Predicting the exit (e.g. bankrupt, acquisition, etc.) of privately held companies is a current and relevant problem for investment firms. The difficulty of the problem stems from the lack of reliable, quantitative and publicly available data. In this paper, we contribute to this endeavour by constructing an exit predictor model based on qualitative data, which blends the outcomes of three classifiers, namely, a Logistic Regression model, a Random Forest model, and a Support Vector Machine model. The output of the combined model is selected on the basis of the majority of the output classes of the component models. The models are trained using data extracted from the Thomson Reuters Eikon repository of 54697 US and European companies over the 1996-2011 time span. Experiments have been conducted for predicting whether the company eventually either gets acquired or goes public (IPO), against the complementary event that it remains private or goes bankrupt, in the considered time window. Our model achieves a 63\% predictive accuracy, which is quite a valuable figure for Private Equity investors, who typically expect very high returns from successful investments.

The global minimum-variance portfolio is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution remains a challenge. In the presence of high-dimensionality in the data, the sample estimator becomes ill-conditioned, which negates the positive effect of diversification in an out-of-sample setting. To address this issue, we review recent covariance matrix estimators and extend the literature by suggesting a multi-fold cross-validation technique. In detail, conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters within the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio. In particular, for cases in which the efficiency of a covariance estimator is strongly influenced by the choice of a tuning parameter, we detect a clear relationship between the optimality criterion for its selection within the cross-validation and the evaluated performance measure. Finally, we show that using cross-validation can improve the performance of highly efficient estimators even when the data-driven covariance parameter deviates from its theoretically optimal value.

Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried out in the mono-asset case. In this work, we show that some specific multivariate rough volatility models arise naturally from microstructural properties of the joint dynamics of asset prices. To do so, we use Hawkes processes to build microscopic models that reproduce accurately high frequency cross-asset interactions and investigate their long term scaling limits. We emphasize the relevance of our approach by providing insights on the role of microscopic features such as momentum and mean-reversion on the multidimensional price formation process. We in particular recover classical properties of high-dimensional stock correlation matrices.

We take a closer look at the life and legacy of Micheal Milken. We discuss why Michael Milken, also know as the Junk Bond King, was not just any other King or run-of-the-mill Junk Dealer, but "The Junk Dealer". We find parallels between the three parts to any magic act and what Micheal Milken did, showing that his accomplishments were nothing short of a miracle. His compensation at that time captures to a certain extent the magnitude of the changes he brought about, the eco-system he created for businesses to flourish, the impact he had on the wider economy and also on the future growth and development of American Industry. We emphasize two of his contributions to the financial industry that have grown in importance over the years. One was the impetus given to the Private Equity industry and the use of LBOs. The second was the realization that thorough research was the key to success, financial and otherwise. Perhaps an unintended consequence of the growth in junk bonds and tailored financing was the growth of Silicon valley and technology powerhouses in the California bay area. Investors witnessed that there was a possibility for significant returns and that financial success could be had due to the risk mitigation that Milken demonstrated by investing in portfolios of so called high risk and low profile companies. We point out the current trend in many regions of the world, which is the birth of financial and technology firms and we suggest that finding innovative ways of financing could be the key to the sustained growth of these eco-systems.

Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this work, we derive mean field game partial differential equation systems from deterministic microscopic agent dynamics. The dynamics are given by a particular class of ordinary differential equations, for which an optimal strategy can be computed (Bressan, Milan Journal of Mathematics, 2011). We use the concept of Nash equilibria and apply the dynamic programming principle to derive the mean field limit equations and we study the scaling behavior of the system as the number of agents tends to infinity and find several mean field game limits. Especially we avoid in our derivation the notion of measure derivatives. Novel scales are motivated by an example of an agent-based financial market model.

This study presents a method to identify treatment effects without exclusion restrictions for randomized experiments with non-compliance. It exploits a baseline survey that is commonly available in randomized control trials. I show the identification of the average treatment effect on the treated (ATT) and the local average treatment effect (LATE), assuming that a baseline variable maintains similar rank orders to the control outcome. I apply this strategy to a microcredit experiment with one-sided non-compliance to identify the ATT. I find that the instrumental variable (IV) estimate of log revenue is 2.2 times larger than my preferred estimate of log revenue.

