Admissible Strategies Research Articles

Sustainable thresholds for cooperative epidemiological models

In this paper, we introduce a method for computing sustainable thresholds for controlled cooperative models described by a system of ordinary differential equations, a property shared by a wide class of compartmental models in epidemiology. The set of sustainable thresholds refers to constraints (e.g., maximal “allowable” number of human infections; maximal “affordable” budget for disease prevention, diagnosis and treatments; etc.), parameterized by thresholds, that can be sustained by applying an admissible control strategy starting at the given initial state and lasting the whole period of the control intervention. This set, determined by the initial state of the dynamical system, virtually provides useful information for more efficient (or cost-effective) decision-making by exhibiting the trade-offs between different types of constraints and allowing the user to assess future outcomes of control measures on transient behavior of the dynamical system. In order to accentuate the originality of our approach and to reveal its potential significance in real-life applications, we present an example relying on the 2013 dengue outbreak in Cali, Colombia, where we compute the set of sustainable thresholds (in terms of the maximal “affordable” budget and the maximal “allowable” levels of active infections among human and vector populations) that could be sustained during the epidemic outbreak.

Race‐conscious admission requires focus, evidence‐based results — not perfection

BOSTON — Colleges and universities have made progress addressing race in the admissions process, but they have a long way to go. “Even as there is work to do, there is much to celebrate,” said Shannon Gundy, director of undergraduate admissions at the University of Maryland. Gundy, along with Art Coleman, co‐founder of EducationCounsel; and Jerry Lucido, executive director for the University of Southern California Center for Enrollment Research, Policy, and Practice, spoke at the annual conference for the National Association for College Admission Counseling in a session that explored the pitfalls and best practices in incorporating or maintaining race‐conscious admissions strategies.

Dividends: From Refracting to Ratcheting

In this paper we consider an alternative dividend payment strategy in risk theory, where the dividend rate can never decrease. This addresses a concern that has often been raised in connection with the practical relevance of optimal classical dividend payment strategies of barrier and threshold type. We study the case where once during the lifetime of the risk process the dividend rate can be increased and derive corresponding formulae for the resulting expected discounted dividend payments until ruin. We first consider a general spectrally-negative Levy risk model, and then re fine the analysis for a diffusion approximation and a compound Poisson risk model. It is shown that for the diffusion approximation the optimal barrier for the ratcheting strategy is characterized by an unexpected relation to the case of refracted dividend payments. Finally, numerical illustrations for the diffusion case indicate that with such a simple ratcheting dividend strategy the expected value of discounted dividends can already get quite close to the respective value of the refracted dividend strategy, the latter being known to be optimal among all admissible dividend strategies.

Stochastic Differential Game in High Frequency Market

This paper presents an application of a linear quadratic stochastic differential game to a financial model that describes trading behaviors of different types of players in a high frequency stock market. Stability of the stock market in a high frequency environment is a central issue in financial markets. Building a model that expresses the trading behaviors of the different types of players and the price actions in a high frequency market helps introduce better regulations for a healthy market. Firstly, we represent trading behaviors of the three types of players, algorithmic traders, general traders, and market makers as well as the mid-price process of a risky asset by a linear quadratic stochastic differential game. Secondly, we obtain a Nash equilibrium for open loop admissible strategies by solving a forward-backward stochastic differential equation (FBSDE) derived from the stochastic maximum principle. Finally, we present numerical examples of the Nash equilibrium for open loop admissible strategies and the corresponding price action of the risky asset, which agree with the empirical findings on the mechanism of high frequency markets. This model can be used to investigate the impact of regulation changes on the market stability as well as trading strategies of the players.

Advancing A Community of Practice: Reflections from the Field One Year Later

A year after embarking on program redesign to align with CPED principles and practices, faculty from a small doctoral program at a private university assessed their work. Specific initiatives such as embedding social justice principles into program components and revising admissions strategies were largely successful. Conversely, attempts to re-conceptualize the Dissertation in Practice met with resistance from numerous stakeholders. The challenges and opportunities of substantively changing a long-standing program have affected the way this faculty work together and envision the future of their program. New approaches to collaboration, innovation, and conflict resolution, viewed from an organizational change perspective, and rooted in the program culture, resulted from their collective efforts to strengthen the education doctorate.

Convex duality for Epstein–Zin stochastic differential utility

AbstractThis paper introduces a dual problem to study a continuous‐time consumption and investment problem with incomplete markets and Epstein–Zin stochastic differential utilities. Duality between the primal and dual problems is established. Consequently, the optimal strategy of this consumption and investment problem is identified without assuming several technical conditions on market models, utility specifications, and agent's admissible strategies. Meanwhile, the minimizer of the dual problem is identified as the utility gradient of the primal value and is economically interpreted as the “least favorable” completion of the market.

