Stable Dividends under Linear-Quadratic Optimization

The optimization criterion for dividends from a risky business is most often formalized in terms of the expected present value of future dividends. That criterion disregards a potential, explicit demand for stability of dividends. In particular, within actuarial risk theory, maximization of future dividends have been intensively studied as the so-called de Finetti problem. However, there the optimal strategies typically become so-called barrier strategies. These are far from stable and suboptimal affine dividend strategies have therefore received attention recently. In contrast, in the class of linear-quadratic problems a demand for stability if explicitly stressed. These have most often been studied in diffusion models different from the actuarial risk models. We bridge the gap between these patterns of thinking by deriving optimal affine dividend strategies under a linear-quadratic criterion for a general L\'evy process. We characterize the value function by the Hamilton-Jacobi-Bellman equation, solve it, and compare the objective and the optimal controls to the classical objective of maximizing expected present value of future dividends. Thereby we provide a framework within which stability of dividends from a risky business, as e.g. in classical risk theory, is explicitly demanded and explicitly obtained

Determination of Heat and Mass Transport Correlations for Hollow Membrane Distillation Modules

Development and optimization of the membrane distillation (MD) process are strongly associated with better understanding of heat and mass transport across the membrane. The current state-of-the-art on heat and mass transport in MD greatly relies upon the use of various empirical correlations for the Nusselt number (Nu), tortuosity factor (τ), and thermal conductivity (κm) of the membrane. However, the current literature lacks investigations about finding the most representative combination of these three parameters for modeling transport phenomena in MD. In this study, we investigated 189 combinations of Nu, κm, and τ to assess their capability to predict the experimental flux and outlet temperatures of feed and permeate streams for hollow fiber MD modules. It was concluded that 31 out of 189 tested combinations could predict the experimental flux with reasonable accuracy (R2 > 0.95). Most of the combinations capable of predicting the flux reasonably well could predict the feed outlet temperature well; however, the capability of the tested combinations to predict the permeate outlet temperatures was poor, and only 13 combinations reasonably predicted the experimental temperature. As a generally observed tendency, it was noted that in the best-performing models, most of the correlations used for the determination of κm were parallel models. The study also identified the best-performing combinations to simultaneously predict flux, feed, and permeate outlet temperatures. Thus, it was noted that the best model to simultaneously predict flux, feed, and permeate outlet temperatures consisted of the following correlations for τ, Nu, and κm: =ε1−1−ε1/3, Nu=0.13Re0.64Pr0.38, κm=1−εκpol+εκair where ε, Re, Pr, κpol, and κair represent membrane porosity, Reynolds number, Prandtl number, thermal conductivities of polymer and air, respectively

Distributed agency in HRI—an exploratory study of a narrative robot design

We explore an alternative approach to the design of robots that deviates from the common envisionment of having one unified agent. What if robots are depicted as an agentic ensemble where agency is distributed over different components? In the project presented here, we investigate the potential contributions of this approach to creating entertaining and joyful human-robot interaction (HRI), which also remains comprehensible to human observers. We built a service robot—which takes care of plants as a Plant-Watering Robot (PWR)—that appears as a small ship controlled by a robotic captain accompanied by kinetic elements. The goal of this narrative design, which utilizes a distributed agency approach, is to make the robot entertaining to watch and foster its acceptance. We discuss the robot’s design rationale and present observations from an exploratory study in two contrastive settings, on a university campus and in a care home for people with dementia, using a qualitative video-based approach for analysis. Our observations indicate that such a design has potential regarding the attraction, acceptance, and joyfulness it can evoke. We discuss aspects of this design approach regarding the field of elderly care, limitations of our study, and identify potential fields of use and further scopes for studies