In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of agents are interacting through the market price. Adopting a mean field game (MFG) approach, we find a special form of forward-backward stochastic differential equations of McKean-Vlasov type with common noise whose solution provides a good approximate of the market price. We show the convergence of the net order flow to zero in the large N-limit and get the order of convergence in N under some conditions. We also extend the model to a setup with multiple populations where the agents within each population share the same cost and coefficient functions but they can be different population by population.

We consider closed-form approximations for European put option prices within several stochastic volatility frameworks with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion around the mean of its argument. The difficulties then faced are simplifying a number of expectations induced by the Taylor expansion. Under the assumption of piecewise-constant parameters, we derive explicit pricing formulas and devise a fast calibration scheme. Furthermore, we perform a numerical error and sensitivity analysis to investigate the quality of our approximation and show that the errors are well within the acceptable range for application purposes. Lastly, we derive bounds on the remainder term generated by the Taylor expansion.

Statistical inference of the dependence between objects often relies on covariance matrices. Unless the number of features (e.g. data points) is much larger than the number of objects, covariance matrix cleaning is necessary to reduce estimation noise. We propose a method that is robust yet flexible enough to account for fine details of the structure covariance matrix. Robustness comes from using a hierarchical ansatz and dependence averaging between clusters; flexibility comes from a bootstrap procedure. This method finds several possible hierarchical structures in DNA microarray gene expression data, and leads to lower realized risk in global minimum variance portfolios than current filtering methods when the number of data points is relatively small.

We develop a simple theoretic game a model to analyze the relationship between electoral sys tems and governments' choice in trade policies. We show that existence of international pressure or foreign lobby changes a government's final decision on trade policy, and trade policy in countries with proportional electoral system is more protectionist than in countries with majoritarian electoral system. Moreover, lobbies pay more to affect the trade policy outcomes in countries with proportional representation systems.

This study estimates the risk contributions of individual European countries regarding the indemnity payments in agricultural insurance. We model the total risk exposure as an insurance portfolio where each country is unique in terms of its risk characteristics. The data has been collected from the recent surveys conducted by the European Commission and the World Bank. Farm Accountancy Data Network is used as well. 22 out of 26 member states are included in the study. The results suggest that the EuroMediterranean countries are the major risk contributors. These countries not only have the highest expected loss but also high volatility of indemnity payments. Nordic countries have the lowest indemnity payments and risk exposure.

The inf-convolution of risk measures is directly related to risk sharing and general equilibrium, and it has attracted considerable attention in mathematical finance and insurance problems. However, the theory is restricted to finite (or at most countable in rare cases) sets of risk measures. In this study, we extend the inf-convolution of risk measures in its convex-combination form to an arbitrary (not necessarily finite or even countable) set of alternatives. The intuitive principle of this approach is to regard a probability measure as a generalization of convex weights in the finite case. Subsequently, we extensively generalize known properties and results to this framework. Specifically, we investigate the preservation of properties, dual representations, optimal allocations, and self-convolution.

On 23rd June 2016, 51.9% of British voters voted to leave the European Union, triggering a process and events that have led to the United Kingdom leaving the EU, an event that has become known as 'Brexit'. In this piece of research, we investigate the effects of this entire process on the currency markets, specifically the GBP/EUR exchange rate. Financial markets are known to be sensitive to news articles and media, and the aim of this research is to evaluate the magnitude of impact of relevant events, as well as whether the impact was positive or negative for the GBP.

An increasing concern in power systems is how to elicit flexibilities in demand, which leads to nontraditional electricity products for accommodating loads of different flexibility levels. We have proposed Multiple-Arrival Multiple-Deadline (MAMD) differentiated energy services for the flexible loads which require constant power for specified durations. Such loads are indifferent to the actual power delivery time as long as the duration requirements are satisfied between the specified arrival times and deadlines. The focus of this paper is the market implementation of such services. In a forward market, we establish the existence of an efficient competitive equilibrium to verify the economic feasibility, which implies that selfish market participants can attain the maximum social welfare in a distributed manner. We also show the strengths of the MAMD services by simulation.

This study examines the monthly returns in Turkish and American stock market indices to investigate whether these markets experience abnormal returns during some months of the calendar year. The data used in this research includes 212 observations between January 1996 and August 2014. I apply statistical summary analysis, decomposition technique, dummy variable estimation, and binary logistic regression to check for the monthly market anomalies. The multidimensional methods used in this article suggest weak evidence against the efficient market hypothesis on monthly returns. While some months tend to show abnormal returns, there is no absolute unanimity in the applied approaches. Nevertheless, there is a strikingly negative May effect on the Turkish stocks following a positive return in April. Stocks tend to be bullish in December in both markets, yet we do not observe anya significant January effect is not observed.

When approximating the expectation of a functional of a certain stochastic process, the efficiency and performance of deterministic quadrature methods, and hierarchical variance reduction methods such as multilevel Monte Carlo (MLMC), is highly deteriorated in different ways by the low regularity of the integrand with respect to the input parameters. To overcome this issue, a smoothing procedure is needed to uncover the available regularity and improve the performance of the aforementioned methods. In this work, we consider cases where we cannot perform an analytic smoothing. Thus, we introduce a novel numerical smoothing technique based on root-finding combined with a one dimensional integration with respect to a single well-chosen variable. We prove that under appropriate conditions, the resulting function of the remaining variables is highly smooth, potentially allowing a higher efficiency of adaptive sparse grids quadrature (ASGQ), in particular when combined with hierarchical representations to treat the high dimensionality effectively. Our study is motivated by option pricing problems and our main focus is on dynamics where a discretization of the asset price is needed. Our analysis and numerical experiments illustrate the advantage of combining numerical smoothing with ASGQ compared to the Monte Carlo method. Furthermore, we demonstrate how numerical smoothing significantly reduces the kurtosis at the deep levels of MLMC, and also improves the strong convergence rate. Given a pre-selected tolerance, $\text{TOL}$, this results in an improvement of the complexity from $\mathcal{O}\left(\text{TOL}^{-2.5}\right)$ in the standard case to $\mathcal{O}\left(\text{TOL}^{-2} \log(\text{TOL})^2\right)$. Finally, we show how our numerical smoothing enables MLMC to estimate density functions, which standard MLMC (without smoothing) fails to achieve.

Skill verification is a central problem in workforce hiring. Companies and academia often face the difficulty of ascertaining the skills of an applicant since the certifications of the skills claimed by a candidate are generally not immediately verifiable and costly to test. Blockchains have been proposed in the literature for skill verification and tamper-proof information storage in a decentralized manner. However, most of these approaches deal with storing the certificates issued by traditional universities on the blockchain. Among the few techniques that consider the certification procedure itself, questions like (a) scalability with limited staff, (b) uniformity of grades over multiple evaluators, or (c) honest effort extraction from the evaluators are usually not addressed. We propose a blockchain-based platform named SkillCheck, which considers the questions above, and ensure several desirable properties. The platform incentivizes effort in grading via payments with tokens which it generates from the payments of the users of the platform, e.g., the recruiters and test-takers. We provide a detailed description of the design of the platform along with the provable properties of the algorithm.