In this paper, the pricing of equity warrants under a class of fractional Brownian motion models is investigated numerically. By establishing a new nonlinear partial differential equation (PDE) system governing the price in terms of the observable stock price, we solve the pricing system effectively by a robust implicit-explicit numerical method. This is fundamentally different from the documented methods, which first solve the price with respect to the firm value analytically, by assuming that the volatility of the firm is constant, and then compute the price with respect to the stock price and estimate the firm volatility numerically. It is shown that the proposed method is stable in the maximum-norm sense. Furthermore, a sharp theoretical error estimate for the current method is provided, which is also verified numerically. Numerical examples suggest that the current method is efficient and can produce results that are, overall, closer to real market prices than other existing approaches. A great advantage of the current method is that it can be extended easily to price equity warrants under other complicated models.

The concept of socioemotional wealth (SEW) has become a dominant perspective in family business studies. In this article, we review the SEW literature, the explanatory power of SEW in family firm behavior, and the heterogeneity of family firms. Although we find that SEW distinguishes the behavior of family firms from that of nonfamily firms, the concept has been used and operationalized differently across studies. The few studies that measure SEW directly do not find clear and consistent explanatory power of the construct. Moreover, not many studies are conducted in Asian countries such as Japan, Korea, and China, raising the question as to whether the concept applies equally across institutional and cultural contexts. This article takes a pragmatic perspective on SEW by discussing and distinguishing between key dimensions of social wealth and emotional wealth, which we believe can enhance understanding of the behavior and heterogeneity of family businesses. Based on our deconstruction of the SEW concept, we propose various directions of future research.

This study aimed to evaluate the performance of Cobas human papillomavirus (HPV) test in cervical cancer screening. A total of 3442 women aged ⩾20 years used Cobas HPV and hybrid capture 2 (HC2) tests were included in this study. Women with any positive result were examined by liquid-based cytology (LBC) test. Then subjects with abnormal LBC or positive Cobas HPV16/18 were further checked by colposcopy to observe the visible lesions to perform the pathological examination. Of these 3442 women, 328 cases were Cobas HPV positive, and the positive rate was 9.53% (95% confidence interval (CI) 8.50–10.53). The positive rate of HPV16, HPV18, and other 12 types of high-risk HPV were 1.54% (95% CI 1.12–1.95), 0.55% (95% CI 0.30–0.80), and 7.44% (95% CI 6.56–8.32), respectively. The coincidence rate of Cobas HPV test and HC2 test was 90% (95% CI 89.00–91.00; Kappa = 0.526) in the primary screening. Age had a non-linear relationship with Cobas HPV positive rate (χ2 = 4.240, P = 0.040) and HPV16/18 typing positive rate (χ2 = 6.610, P = 0.010). Compared with the LBC test, the Cobas HPV test had higher sensitivity when detecting patients with high cervical intraepithelial neoplasia (CIN2+ and CIN3+).

We consider the pricing of European options under a modified Black–Scholes equation having fractional derivatives in the “spatial” (price) variable. To be specific, the underlying price is assumed to follow a geometric Koponen–Boyarchenko–Levendorski process. This pure jump Lévy process could better capture the real behaviour of market data. Despite many difficulties caused by the “globalness” of the fractional derivatives, we derive an explicit closed-form analytical solution by solving the fractional partial differential equation analytically, using the Fourier transform technique. Based on the newly derived formula, we also examine, in theory, many basic properties of the option price under the current model. On the other hand, for practical purposes, we impose a reliable implementation method for the current formula so that it can be easily used in the trading market. With the numerical results, the impact of different parameters on the option price are also investigated.

Totems are symbols or representations of human's affiliations with, and/or categorizations of, animals, plants and inanimate objects. Totemism is related to fundamental human belief systems based on totems. Investigating totems and totemism psychologically is a unique way to explore human minds. We have critically examined Wundt, Freud and many other scholars and scientists who made distinguished contributions to scientific research on totems and totemism almost in the past two centuries –i.e., totemic psychology, which is the study of our mind's categorization and affiliation in the human and natural world today. Understanding and appreciating their totemic psychology can help psychologists today enhance their understanding in other fields—e.g., ecological and environmental psychology, biological psychology, cognitive psychology, personality, social and ethnic psychology, clinical and counseling psychology, cultural psychology, and religious or spiritual psychology. Unfortunately, recent data from a content analysis via PsycInfo and a cross-cultural survey study (N=273) showed that well-trained psychologists around the world and psychology students in the United States and in China are unfamiliar with Wundt and Freud's totemic contributions to psychology today. The implications, benefits, and lessons of totems and today's totemic psychology are discussed here.

In this paper, we propose an integral equation approach for pricing an American-style Parisian up-and-out call option under the Black–Scholes framework. The main difficulty of pricing this option lies in the determination of its optimal exercise price, which is a three-dimensional surface, instead of a two-dimensional (2-D) curve as is the case for a “one-touch” barrier option. In our approach, we first reduce the 3-D pricing problem to a 2-D one by using the “moving window” technique developed by Zhu and Chen (2013, Pricing Parisian and Parasian options analytically. Journal of Economic Dynamics and Control, 37(4): 875-896), then apply the Fourier sine transform to the 2-D problem to obtain two coupled integral equations in terms of two unknown quantities: the option price at the asset barrier and the optimal exercise price. Once the integral equations are solved numerically by using an iterative procedure, the calculation of the option price and the hedging parameters is straightforward from their integral representations. Our approach is validated by a comparison between our results and those of the trusted finite difference method. Numerical results are also provided to show some interesting features of the prices of American-style Parisian up-and-out call options and the behaviour of the associated optimal exercise boundaries.

It is proved that every abelian VNL-ring is an SVNL-ring, which gives a positive answer to a question of Osba et al. [7]. Some characterizations of duo VNL-rings are given and some main results of Osba et al. [7] on commutative VNL-rings are extended to right duo VNL-rings and even abelian GVNL-rings.