This paper constructs a global economic policy uncertainty index through the principal component analysis of the economic policy uncertainty indices for twenty primary economies around the world. We find that the PCA-based global economic policy uncertainty index is a good proxy for the economic policy uncertainty on a global scale, which is quite consistent with the GDP-weighted global economic policy uncertainty index. The PCA-based economic policy uncertainty index is found to be positively related with the volatility and correlation of the global financial market, which indicates that the stocks are more volatile and correlated when the global economic policy uncertainty is higher. The PCA-based global economic policy uncertainty index performs slightly better because the relationship between the PCA-based uncertainty and market volatility and correlation is more significant.

We study the application of dynamic pricing to insurance. We view this as an online revenue management problem where the insurance company looks to set prices to optimize the long-run revenue from selling a new insurance product. We develop two pricing models: an adaptive Generalized Linear Model (GLM) and an adaptive Gaussian Process (GP) regression model. Both balance between exploration, where we choose prices in order to learn the distribution of demands & claims for the insurance product, and exploitation, where we myopically choose the best price from the information gathered so far. The performance of the pricing policies is measured in terms of regret: the expected revenue loss caused by not using the optimal price. As is commonplace in insurance, we model demand and claims by GLMs. In our adaptive GLM design, we use the maximum quasi-likelihood estimation (MQLE) to estimate the unknown parameters. We show that, if prices are chosen with suitably decreasing variability, the MQLE parameters eventually exist and converge to the correct values, which in turn implies that the sequence of chosen prices will also converge to the optimal price. In the adaptive GP regression model, we sample demand and claims from Gaussian Processes and then choose selling prices by the upper confidence bound rule. We also analyze these GLM and GP pricing algorithms with delayed claims. Although similar results exist in other domains, this is among the first works to consider dynamic pricing problems in the field of insurance. We also believe this is the first work to consider Gaussian Process regression in the context of insurance pricing. These initial findings suggest that online machine learning algorithms could be a fruitful area of future investigation and application in insurance.

We show that, for a class of mean-reverting models, the correlation function of stochastic variance (squared volatility) contains only one -- relaxation -- parameter. We generalize and simplify the expression for leverage for this class of models. We apply our results to specific examples of such models -- multiplicative, Heston, and combined multiplicative-Heston -- and use historic stock market data to obtain parameters of their steady-state distributions and cross-correlations between Weiner processes in the models for stock returns and stochastic variance.

We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous L\'{e}vy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. This includes the existence of Esscher martingale measures and martingale measures having minimal distance to the physical probability measure. Moreover, we provide pricing formulae for European call options and perform a case study.

In this work we will develop a new approach to solve the non repayment problem in microfinance due to the problem of asymmetric information. This approach is based on modeling and simulation of ordinary differential systems where time remains a primordial component, they thus enable microfinance institutions to manage their risk portfolios by a prediction of numbers of solvent and insolvent borrowers ever a period, in order to define or redefine its development strategy, investment and management in an area, where the population is often poor and in need a mechanism of financial inclusion.

When choosing the right copula for our data a key point is to distinguish the family that describes it at the best. In this respect, a better choice of the copulas could be obtained through the information about the (non)symmetry of the data. Exchangeability as a probability concept (first next to independence) has been studied since 1930's, copulas have been studied since 1950's, and even the most important class of copulas from the point of view of applications, i.e. the ones arising from shock models s.a. Marshall's copulas, have been studied since 1960's. However, the point of non-exchangeability of copulas was brought up only in 2006 and has been intensively studied ever since. One of the main contributions of this paper is the maximal asymmetry function for a family of copulas. We compute this function for the major families of shock-based copulas, i.e. Marshall, maxmin and reflected maxmin (RMM for short) copulas and also for some other important families. We compute the sharp bound of asymmetry measure $\mu_\infty$, the most important of the asymmetry measures, for the family of Marshall copulas and the family of maxmin copulas, which both equal to $\frac{4}{27}\ (\approx 0.148)$. One should compare this bound to the one for the class of PQD copulas to which they belong, which is $3-2\sqrt{2}\ \approx 0.172)$, and to the general bound for all copulas that is $\frac13$. Furthermore, we give the sharp bound of the same asymmetry measure for RMM copulas which is $3-2\sqrt{2}$, compared to the same bound for NQD copulas, where they belong, which is $\sqrt{5}-2\ (\approx 0.236)$. One of our main results is also the statistical interpretation of shocks in a given model at which the maximal asymmetry measure bound is attained. These interpretations for the three families studied are illustrated by examples that should be helpful to practitioners when choosing the model for their data.

Player-Compatible Equilibrium (PCE) imposes cross-player restrictions on the magnitudes of the players' "trembles" onto different strategies. These restrictions capture the idea that trembles correspond to deliberate experiments by agents who are unsure of the prevailing distribution of play. PCE selects intuitive equilibria in a number of examples where trembling-hand perfect equilibrium (Selten, 1975) and proper equilibrium (Myerson, 1978) have no bite. We show that rational learning and some near-optimal heuristics imply our compatibility restrictions in a steady-state setting.

We investigate the existence of affine realizations for L\'{e}vy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral approach concerning the existence of affine realizations are transferred to the general case. A similar result holds true for models driven by compound Poisson processes with finite jump size distributions. However, in the presence of jumps with infinite activity we obtain severe restrictions on the structure of the market price of risk; typically, it must even be constant.

Countless natural and social multivariate systems are studied through sets of simultaneous and time-spaced measurements of the observables that drive their dynamics, i.e., through sets of time series. Typically, this is done via hypothesis testing: the statistical properties of the empirical time series are tested against those expected under a suitable null hypothesis. This is a very challenging task in complex interacting systems, where statistical stability is often poor due to lack of stationarity and ergodicity. Here, we describe an unsupervised, data-driven framework to perform hypothesis testing in such situations. This consists of a statistical mechanical theory - derived from first principles - for ensembles of time series designed to preserve, on average, some of the statistical properties observed on an empirical set of time series. We showcase its possible applications on a set of stock market returns from the NYSE.

We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations and compute their $p$-variation indices. Exponential stock models driven by tempered stable processes are discussed as well.