A cross-continental analysis of weight gain, psychiatric diagnoses and medication use during inpatient psychiatric treatment. The international study on physical illness in mentally ill

Weight gain among psychiatric inpatients is a widespread phenomenon. This change in body mass index (BMI) can be caused by several factors. Based on recent research, we assume the following factors are related to weight gain during psychiatric inpatient treatment: psychiatric medication, psychiatric diagnosis, sex, age, weight on admission and geographic region of treatment.876 of originally recruited 2328 patients met the criteria for our analysis. Patients were recruited and examined in mental health care centres in Nigeria (N = 265), Japan (N = 145) and Western-Europe (Denmark, Germany and Switzerland; N = 466).There was a significant effect of psychiatric medication, psychiatric diagnoses and geographic region, but not age and sex, on BMI changes. Geographic region had a significant effect on BMI change, with Nigerian patients gaining significantly more weight than Japanese and Western European patients. Moreover, geographic region influenced the type of psychiatric medication prescribed and the psychiatric diagnoses. The diagnoses and psychiatric medication prescribed had a significant effect on BMI change.In conclusion, we consider weight gain as a multifactorial phenomenon that is influenced by several factors. One can discuss a number of explanations for our findings, such as different clinical practices in the geographical regions (prescribing or admission strategies and access-to-care aspects), as well as socio-economic and cultural differences.

On the structure of multifactor optimal portfolio strategies

The paper studies problem of optimal portfolio selection. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed using a limited number of fixed processes (mutual funds), for a market with a larger number of available risky stocks. This implies dimension reduction for the optimal portfolio selection problem: all rational investors may achieve optimality using the same mutual funds plus a saving account. This result is obtained under mild restrictions for the utility functions without any assumptions on regularity of the value function. The proof is based on the method of dynamic programming applied indirectly to some convenient approximations of the original problem that ensure certain regularity of the value functions. To overcome technical difficulties, we use special time dependent and random constraints for admissible strategies such that the corresponding HJB (Hamilton–Jacobi–Bellman) equation admits “almost explicit” solutions generating near optimal admissible strategies featuring sufficient regularity and integrability.

Optimal Portfolio under Fast Mean-Reverting Fractional Stochastic Environment

Empirical studies indicate the existence of long-range dependence in the volatility of the underlying asset. This feature can be captured by modeling its return and volatility using functions of a stationary fractional Ornstein--Uhlenbeck (fOU) process with Hurst index $H \in (\frac{1}{2}, 1)$. In this paper, we analyze the nonlinear optimal portfolio allocation problem under this model and in the regime where the fOU process is fast mean-reverting. We first consider the case of power utility, and rigorously give first order approximations of the value and the optimal strategy by a martingale distortion transformation. We also establish the asymptotic optimality in all admissible controls of a zeroth order trading strategy. Then, we consider the case with general utility functions using the epsilon-martingale decomposition technique, and we obtain similar asymptotic optimality results within a specific family of admissible strategies.

Defining Underrepresented Minorities and Promoting Holistic Review Admission Strategies in Physical Therapist Education

Background and Purpose. Given the changing demographics of the United States, it is important for Doctor of Physical Therapy (DPT) education programs to address how best to recruit and retain students who will be able to provide culturally competent and sensitive care. Compared with the general population, the racial and ethnic diversity of professional membership in the American Physical Therapy Association and applications to and acceptance in professional physical therapist education programs has remained relatively static and does not mirror the diversity of the population at large. Position and Rationale. To best determine effective recruitment and retention strategies to address this shortfall in PT education, it is necessary to have (1) a unifying definition of underrepresented minorities (URMs) in physical therapy education and (2) an understanding of what is currently being done to promote a diverse student body. The American Council of Academic Physical Therapy empaneled its Diversity Task Force in January 2013 to address these two issues. This position paper reports on the efforts of the Diversity Task Force in developing a working definition of URMs in physical therapy education that reaches beyond traditional racial and ethnic descriptors, along with supporting information from a survey of entry-level DPT program directors on barriers to increasing diversity within the professional PT student population and strategies currently in place to overcome them. Discussion and Conclusion. Based on a uniform definition of URMs and the current status of recruitment/retention policies and practices designed to foster a diverse student population, we conclude that ongoing work is needed to increase diversity within DPT education and that utilization of a holistic application review process for admissions is one method to increase diversity.

