growth and IP, followed by an understanding of Intellectual Property Rights (IPR) development in the US, a leading proponent of robust IPR protection internationally. The next section compares the IPR in the Global North and South and undertakes an analysis of the diverse factors that result in these differences. The paper uses the case study of the Indian Pharmaceutical Industry to understand how IPR may differentially affect economies and conclude that there may not yet be a one size fits all policy for the adoption of Intellectual Property Rights.

We develop a general approach for stress testing correlations of financial asset portfolios. The correlation matrix of asset returns is specified in a parametric form, where correlations are represented as a function of risk factors, such as country and industry factors. A sparse factor structure linking assets and risk factors is built using Bayesian variable selection methods. Regular calibration yields a joint distribution of economically meaningful stress scenarios of the factors. As such, the method also lends itself as a reverse stress testing framework: using the Mahalanobis distance or highest density regions (HDR) on the joint risk factor distribution allows to infer worst-case correlation scenarios. We give examples of stress tests on a large portfolio of European and North American stocks.

We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be used to implement a stochastic implied volatility model in the following two steps: 1. Train a market simulator for option prices, as discussed for example in our recent; 2. Find a risk-neutral density, specifically the minimal entropy martingale measure. The resulting model can be used for risk-neutral pricing, or for Deep Hedging in the case of transaction costs or trading constraints. To motivate the proposed approach, we also show that market dynamics are free from "statistical arbitrage" in the absence of transaction costs if and only if they follow a risk-neutral measure. We additionally provide a more general characterization in the presence of convex transaction costs and trading constraints. These results can be seen as an analogue of the fundamental theorem of asset pricing for statistical arbitrage under trading frictions and are of independent interest.

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017--2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and $q$-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called "inverse-cubic power-law" still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors -- speed of the market time flow and the asset cross-correlation magnitude -- while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.

Investor awareness about impending regulations requiring firms to reduce their carbon footprint has introduced a carbon transition risk premium in the stocks of firms. On performing a cross-section analysis, a significant premium was estimated among large caps in the US markets. The existence of a risk premium indicates investor awareness about future exposure to low-carbon transition. A new measure, the Single Event Transition Risk (SETR), was developed to model the maximum exposure of a firm to carbon transition risk, and a functional form for the same was determined, in terms of risk premia. Different classes of distributions for arrival processes of transition events were considered and the respective SETRs were determined and studied. The trade-off between higher premia and higher risks was studied for the different processes, and it was observed that, based on the distributions of arrival times, investors could have a lower, equal or higher probability of positive returns (from the premium-risk trade-off), and that despite a fair pricing of the carbon premium, decisions by investors to take long or short positions on a stock could still be biased.

We establish general "collapse to the mean" principles that provide conditions under which a law-invariant functional reduces to an expectation. In the convex setting, we retrieve and sharpen known results from the literature. However, our results also apply beyond the convex setting. We illustrate this by providing a complete account of the "collapse to the mean" for quasiconvex functionals. In the special cases of consistent risk measures and Choquet integrals, we can even dispense with quasiconvexity. In addition, we relate the "collapse to the mean" to the study of solutions of a broad class of optimisation problems with law-invariant objectives that appear in mathematical finance, insurance, and economics. We show that the corresponding quantile formulations studied in the literature are sometimes illegitimate and require further analysis.

It is argued that Marxism, being based on contradictions, is an illogical method. More specifically, we present a rejection of Marx's thesis that the rate of profit has a long-term tendency to fall.

While the original Ait-Sahalia interest rate model has been found considerable use as a model for describing time series evolution of interest rates, it may not possess adequate specifications to explain responses of interest rates to empirical phenomena such as volatility 'skews' and 'smiles', jump behaviour, market regulatory lapses, economic crisis, financial clashes, political instability, among others collectively. The aim of this paper is to propose a modified version of this model by incorporating additional features to collectively describe these empirical phenomena adequately. Moreover, due to lack of a closed-form solution to the proposed model, we employ several new truncated EM techniques to numerically study this model and justify the scheme within Monte Carlo framework to compute some financial quantities such as a bond and a barrier option.

For many financial applications, it is important to have reliable and tractable models for the behavior of assets and indexes, for example in risk evaluation. A successful approach is based on ARCH processes, which strike the right balance between statistical properties and ease of computation. This study focuses on quadratic ARCH processes and the theoretical conditions to have a stable long-term behavior. In particular, the weights for the variance estimators should sum to 1, and the variance of the innovations should be 1. Using historical data, the realized empirical innovations can be computed, and their statistical properties assessed. Using samples of 3 to 5 decades, the variance of the empirical innovations are always significantly above 1, for a sample of stock indexes, commodity indexes and FX rates. This departure points to a short term instability, or to a fast adaptability due to changing conditions. Another theoretical condition on the innovations is to have a zero mean. This condition is also investigated empirically, with some time series showing significant departure from zero.

In this article we consider the optimal investment-consumption problem for an agent with preferences governed by Epstein-Zin stochastic differential utility who invests in a constant-parameter Black-Scholes-Merton market.

The paper has three main goals: first, to provide a detailed introduction to infinite-horizon Epstein-Zin stochastic differential utility, including a discussion of which parameter combinations lead to a well-formulated problem; second, to prove existence and uniqueness of infinite horizon Epstein-Zin stochastic differential utility under a restriction on the parameters governing the agent's risk aversion and temporal variance aversion; and third, to provide a verification argument for the candidate optimal solution to the investment-consumption problem among all admissible consumption streams.

To achieve these goals, we introduce a slightly different formulation of Epstein-Zin stochastic differential utility to that which is traditionally used in the literature. This formulation highlights the necessity and appropriateness of certain restrictions on the parameters governing the stochastic differential utility function.

In this paper, a dividend optimization problem with a terminal value at creeping ruin for Levy risk models has been investigated. We consider an insurance company whose surplus process evolves as a spectrally negative Levy process with a Gaussian part and its objective function is given by cumulative discounted dividend payments and a terminal value at creeping ruin. In views of identities from fluctuation theory, under the restriction on the negative terminal value, we show that the threshold strategy turns out to be the optimal one with threshold level at zero over an admissible class with restricted dividend rates. Furthermore, some sufficient conditions for the positive one also have been given.

An approach to modelling volatile financial return series using stationary d-vine copula processes combined with Lebesgue-measure-preserving transformations known as v-transforms is proposed. By developing a method of stochastically inverting v-transforms, models are constructed that can describe both stochastic volatility in the magnitude of price movements and serial correlation in their directions. In combination with parametric marginal distributions it is shown that these models can rival and sometimes outperform well-known models in the extended GARCH family.

We aim to identify winners and losers of a sudden inflow of low-skilled immigrants using a general equilibrium search and matching model in which employees, either native or non-native, are heterogeneous with respect to their skill level and produce different types of goods and Government expenditure in public goods is financed by a progressive taxation on wages and profits. We estimate the short-term impact of this shock for Italy in each year in the period 2008-2017 to be sizeable and highly asymmetric. In 2017, the real wages of low-skilled and high-skilled employees were 4% lower and 8% higher, respectively, compared to a counter-factual scenario with no non-natives. Similarly, employers working in the low-skilled market experienced a drop in profits of comparable magnitude, while the opposite happened to employers operating in the high-skilled market. Finally, the presence of non-natives led to a 14% increase in GDP and to an increment of approximately 70 billion euros in government revenues and 18 billion euros in social security contributions.