We consider De Finetti’s control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized mean-reverting strategy is optimal in a Brownian model. In order to solve this problem, we need to deal with a nonlinear Ornstein–Uhlenbeck process. Despite the level of generality of the bound imposed on the rate, an explicit expression for the value function is obtained up to the evaluation of two functions. This optimal control problem has, as special cases, those solved in Jeanblanc-Picqué and Shiryaev (1995) and Renaud and Simard (2021) when the control rate is bounded by a constant and a linear function, respectively.

We used a diffusion model to examine the effects of response-bias manipulations on response time (RT) and accuracy data collected in two experiments involving a two-choice decision making task. We asked 18 subjects to respond “low” or “high” to the number of asterisks in a 10×10 grid, based on an experimenter-determined decision cutoff. In the model, evidence is accumulated until either a “low” or “high” decision criterion is reached, and this, in turn, initiates a response. We performed two experiments with four experimental conditions. In conditions 1 and 2, the decision cutoff between low and high judgments was fixed at 50. In condition 1, we manipulated the frequency with which low- and high-stimuli were presented. In condition 2, we used payoff structures that mimicked the frequency manipulation. We found that manipulating stimulus frequency resulted in a larger effect on RT and accuracy than did manipulating payoff structure. In the model, we found that manipulating stimulus frequency produced greater changes in the starting point of the evidence accumulation process than did manipulating payoff structure. In conditions 3 and 4, we set the decision cutoff at 40, 50, or 60 (Experiment 1) and at 45 or 55 (Experiment 2). In condition 3, there was an equal number of low- and high-stimuli, whereas in condition 4 there were unequal proportions of low- and high-stimuli. The model analyses showed that starting-point changes accounted for biases produced by changes in stimulus proportions, whereas evidence biases accounted for changes in the decision cutoff.

Every day, people struggle to make healthy eating decisions. Nutrition labels have been used to help people properly balance the tradeoff between healthiness and taste, but research suggests that these labels vary in their effectiveness. Here, we investigated the cognitive mechanism underlying value-based decisions with nutrition labels as modulators of value.

More specifically, we used a binary decision task between products along with two different nutrition labels to examine how salient, color-coded labels, compared to purely information-based labels, alter the choice process. Using drift-diffusion modeling, we investigated whether color-coded labels alter the valuation process, or whether they induce a simple stimulus-response association consistent with the traffic-light colors irrespective of the features of the item, which would manifest in a starting point bias in the model. We show that color-coded labels significantly increased healthy choices by increasing the rate of preference formation (drift rate) towards healthier options without altering the starting point. Salient labels increased the sensitivity to health and decreased the weight on taste, indicating that the integration of health and taste attributes during the choice process is sensitive to how information is displayed. Salient labels proved to be more effective in altering the valuation process towards healthier, goal-directed decisions.

The word frequency effect is stronger in second language (L2) processing than in first language (L1) processing. According to the lexical entrenchment hypothesis, this difference is not due to a qualitative difference in word processing between L1 and L2, but can be explained by differences in exposure to the target language: People with less exposure to a language show a steeper frequency curve for that language. Exposure differences can be measured with a vocabulary test. The present study tested whether the lexical entrenchment hypothesis provides an adequate explanation for differences in lexical decision times. To this end, we compared the performance of 56 Dutch–English bilinguals to that of 1011 English L1 speakers on 420 English six-letter words. In line with previous research, the differences in the word frequency effect between word processing in L1 and in L2 became vanishingly small once vocabulary size was entered as a predictor. Only in a diffusion model analysis did we find some evidence that the information build-up may be slower in L1 than in L2, independent of vocabulary size. We further report effects of cognates, age-of-acquisition, and neighborhood size that can also be explained in terms of differences in exposure.

A simple fluorescence microscopy technique is developed and presented to investigate heterogeneities in emission intensity and quenching responses of luminescence sensors and to measure diffusion and permeation coefficients of oxygen in polymers. Most luminescence oxygen sensors do not follow linearity of the Stern-Volmer (SV) equation due to heterogeneity of luminophore in the polymer matrix. To circumvent this limitation, inverted fluorescence microscopy is utilized in this work to investigate the SV response of the sensors at the micron scale. It was found that intensity is higher in regions where the luminophore is aggregated, but the response is poorer to oxygen concentration. In contrast, the nearly homogeneous regions exhibit linearity with high SV constants. In these diffusion experiments, oxygen concentration was measured by luminescence changes in regions with high SV constants and good linearity. Two diffusion experiments were performed—termed film-on-sensor and accumulation-in-volume techniques. A new Fick's law based quasi-steady-state diffusion model was developed and combined with the SV equation to obtain effective permeation coefficients for the accumulation-in-volume technique. Using these experimental techniques, oxygen diffusion properties in free-standing Teflon polymer films, cast silicon elastomers, and cast polydimethylsiloxane films containing different weight percentages of zeolite were determined with good precision.

The problem of optimal dividends paid until absorbtion at zero is considered for a rather general diffusion model. With each dividend payment there is a proportional cost and a fixed cost. It is shown that there can be essentially three different solutions depending on the model parameters and the costs. (i) Whenever assets reach a barrier y*, they are reduced to y* - δ* through a dividend payment, and the process continues. (ii) Whenever assets reach a barrier y*, everything is paid out as dividends and the process terminates. (iii) There is no optimal policy, but the value function is approximated by policies of one of the two above forms for increasing barriers. A method to numerically find the optimal policy (if it exists) is presented and numerical examples are given.

The problem discussed is that of controlling optimally the release of water from a finite dam, when the release rate may vary continuously and the optimality is defined in terms of a cost structure imposed on the operation of the dam. A diffusion model is suggested and by considering a family of plausible output policies, the control problem is reduced to the solution of a free boundary problem associated with a certain partial differential equation. A set of necessary conditions for the optimal choice of these boundaries is established and a method of solution is suggested. By using this method, together with well-established computational techniques, numerical solutions are obtained. These numerical solutions indicate that this optimal policy does not result in very much improvement over a much simpler policy where the output rate is constrained to take only two values.

The problem discussed is that of determining optimal release rates for finite dams when the release rate may take one of two values and specific costs are involved in increasing and decreasing this release rate. From another point of view, this is a problem of controlling the output simply by switching on and off. A diffusion model is suggested and by considering a family of plausible output policies an optima procedure, which minimises the long-term average cost of operating the dam, is established. Various properties of this output policy are given.