Adachi and Ryu introduced a category Prob of probability spaces whose objects are all probability spaces and whose arrows correspond to measurable functions satisfying an absolutely continuous requirement in [Adachi and Ryu, 2019]. In this paper, we develop a binomial asset pricing model based on Prob. We introduce generalized filtrations with which we can represent situations such as some agents forget information at some specific time. We investigate the valuations of financial claims along this type of non-standard filtrations.

The automation technology is emerging, but the adoption rate of autonomous vehicles (AV) will largely depend upon how policymakers and the government address various challenges such as public acceptance and infrastructure development. This study proposes a five-step method to understand these barriers to AV adoption. First, based on a literature review followed by discussions with experts, ten barriers are identified. Second, the opinions of eighteen experts from industry and academia regarding inter-relations between these barriers are recorded. Third, a multicriteria decision making (MCDM) technique, the grey-based Decision-making Trial and Evaluation Laboratory (Grey-DEMATEL), is applied to characterize the structure of relationships between the barriers. Fourth, robustness of the results is tested using sensitivity analysis. Fifth, the key results are depicted in a causal loop diagram (CLD), a systems thinking approach, to comprehend cause-and-effect relationships between the barriers. The results indicate that the lack of customer acceptance (LCA) is the most prominent barrier, the one which should be addressed at the highest priority. The CLD suggests that LCA can be rather mitigated by addressing two other prominent, yet more tangible, barriers -- lack of industry standards and the absence of regulations and certifications. The study's overarching contribution thus lies in bringing to fore multiple barriers to AV adoption and their potential influences on each other. Moreover, the insights from this study can help associations related to AVs prioritize their endeavors to expedite AV adoption. From the methodological perspective, this is the first study in transportation literature that integrates Grey-DEMATEL with systems thinking.

We consider an environment where a finite number of players need to decide whether to buy a certain product (or adopt a trend) or not. The product is either good or bad, but its true value is not known to the players. Instead, each player has her own private information on the quality of the product. Each player can observe the previous actions of other players and estimate the quality of the product. A player can only buy the product once. In contrast to the existing literature on informational cascades, in this work players get more than one opportunity to act. In each turn, a player is chosen uniformly at random from all players and can decide to buy or not to buy. His utility is the total expected discounted reward, and thus myopic strategies may not constitute equilibria. We provide a characterization of structured perfect Bayesian equilibria (sPBE) with forward-looking strategies through a fixed-point equation of dimensionality that grows only quadratically with the number of players. In particular, a sufficient state for players' strategies at each time instance is a pair of two integers, the first corresponding to the estimated quality of the good and the second indicating the number of players that cannot offer additional information about the good to the rest of the players. We show existence of such equilibria and characterize equilibria with threshold strategies w.r.t. the two aforementioned integers. Based on this characterization we study informational cascades and show that they happen with high probability for a large number of players. Furthermore, only a small portion of the total information in the system is revealed before a cascade occurs.

We study the role of co-jumps in the interest rate futures markets. To disentangle continuous part of quadratic covariation from co-jumps, we localize the co-jumps precisely through wavelet coefficients and identify statistically significant ones. Using high frequency data about U.S. and European yield curves we quantify the effect of co-jumps on their correlation structure. Empirical findings reveal much stronger co-jumping behavior of the U.S. yield curves in comparison to the European one. Further, we connect co-jumping behavior to the monetary policy announcements, and study effect of 103 FOMC and 119 ECB announcements on the identified co-jumps during the period from January 2007 to December 2017.

Quality data is a fundamental contributor to success in statistics and machine learning. If a statistical assessment or machine learning leads to decisions that create value, data contributors may want a share of that value. This paper presents methods to assess the value of individual data samples, and of sets of samples, to apportion value among different data contributors. We use Shapley values for individual samples and Owen values for combined samples, and show that these values can be computed in polynomial time in spite of their definitions having numbers of terms that are exponential in the number of samples.

We approach the continuous-time mean-variance (MV) portfolio selection with reinforcement learning (RL). The problem is to achieve the best tradeoff between exploration and exploitation, and is formulated as an entropy-regularized, relaxed stochastic control problem. We prove that the optimal feedback policy for this problem must be Gaussian, with time-decaying variance. We then establish connections between the entropy-regularized MV and the classical MV, including the solvability equivalence and the convergence as exploration weighting parameter decays to zero. Finally, we prove a policy improvement theorem, based on which we devise an implementable RL algorithm. We find that our algorithm outperforms both an adaptive control based method and a deep neural networks based algorithm by a large margin in our simulations.

Various valuation adjustments, or XVAs, can be written in terms of non-linear PIDEs equivalent to FBSDEs. In this paper we develop a Fourier-based method for solving FBSDEs in order to efficiently and accurately price Bermudan derivatives, including options and swaptions, with XVA under the flexible dynamics of a local L\'evy model: this framework includes a local volatility function and a local jump measure. Due to the unavailability of the characteristic function for such processes, we use an asymptotic approximation based on the adjoint formulation of the problem.

