In this paper we study the problem of nonlinear pricing of an American option with a right-continuous left-limited (RCLL) payoff process in an incomplete market with default, from the buyer's point of view. We show that the buyer's price process can be represented as the value of a stochastic control/optimal stopping game problem with nonlinear expectations, which corresponds to the maximal subsolution of a constrained reflected Backward Stochastic Differential Equation (BSDE). We then deduce a nonlinear optional decomposition of the buyer's price process. To the best of our knowledge, no dynamic dual representation (resp. no optional decomposition) of the buyer's price process can be found in the literature, even in the case of a linear incomplete market and brownian filtration. Finally, we prove the "infimum" and the "supremum" in the definition of the stochastic game problem can be interchanged. Our method relies on new tools, as simultaneous nonlinear Doob-Meyer decompositions of processes which have a $\mathscr{Y}^\nu$-submartingale property for each admissible control $\nu$.

We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The method is based on a quadrature technique, and it employs only elementary calculations and a fixed one-dimensional uniform grid. The convergence rate is $O(1/N^4)$ and the complexity is $O(MN\log N)$, where $N$ is the number of grid points and $M$ is the number of observation dates.

While the disruptive potential of artificial intelligence (AI) and Big Data has been receiving growing attention and concern in a variety of research and application fields over the last few years, it has not received much scrutiny in contemporary entrepreneurship research so far. Here we present some reflections and a collection of papers on the role of AI and Big Data for this emerging area in the study and application of entrepreneurship research. While being mindful of the potentially overwhelming nature of the rapid progress in machine intelligence and other Big Data technologies for contemporary structures in entrepreneurship research, we put an emphasis on the reciprocity of the co-evolving fields of entrepreneurship research and practice. How can AI and Big Data contribute to a productive transformation of the research field and the real-world phenomena (e.g., 'smart entrepreneurship')? We also discuss, however, ethical issues as well as challenges around a potential contradiction between entrepreneurial uncertainty and rule-driven AI rationality. The editorial gives researchers and practitioners orientation and showcases avenues and examples for concrete research in this field. At the same time, however, it is not unlikely that we will encounter unforeseeable and currently inexplicable developments in the field soon. We call on entrepreneurship scholars, educators, and practitioners to proactively prepare for future scenarios.

We apply the procedure of Lee et al. to the problem of performing inference on the signal noise ratio of the asset which displays maximum sample Sharpe ratio over a set of possibly correlated assets. We find a multivariate analogue of the commonly used approximate standard error of the Sharpe ratio to use in this conditional estimation procedure. Testing indicates this procedure achieves the nominal type I rate, and does not appear to suffer from non-normality of returns. The conditional estimation test has low power under the alternative where there is little spread in the signal noise ratios of the assets, and high power under the alternative where a single asset has high signal noise ratio.

This paper contributes a new machine learning solution for stock movement prediction, which aims to predict whether the price of a stock will be up or down in the near future. The key novelty is that we propose to employ adversarial training to improve the generalization of a neural network prediction model. The rationality of adversarial training here is that the input features to stock prediction are typically based on stock price, which is essentially a stochastic variable and continuously changed with time by nature. As such, normal training with static price-based features (e.g. the close price) can easily overfit the data, being insufficient to obtain reliable models. To address this problem, we propose to add perturbations to simulate the stochasticity of price variable, and train the model to work well under small yet intentional perturbations. Extensive experiments on two real-world stock data show that our method outperforms the state-of-the-art solution with 3.11% relative improvements on average w.r.t. accuracy, validating the usefulness of adversarial training for stock prediction task.

We apply the recently developed reduced Google matrix algorithm for the analysis of the OECD-WTO world network of economic activities. This approach allows to determine interdependences and interactions of economy sectors of several countries, including China, Russia and USA, properly taking into account the influence of all other world countries and their economic activities. Within this analysis we also obtain the sensitivity of economy sectors and EU countries to petroleum activity sector. We show that this approach takes into account multiplicity of network links with economy interactions between countries and activity sectors thus providing more rich information compared to the usual export-import analysis.