Portfolio optimization of credit swap under funding costs

We develop a dynamic optimization framework to assess the impact of funding costs on credit swap investments. A defaultable investor can purchase CDS upfronts, borrow at a rate depending on her credit quality, and invest in the money market account. By viewing the concave drift of the wealth process as a continuous function of admissible strategies, we characterize the optimal strategy in terms of a relation between a critical borrowing threshold and two solutions of a suitably chosen system of first order conditions. Contagion effects between risky investor and reference entity make the optimal strategy coupled with the value function of the control problem. Using the dynamic programming principle, we show that the latter can be recovered as the solution of a nonlinear HJB equation whose coeffcients admit singular growth. By means of a truncation technique relying on the locally Lipschitz-continuity of the optimal strategy, we establish existence and uniqueness of a global solution to the HJB equation.

Maximization of viability time in a mathematical model of cancer therapy

In this paper, we study a dynamic optimization problem for a general nonlinear mathematical model for therapy of a lethal form of cancer. The model describes how the populations of cancer and normal cells evolve under the influence of the concentrations of nutrients (oxygen, glucose, etc.) and the applied therapeutic agent (drug). Regulated intensity of the therapy is interpreted as a time-dependent control strategy. The therapy (control) goal is to maximize the viability time, i. e., the duration of staying in a so-called safety region (which specifies safe living conditions of a patient in terms of constraints on the amounts of cancer and normal cells), subject to limited resources of the therapeutic agent. In a specific benchmark case, a novel optimality principle for admissible therapy strategies is established. It states that the optimal trajectories should finally reach a certain corner of the safety region or at least the upper constraint on the quantity of cancer cells. The results of numerical simulations appear to be in good agreement with the proposed principle. Typical qualitative structures of optimal treatment strategies are also obtained. Furthermore, important characteristics of the model are the competition coefficient (describing the negative influence of cancer cells on normal cells), the upper bound in the drug integral constraint, and the ratio between the therapy and damage coefficients (i. e., the ratio between the positive primary and negative side effects of the therapy).

Only STEM Can Save Us? Examining Race, Place, and STEM Education as Property

The rhetoric about science, technology, engineering, and mathematics (STEM) education in urban schools reflects a desire to imagine a new city that is poised to compete in a STEM-centered future. Therefore, STEM has been positioned as a critical part of urban education reform efforts. In various US cities, schools labeled as failing are being repurposed as selective STEM-intensive academies to build a STEM education infrastructure. In Memphis, Tennessee, this process makes visible issues with educational inequity, exacerbated by school choice and gentrification processes. In this article, I use whiteness as property, a tenet of critical race theory, to examine STEM education in Memphis as a case of urban STEM-based education reform in the United States. I describe claiming STEM education as property as a 2-phase process in which middle-class Whites in urban areas participate to secure STEM education by repurposing failed Black schools and to maintain it by institutionalizing selective admissions strategies.

DTMR: delay-aware traffic admission, mode selection, and resource allocation for D2D communication

In device-to-device (D2D) communication underlaying a cellular network, the resource control involves traffic admission, mode selection, orthogonal channel assignment, and power control. Traffic admission limits queueing delay, mode selection exploits the proximity gain, and resource allocation guarantees user performance. Jointly optimizing these factors is highly challenging due to the stochastic nature of the system and the coupled control actions. Many previous works only consider a subset of these factors. In this paper, we tackle the joint optimization problem for delay-aware D2D communication. In particular, considering both dynamic traffic arrival and time-varying channel fading, we aim to maximize the time-average sum-rate of the network subject to the time-average throughput guarantee of users and resource allocation constraints. Thus, through presenting a Lyapunov optimization framework, we design an optimal delay-aware traffic admission, mode selection, and resource allocation (DTMR) strategy with polynomial time complexity based on dual optimization and ellipsoid search. We also analytically derive lower bound of the time-average sum-rate achieved by the proposed DTMR strategy. Further, we develop a fast heuristic strategy by decoupling the binary constraints of mode selection and channel assignment. Finally, simulation results demonstrate the superiority of the DTMR strategy against alternative strategies.

A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

AbstractA single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered. Type-1 customers have limited preemptive priority over type-2 customers. There is an infinite buffer for type-2 customers and no buffer for type-1 customers. There is also a finite buffer (stock) for consumable additional items (semi-products, half-stocks, etc.) which arrive according to the Markovian arrival process. Service of a customer requires a fixed number of consumable additional items depending on the type of the customer. The service time has a phase-type distribution depending on the type of the customer. Customers in the buffer are impatient and may leave the system without service after an exponentially distributed amount of waiting time. Aiming to minimize the loss probability of type-1 customers and maximize throughput of the system, a threshold strategy of admission to service of type-2 customers is offered. Service of type-2 customer can start only if the server is idle and the number of consumable additional items in the stock exceeds the fixed threshold. Stationary distributions of the system states and the waiting time are computed. In the numerical example, we show some interesting effects and illustrate a possibility of application of the presented results for solution of optimization problems.