This paper considers an often forgotten relationship, the time delay between a cause and its effect in economies and finance. We treat the case of Foreign Direct Investment (FDI) and economic growth, - measured through a country Gross Domestic Product (GDP). The pertinent data refers to 43 countries, over 1970-2015, - for a total of 4278 observations. When countries are grouped

according to the Inequality-Adjusted Human Development Index (IHDI), it is found that a time lag dependence effect exists in FDI-GDP correlations.

This is established through a time-dependent Pearson 's product-moment correlation coefficient matrix.

Moreover, such a Pearson correlation coefficient is observed to evolve from positive

to negative values depending on the IHDI, from low to high. It is "politically and policy

"relevant" that

the correlation is statistically significant providing the time lag is less than 3 years. A "rank-size" law is demonstrated.

It is recommended to reconsider such a time lag effect when discussing previous analyses whence conclusions on international business, and thereafter on forecasting.

We extend Donsker's approximation of Brownian motion to fractional Brownian motion with Hurst exponent $H \in (0,1)$ and to Volterra-like processes. Some of the most relevant consequences of our `rough Donsker (rDonsker) Theorem' are convergence results for discrete approximations of a large class of rough models. This justifies the validity of simple and easy-to-implement Monte-Carlo methods, for which we provide detailed numerical recipes. We test these against the current benchmark Hybrid scheme \cite{BLP15} and find remarkable agreement (for a large range of values of~$H$). This rDonsker Theorem further provides a weak convergence proof for the Hybrid scheme itself, and allows to construct binomial trees for rough volatility models, the first available scheme (in the rough volatility context) for early exercise options such as American or Bermudan.

We show that the lack of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures together with an adapted process between the bid-ask spreads that satisfies the martingale property with respect to each of the measures. This extends Harrison and Pliska's classical Fundamental Theorem of Asset Pricing to the case of combined fixed and proportional transaction costs.

In this paper, we study Gaussian stochastic volatility models. The evolution of volatility in such a model is described by a stochastic process, which can be represented as a nonnegative continuous function of a continuous Gaussian process. If the volatility process exhibits fractional features, then the model is called a Gaussian fractional stochastic volatility model. Important examples of fractional volatility processes are fractional Brownian motion, the Riemann-Liouville fractional Brownian motion, and the fractional Ornstein-Uhlenbeck process. If the volatility process admits a Volterra type representation, then the model is of Volterra type. In the paper, we provide a unified approach to various scaling regimes associated with Gaussian models. More precisely, large deviation, moderate deviation, and central limit scalings are introduced in the paper. We prove a sample path large deviation principle for the log-price process in a Volterra type Gaussian stochastic volatility model and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility model. We also study the asymptotic behavior of call pricing functions and the implied volatility in mixed scaling regimes. It is also shown that tail estimates arising in the large deviation theory are locally uniform. Another problem addressed in the paper concerns moment explosions for the asset price process in a Gaussian stochastic volatility model. We prove that for the asset price process in an uncorrelated Gaussian stochastic volatility model with the volatility function growing faster than linearly, all the moments of order greater than one are infinite. Explosions of all the moments of order $\gamma>(1-\rho^2)^{-1}$, where $\rho$ is the correlation coefficient, are shown for correlated models, and partial results are obtained for the case where $\gamma=(1-\rho^2)^{-1}$.

The fast pace of artificial intelligence (AI) and automation is propelling strategists to reshape their business models. This is fostering the integration of AI in the business processes but the consequences of this adoption are underexplored and need attention. This paper focuses on the overall impact of AI on businesses - from research, innovation, market deployment to future shifts in business models. To access this overall impact, we design a three-dimensional research model, based upon the Neo-Schumpeterian economics and its three forces viz. innovation, knowledge, and entrepreneurship. The first dimension deals with research and innovation in AI. In the second dimension, we explore the influence of AI on the global market and the strategic objectives of the businesses and finally, the third dimension examines how AI is shaping business contexts. Additionally, the paper explores AI implications on actors and its dark sides.

We make use of a family of primitive securities, in the spirit of Arrow-Debreu, to price and hedge in a model-free way path-dependent exotic derivatives in discrete time. These primitive securities are called signature payoffs. First, we show that cash flows of exotic derivatives in discrete time can be approximated arbitrarily well by these primitive securities, and we then conclude that signature payoffs can be used to price path-dependent exotic derivatives. Second, signature payoffs are used to derive a numerically feasible methodology to dynamically hedging exotic derivatives. It turns out that the only information one needs about the market to dynamically hedge exotic derivatives is the prices of these signature payoffs. These two aspects lead to a model-free approach to numerically price and hedge exotic derivatives from market data - more specifically, from market prices of other exotic derivatives. We demonstrate the feasibility of our approach in several numerical experiments.

This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is formulated as a continuous time stochastic optimal control problem aiming at maximizing a generalized risk-adjusted profit and loss function. The expression of the risk adjustment is derived from the general theory of dynamic risk measures and is selected in the class of $g$-conditional risk measures. The resulting theoretical framework is nonclassical since the target function depends on backward components. We show that, under a quadratic specification of the driver of a backward stochastic differential equation, it is possible to find a closed form solution and an explicit expression of the optimal liquidation policies. In this way it is immediate to quantify the impact of risk-adjustment on the profit and loss and on the expression of the optimal liquidation policies.