Foreign power interference in domestic elections is an age-old, existential threat to societies. Manifested through myriad methods from war to words, such interference is a timely example of strategic interaction between economic and political agents. We model this interaction between rational game players as a continuous-time differential game, constructing an analytical model of this competition with a variety of payoff structures. Structures corresponding to all-or-nothing attitudes regarding the effect of the interference operations by only one player lead to an arms race in which both countries spend increasing amounts on interference and counter-interference operations. We then confront our model with data pertaining to the Russian interference in the 2016 United States presidential election contest, introducing and estimating a Bayesian structural time series model of election polls and social media posts by Russian internet trolls. We show that our analytical model, while purposefully abstract and simple, adequately captures many temporal characteristics of the election and social media activity.

This paper proves equivalences of portfolio optimization problems with negative expectile and omega ratio. We derive subgradients for the negative expectile as a function of the portfolio from a known dual representation of expectile and general theory about subgradients of risk measures. We also give an elementary derivation of the gradient of negative expectile under some assumptions and provide an example where negative expectile is demonstrably not differentiable. We conducted a case study and solved portfolio optimization problems with negative expectile objective and constraint.

Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave functions on the unit simplex measure the concentration of capital, and their gradient maps define novel investment strategies. The gradient maps may also be regarded as optimal transport maps on the simplex. In this paper we construct and study probability measures supported on spaces of concave functions. These measures may serve as prior distributions in Bayesian statistics and Cover's universal portfolio, and induce distribution-valued random variables via optimal transport. The random concave functions are constructed on the unit simplex by taking a suitably scaled (mollified, or soft) minimum of random hyperplanes. Depending on the regime of the parameters, we show that as the number of hyperplanes tends to infinity there are several possible limiting behaviors. In particular, there is a transition from a deterministic almost sure limit to a non-trivial limiting distribution that can be characterized using convex duality and Poisson point processes.

This note examines financial distributions to competing teams at the end of the most famous multiple stage professional (male) bicyclist race, TOUR DE FRANCE. A rank-size law (RSL) is calculated for the team financial gains. The RSL is found to be hyperbolic with a surprisingly simple decay exponent (about equal to -1). Yet, the financial gain distributions unexpectedly do not obey Pareto principle of factor sparsity. Next, several (8) inequality indices are considered : the Entropy, the Hirschman-Herfindahl, Theil, Pietra-Hoover, Gini, Rosenbluth indices, the Coefficient of Variation and the Concentration Index are calculated for outlining diversity measures. The connection between such indices and their concentration aspects meanings are presented as support of the RSL findings. The results emphasize that the sum of skills and team strategies are effectively contributing to the financial gains distributions. From theoretical and practical points of view, the findings suggest that one should investigate other "long multiple stage races" and rewarding rules. Indeed, money prize rules coupling to stage difficulty might influence and maybe enhance (or deteriorate) purely sportive aspects in group competitions. Due to the delay in the peer review process, the 2019 results can be examined. They are discussed in an Appendix; the value of the exponent (-1.2) is pointed out to mainly originating from the so called "king effect"; the tail of the RSL rather looks like an exponential.

We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic setting is time-inconsistency, that is, the usual "tower property" fails. By localizing the probability distortion and restricting to a smaller class of random variables, we introduce a so-called distorted probability and construct a conditional expectation in such a way that it coincides with the original nonlinear expectation at time zero, but has a time-consistent dynamics in the sense that the tower property remains valid. Furthermore, we show that in the continuous time model this conditional expectation corresponds to a parabolic differential equation whose coefficient involves the law of the underlying diffusion. This work is the first step towards a new understanding of nonlinear expectations under probability distortion, and will potentially be a helpful tool for solving time-inconsistent stochastic optimization problems.

We utilize the symmetric thermal optimal path (TOPS) method to examine the dynamic interaction patterns between the VIX and VIX futures markets. We document that the VIX dominates the VIX futures more in the first few years, especially before the introduction of VIX options. We further observe that the TOPS paths show an alternate lead-lag relationship instead of a dominance between the VIX and VIX futures in most of the time periods. Meanwhile, we find that the VIX futures have been increasingly more important in the price discovery since the launch of several VIX ETPs.