In this paper we study a two person zero sum stochastic differential game in weak formulation. Unlike standard literature which uses strategy type of controls, the weak formulation allows us to consider the game with control against control. We shall prove the existence of game value under natural conditions. Another main feature of the paper is that we allow for non-Markovian structure, and thus the game value is a random process. We characterize the value process as the unique viscosity solution of the corresponding path dependent Bellman-Isaacs equation, a notion recently introduced by Ekren, Keller, Touzi and Zhang [14] and Ekren, Touzi and Zhang [15,16,17].

In this paper we introduce a new type of norms for semimartingales, under both linear and nonlinear expectations. Our norm is defined in the spirit of quasimartingales, and it characterizes square integrable semimartingales. This work is motivated by our study of zero-sum stochastic differential games [21], whose value process is conjectured to be a semimartingale under a class of probability measures. As a by product, we establish some a priori estimates for doubly reflected BSDEs without imposing the Mokobodski's condition directly.

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Purpose: Perfectionism is considered a multidimensional construct with adaptive and maladaptive features. It was hypothesized that the diverse perfectionism components would predict well-being outcomes of similar valence. Method: The current study investigated perfectionism and mental, social, and physical health outcomes of graduate students in health science disciplines, across two semesters. We utilized two approaches in our empirical analysis. We first examined the continuous relationships between perfectionistic strivings, perfectionistic concerns, and health-related outcomes of graduate students. Additionally, we assessed differences between three perfectionism groups (i.e., adaptive, maladaptive, or non-perfectionist) on these well-being outcomes. Results: Results indicated that generally, adaptive perfectionism was related to better mental health, quality of life, and social functioning; maladaptive perfectionism was related to worse outcomes. The groups, however, did not statistically differ in general physical health. Conclusions: Overall, our results support a conceptualization of perfectionism that is differentially related to graduate student well-being. Thus, supportive networks may be fostered by differentiating between adaptive and maladaptive features of perfectionism. Moreover, we highlight the need for further discussion relative to determining perfectionism in high-achieving populations, in particular, graduate students in the health sciences.

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