We study the Fundamental Theorem of Asset Pricing for a general financial market under Knightian Uncertainty. We adopt a functional analytic approach which require neither specific assumptions on the class of priors $\mathcal{P}$ nor on the structure of the state space. Several aspects of modeling under Knightian Uncertainty are considered and analyzed. We show the need for a suitable adaptation of the notion of No Free Lunch with Vanishing Risk and discuss its relation to the choice of an appropriate filtration. In an abstract setup, we show that absence of arbitrage is equivalent to the existence of \emph{approximate} martingale measures sharing the same polar set of $\mathcal{P}$. We then specialize the results to a discrete-time framework in order to obtain true martingale measures.

We define a notion of isomorphism for financial markets in both discrete and continuous time. We classify complete one-period markets. We define an invariant of continuous time complete markets which we call the absolute market price of risk. This invariant plays a role analogous to the curvature in Riemannian geometry. We classify markets when this invariant takes a simple form. We show that in general markets with non-trivial automorphism groups admit mutual fund theorems and prove a number of such theorems.

Several systematic studies have suggested that a large fraction of published research is not reproducible. One probable reason for low reproducibility is insufficient sample size, resulting in low power and low positive predictive value. It has been suggested that insufficient sample-size choice is driven by a combination of scientific competition and 'positive publication bias'. Here we formalize this intuition in a simple model, in which scientists choose economically rational sample sizes, balancing the cost of experimentation with income from publication. Specifically, assuming that a scientist's income derives only from 'positive' findings (positive publication bias) and that individual samples cost a fixed amount, allows to leverage basic statistical formulas into an economic optimality prediction. We find that if effects have i) low base probability, ii) small effect size or iii) low grant income per publication, then the rational (economically optimal) sample size is small. Furthermore, for plausible distributions of these parameters we find a robust emergence of a bimodal distribution of obtained statistical power and low overall reproducibility rates, matching empirical findings. Overall, the model describes a simple mechanism explaining both the prevalence and the persistence of small sample sizes. It suggests economic rationality, or economic pressures, as a principal driver of irreproducibility.

Recent studies have shown that online portfolio selection strategies that exploit the mean reversion property can achieve excess return from equity markets. This paper empirically investigates the performance of state-of-the-art mean reversion strategies on real market data. The aims of the study are twofold. The first is to find out why the mean reversion strategies perform extremely well on well-known benchmark datasets, and the second is to test whether or not the mean reversion strategies work well on recent market data. The mean reversion strategies used in this study are the passive aggressive mean reversion (PAMR) strategy, the on-line moving average reversion (OLMAR) strategy, and the transaction cost optimization (TCO) strategies. To test the strategies, we use the historical prices of the stocks that constitute S\&P 500 index over the period from 2000 to 2017 as well as well-known benchmark datasets. Our findings are that the well-known benchmark datasets favor mean reversion strategies, and mean reversion strategies may fail even in favorable market conditions, especially when there exist explicit or implicit transaction costs.

Many factors such as economy size, capital resources, and size of national publication market seem to be related to the scientific performance of nations. In this paper we link the national culture values with scientific performance of 53 nations. We focus on the year 2010. Our study uses three datasets: 1) Hofstede's data on national culture, 2) data on migration share of societies, and 3) citation impact data. We found that four dimensions of culture (i.e. individualism, power distance, uncertainty avoidance, and indulgence) correlate practically and statistically significantly with scientific impact of nations. The findings are discussed in mirror of cultural theories.

We consider the optimal portfolio problem where the interest rate is stochastic and the agent has insider information on its value at a finite terminal time. The agent's objective is to optimize the terminal value of her portfolio under a logarithmic utility function. Using techniques of initial enlargement of filtration, we identify the optimal strategy and compute the value of the information. The interest rate is first assumed to be an affine diffusion, then more explicit formulas are computed for the Vasicek interest rate model where the interest rate moves according to an Ornstein-Uhlenbeck process. Incidentally we show that an affine process conditioned to its future value is still an affine process. When the interest rate process is correlated with the price process of the risky asset, the value of the information is proved to be infinite, as is usually the case for initial-enlargement-type problems. However, weakening the information own by the agent and assuming that she only knows a lower-bound or both, a lower and an upper bound, for the terminal value of the interest rate process, we show that the value of the information is finite. This solves by an analytical proof a conjecture stated in Pikovsky and Karatzas (1996).

We study dynamic optimal portfolio allocation for monotone mean--variance preferences in a general semimartingale model. Armed with new results in this area we revisit the work of Cui, Li, Wang and Zhu (2012, MAFI) and fully characterize the circumstances under which one can set aside a non-negative cash flow while simultaneously improving the mean--variance efficiency of the left-over wealth. The paper analyzes, for the first time, the monotone hull of the Sharpe ratio and highlights its relevance to the problem at hand.

We examine the impact of a new tool for suppressing the expression of dissent---a daily tax on social media use. Using a synthetic control framework, we estimate that the tax reduced the number of georeferenced Twitter users in Uganda by 13 percent. The estimated treatment effects are larger for poorer and less frequent users. Despite the overall decline in Twitter use, tweets referencing collective action increased by 31 percent and observed protests increased by 47 percent. These results suggest that taxing social media use may not be an effective tool for reducing political dissent.

Reinsurance counterparty credit risk (RCCR) is the risk of a loss arising from the fact that a reinsurance company is unable to fulfill her contractual obligations towards the ceding insurer. RCCR is an important risk category for insurance companies which, so far, has been addressed mostly via qualitative approaches. In this paper we therefore study value adjustments and dynamic hedging for RCCR. We propose a novel model that accounts for contagion effects between the default of the reinsurer and the price of the reinsurance contract. We characterize the value adjustment in a reinsurance contract via a partial integro-differential equation (PIDE) and derive the hedging strategies using a quadratic method. The paper closes with a simulation study which shows that dynamic hedging strategies have the potential to significantly reduce RCCR.