A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance theory and other known portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality and ultimately relies on the minimization of ratios of convex functions. The latter arises naturally due to our requirements that diversification measures should be leverage invariant and related to the tail properties of the distribution of portfolio returns. This paper introduces this new framework and its relationship to standardized higher order moments of portfolio returns. Moreover, it addresses the main drawbacks of standard diversification methodologies which are based primarily on estimates of covariance matrices. Maximizing portfolio dimensionality leads to highly non-trivial optimization problems with objective functions which are typically non-convex with potentially multiple local optima. Two complementary global optimization algorithms are thus presented. For problems of moderate size, a deterministic Branch and Bound algorithm is developed, whereas for problems of larger size a stochastic global optimization algorithm based on Gradient Langevin Dynamics is given. We demonstrate through numerical experiments that the introduced diversification measures possess desired properties as introduced in the portfolio diversification literature.

We propose how to quantify high-frequency market sentiment using high-frequency news from NASDAQ news platform and support vector machine classifiers. News arrive at markets randomly and the resulting news sentiment behaves like a stochastic process. To characterize the joint evolution of sentiment, price, and volatility, we introduce a unified continuous-time sentiment-driven stochastic volatility model. We provide closed-form formulas for moments of the volatility and news sentiment processes and study the news impact. Further, we implement a simulation-based method to calibrate the parameters. Empirically, we document that news sentiment raises the threshold of volatility reversion, sustaining high market volatility.

In this paper, we propose a novel investment strategy for portfolio optimization problems. The proposed strategy maximizes the expected portfolio value bounded within a targeted range, composed of a conservative lower target representing a need for capital protection and a desired upper target representing an investment goal. This strategy favorably shapes the entire probability distribution of returns, as it simultaneously seeks a desired expected return, cuts off downside risk and implicitly caps volatility and higher moments. To illustrate the effectiveness of this investment strategy, we study a multiperiod portfolio optimization problem with transaction costs and develop a two-stage regression approach that improves the classical least squares Monte Carlo (LSMC) algorithm when dealing with difficult payoffs, such as highly concave, abruptly changing or discontinuous functions. Our numerical results show substantial improvements over the classical LSMC algorithm for both the constant relative risk-aversion (CRRA) utility approach and the proposed skewed target range strategy (STRS). Our numerical results illustrate the ability of the STRS to contain the portfolio value within the targeted range. When compared with the CRRA utility approach, the STRS achieves a similar mean-variance efficient frontier while delivering a better downside risk-return trade-off.

The continuous observation of the financial markets has identified some stylized facts which challenge the conventional assumptions, promoting the born of new approaches. On the one hand, the long-range dependence has been faced replacing the traditional Gauss-Wiener process (Brownian motion), characterized by stationary independent increments, by a fractional version. On the other hand, the CEV model addresses the Leverage effect and smile-skew phenomena, efficiently. In this paper, these two insights are merging and both the fractional and mixed-fractional extensions for the CEV model, are developed. Using the fractional versions of both the Ito's calculus and the Fokker-Planck equation, the transition probability density function of the asset price is obtained as the solution of a non-stationary Feller process with time-varying coefficients, getting an analytical valuation formula for a European Call option. Besides, the Greeks are computed and compared with the standard case.

A methodology is presented to rank universities on the basis of the lists of programmes the students applied for. We exploit a crucial feature of the centralised assignment system to higher education in Hungary: a student is admitted to the first programme where the score limit is achieved. This makes it possible to derive a partial preference order of each applicant. Our approach integrates the information from all students participating in the system, is free of multicollinearity among the indicators, and contains few ad hoc parameters. The procedure is implemented to rank faculties in the Hungarian higher education between 2001 and 2016. We demonstrate that the ranking given by the least squares method has favourable theoretical properties, is robust with respect to the aggregation of preferences, and performs well in practice. The suggested ranking is worth considering as a reasonable alternative to the standard composite indices.