This paper introduces a theory of equivalent expectation measures, such as the R measure and the RT1 measure, generalizing the martingale pricing theory of Harrison and Kreps (1979) for deriving analytical solutions of expected prices - both the expected current price and the expected future price - of contingent claims. We also present new R-transforms which extend the Q-transforms of Bakshi and Madan (2000) and Duffie et al. (2000), for computing the expected prices of a variety of standard and exotic claims under a broad range of stochastic processes. Finally, as a generalization of Breeden and Litzenberger (1978), we propose a new concept of the expected future state price density which allows the estimation of the expected future prices of complex European contingent claims as well as the physical density of the underlying asset's future price, using the current prices and only the first return moment of standard European OTM call and put options.

We show how increasing returns to scale in urban scaling can artificially emerge, systematically and predictably, without any sorting or positive externalities. We employ a model where individual productivities are independent and identically distributed lognormal random variables across all cities. We use extreme value theory to demonstrate analytically the paradoxical emergence of increasing returns to scale when the variance of log-productivity is larger than twice the log-size of the population size of the smallest city in a cross-sectional regression. Our contributions are to derive an analytical prediction for the artificial scaling exponent arising from this mechanism and to develop a simple statistical test to try to tell whether a given estimate is real or an artifact. Our analytical results are validated analyzing simulations and real microdata of wages across municipalities in Colombia. We show how an artificial scaling exponent emerges in the Colombian data when the sizes of random samples of workers per municipality are $1\%$ or less of their total size.

It is generally understood that a given one-dimensional diffusion may be transformed by Cameron-Martin-Girsanov measure change into another one-dimensional diffusion with the same volatility but a different drift. But to achieve this we have to know that the change-of-measure local martingale that we write down is a true martingale; we provide a complete characterization of when this happens. This is then used to discuss absence of arbitrage in a generalized Heston model including the case where the Feller condition for the volatility process is violated.

In this paper we present a duality theory for the robust utility maximization problem in continuous time for utility functions defined on the positive real axis. Our results are inspired by -- and can be seen as the robust analogues of -- the seminal work of Kramkov & Schachermayer [21]. Namely, we show that if the set of attainable trading outcomes and the set of pricing measures satisfy a bipolar relation, then the utility maximization problem is in duality with a conjugate problem. We further discuss the existence of optimal trading strategies. In particular, our general results include the case of logarithmic and power utility, and they apply to drift and volatility uncertainty.

We study an $N$-player and a mean field exponential utility game. Each player manages two stocks; one is driven by an individual shock and the other is driven by a common shock. Moreover, each player is concerned not only with her own terminal wealth but also with the relative performance of her competitors. We use the probabilistic approach to study these two games. We show the unique equilibrium of the $N$-player game and the mean field game can be characterized by a novel multi-dimensional FBSDE with quadratic growth and a novel mean-field FBSDEs, respectively. The well-posedness result and the convergence result are established.

We construct models for the pricing and risk management of inflation-linked derivatives. The models are rational in the sense that linear payoffs written on the consumer price index have prices that are rational functions of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that allows for closed-form pricing of vanilla inflation products suchlike zero-coupon swaps, year-on-year swaps, caps and floors, and the exotic limited-price-index swap. We study the conditions necessary for the multiplicative nominal pricing kernel to give rise to short rate models for the nominal interest rate process. The proposed class of pricing kernel models retains the attractive features of a nominal multi-curve interest rate model, such as closed-form pricing of nominal swaptions, and it isolates the so-called inflation convexity-adjustment term arising from the covariance between the underlying stochastic drivers. We conclude with examples of how the model can be calibrated to EUR data.

An important theme is how to maximize the cooperation of employees when dealing with crisis measures taken by the company. Therefore, to find out what kind of employees have cooperated with the company's measures in the current corona (COVID-19) crisis, and what effect the cooperation has had to these employees/companies to get hints for preparing for the next crisis, the pass analysis was carried out using awareness data obtained from a questionnaire survey conducted on 2,799 employees of Japanese companies in China. The results showed that employees with higher social capital and resilience were more supportive of the company's measures against corona and that employees who were more supportive of corona measures were less likely to leave their jobs. However, regarding fatigue and anxiety about the corona felt by employees, it was shown that it not only works to support cooperation in corona countermeasures but also enhances the turnover intention. This means that just by raising the anxiety of employees, even if a company achieves the short-term goal of having them cooperate with the company's countermeasures against corona, it may not reach the longer-term goal by making them increase their intention to leave. It is important for employees to be aware of the crisis and to fear it properly. But more than that, it should be possible for the company to help employees stay resilient, build good relationships with them, and increase their social capital to make them support crisis measurement of the company most effectively while keeping their turnover intention low.

It is hard to overstate the importance that the concept of symmetry has had in every field of physics, a fact alluded to by the Nobel Prize winner P.W. Anderson, who once wrote that physics is the study of symmetry. Whereas the idea of symmetry is widely used in science in general, very few (if not almost no) applications has found its way into the field of finance. Still, the phenomenon appears relevant in terms of for example the symmetry of strategies that can happen in the decision making to buy or sell financial shares. Game theory is therefore one obvious avenue where to look for symmetry, but as will be shown, also technical analysis and long term economic growth could be phenomena which show the hallmark of a symmetry

In the present work we develop a formalism to tackle the problem of optimal execution when trading market securities. More precisely, we introduce a utility function that balances market impact and timing risk, with this last being modelled as the very negative transaction costs incurred by our order execution. The framework is built upon existing theory on optimal trading strategies, but incorporates characteristics that enable distinctive execution strategies. The formalism is complemented by an analysis of various impact models and different distributional properties of market returns.

Given the success and almost universal acceptance of the simple linear regression three-factor model, it is interesting to analyze the informational content of the three factors in explaining stock returns when the analysis is allowed to consider non-linear dependencies between factors and stock returns. In order to better understand factor-based conditioning information with respect to expected stock returns within a regression tree setting, the analysis of stock returns is demonstrated using daily stock return data for 5 major US corporations. The first finding is that in all cases (solo and joint) the most informative factor is always the market excess return factor. Further, three major issues are discussed: a) the balance of a depth=1 tree as it relates to properties of the stock return distribution, b) the mechanism behind depth=1 tree balance in a joint regression tree and c) the dominant stock in a joint regression tree. It is shown that high skew values alone cannot explain the imbalance of the resulting tree split as stocks with pronounced skew may produce balanced tree splits.