Optimal dividend strategies for two collaborating insurance companies

Abstract We consider a two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes, who collaborate by paying each other's deficit when possible. We study the stochastic control problem of maximizing the weighted sum of expected discounted dividend payments (among all admissible dividend strategies) until ruin of both companies, by extending results of univariate optimal control theory. In the case that the dividends paid by the two companies are equally weighted, the value function of this problem compares favorably with the one of merging the two companies completely. We identify the optimal value function as the smallest viscosity supersolution of the respective Hamilton–Jacobi–Bellman equation and provide an iterative approach to approximate it numerically. Curve strategies are identified as the natural analogue of barrier strategies in this two-dimensional context. A numerical example is given for which such a curve strategy is indeed optimal among all admissible dividend strategies, and for which this collaboration mechanism also outperforms the suitably weighted optimal dividend strategies of the two stand-alone companies.

Sex differences in management and outcomes of patients with atrial fibrillation in the Middle East: Gulf survey of atrial fibrillation events (Gulf SAFE).

Differences in the management of atrial fibrillation (AF) between men and women were investigated by using Gulf SAFE data in the Middle East. The study included 2,043 patients presenting with AF to emergency room (ER) were prospectively enrolled and followed for one-year. Women were older, have higher body mass index (BMI), comorbidities, and health complications than men. With regard to management of AF, cardioversion was recommended more often for men (16.7% vs. 9.3%), and underwent electrical cardioversion (2.2% vs. 1.1%). Women were prescribed digoxin more frequently than men (25.6% vs. 17.4%) and a significant number women received warfarin alone (31.1% vs. 8.7%). No difference between the sexes was noticed in One-year rates of stroke/transient ischemic attacks (TIA) and all-cause of mortality after one-year follow-up (3.1% men vs. 3.3% women, and 7.5% vs. 7.4%). Older age (≥ 65 years), smoking, alcohol use, CHADS2 scores ≥5 were some of the significant risk factors in men with AF. Suboptimal use of anticoagulants, higher mortality and stroke/TIA events at one year are high but similar between the sexes. ER management revealed high use of rate control strategy and high rate of hospital admission was noticed in women.

On Defining Ex Ante Payoffs in Games with Diffuse Prior

We formalize the notion of a diffuse prior and show that, in stationary games, strategies which admit well-defined expected payoffs under the diffuse prior are essentially stationary. We define the diffuse prior through a limit construction, using sequences of well-defined priors that become increasingly dispersed. Admissible strategies are those for which ex ante payoffs along these sequences converge to a limit that does not depend on the particular sequence. A secondary contribution of the paper is a generalization of the concept of distributional strategies (Milgrom and Weber, 1985) to multistage games.

Boundary Determination of the Inverse Heat Conduction Problem in One and Two Dimensions via the Collocation Method Based on the Satisfier Functions

In this paper, we are concerned with the numerical solutions of the inverse heat conduction problems (IHCP) in one and two dimensions with free boundary conditions. For the one-dimensional problem, we first apply the Landau’s transformation to replace the physical domain with a rectangular one. Reciprocally, some nonlinear terms appear thus an iterative scheme based on the application of the satisfier function is proposed for solving the problem. Second, we treat with the nonlinear two-dimensional problem by providing a collocation technique which takes advantage of the satisfier functions. Throughout this work, the presented schemes make the reader free of solving any nonlinear system of algebraic equations. Moreover, an admissible regularization strategy, namely, the Landweber’s iterations method is used to overcome the numerical instability and achieve the acceptable approximations. Illustrative examples are included to show the efficiency of the presented algorithms.

Concurrent Learning Based Finite-Time Parameter Estimation in Adaptive Control of Uncertain Switched Nonlinear Systems

In this paper, We propose concurrent learning adaptive controller, which uses recorded and current data concurrently for adaptation, to model reference adaptive control (MRAC) of uncertain switched systems. In standard MRAC architecture for switched systems, the adaptive update laws are derived based on the gradient descent scheme, but here we developed two novel parameter estimation schemes by using modification terms in adaptation laws in which recorded data is used simultaneously with current data and a triggering time is considered in which a sufficient condition on the linear independence of the recorded data is obtained to guarantee the exponential convergence of tracking error and parameter estimation error to zero for the uncertain switched system under all admissible switching strategy. The convergence of the parameters to the ideal values makes an on-line learned model of the system available. This sufficient condition is easily verifiable in comparison to the restrictive persistence of excitation (PE) condition of the standard MRAC structures in practical applications. Finally a simulation example is given to illustrate the efficacy of the proposed method.