Barrier Strategy Research Articles

An Optimal Multibarrier Strategy for a Singular Stochastic Control Problem with a State-Dependent Reward

We consider a singular control problem that aims to maximize the expected cumulative rewards, where the instantaneous returns depend on the state of a controlled process. The contributions of this paper are twofold. Firstly, to establish sufficient conditions for determining the optimality of the one-barrier strategy when the uncontrolled process X follows a spectrally negative Lévy process with a Lévy measure defined by a completely monotone density. Secondly, to verify the optimality of the (2n+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2n+1)$$\\end{document}-barrier strategy when X is a Brownian motion with a drift. Additionally, we provide an algorithm to compute the barrier values in the latter case.

Ferroelectric tunnel junctions based on a HfO2/dielectric composite barrier

The ferroelectric tunnel junction (FTJ), which possesses a simple structure, low power consumption, high operation speed, and nondestructive reading, has attracted great attention for the application of next-generation nonvolatile memory. The complementary metal–oxide–semiconductor-compatible hafnium oxide (HfO2) ferroelectric thin film found in the recent decade is promising for the scalability and industrialization of FTJs. However, the electric performance, such as the tunneling electroresistance (TER) effect, of the current HfO2-based FTJs is not very satisfactory. In this work, we propose a type of high-performance HfO2-based FTJ by utilizing a ferroelectric/dielectric composite barrier strategy. Using density functional theory calculations, we study the electronic and transport properties of the designed Ni/HfO2/MgS/Ni (001) FTJ and demonstrate that the introduction of an ultra-thin non-polar MgS layer facilitates the ferroelectric control of effective potential barrier thickness and leads to a significant TER effect. The OFF/ON resistance ratio of the designed FTJ is found to exceed 4 × 103 based on the transmission calculation. Such an enhanced performance is driven by the resonant tunneling effect of the ON state, which significantly increases transmission across the FTJ when the ferroelectric polarization of HfO2 is pointing to the non-polar layer due to the aroused electron accumulation at the HfO2/MgS interface. Our results provide significant insight for the understanding and development of the FTJs based on the HfO2 ferroelectric/non-polar composite barrier.

Optimal dividends and capital injection: A general Lévy model with extensions to regime-switching models

This paper studies a general Lévy process model of the bail-out optimal dividend problem with an exponential time horizon, and further extends it to the regime-switching model. We first show the optimality of a double barrier strategy in the single-regime setting with a concave terminal payoff function. This is then applied to show the optimality of a Markov-modulated double barrier strategy in the regime-switching model via contraction mapping arguments. We solve these for a general Lévy model with both positive and negative jumps, greatly generalizing the existing results on spectrally one-sided models.

Optimal reinsurance under a new design: two layers and multiple reinsurers

We investigate the optimal reinsurance problem considering a more realistic two-layer design involving excess-of-loss reinsurance and multiple reinsurers. Unlike the commonly assumed single-layer design in the existing literature, our approach involves a top layer consisting of excess-of-loss reinsurance and the involvement of multiple reinsurers. Our focus is on the insurer's management of risk exposure and costly capital reinvestment strategies to maximize the company value. We formulate this problem as an optimization problem with constrained multivariate reinsurance exposure variables, and capital injection control. Our findings show that, from a profitability standpoint, when the surplus is low and the excess-of-loss reinsurance is not too expensive, the insurer should obtain a two-layer reinsurance with an excess-of-loss reinsurance at the top layer and a combination of proportional reinsurance from multiple reinsurers at the bottom layer. In contrast, when the surplus is relatively large or the excess-of-loss reinsurance is too expensive, the insurer should purchase a single-layer proportional reinsurance from multiple reinsurers. When the surplus is large enough, the insurer should not acquire any reinsurance. Our results suggest that stand-alone excess-of-loss reinsurance is never optimal when there is also proportional reinsurance with a variance premium principle available for losses below the excess threshold, and we theoretically confirm that a multi-layer reinsurance design is preferable over a single-layer design. Furthermore, our results demonstrate that in order to maximize the company's value, dividends should be paid according to the lump-sum barrier strategy, and capital injections should be considered only if the surplus is null and the transaction costs on capital injections are not too high.

Optimal payout strategies when Bruno de Finetti meets model uncertainty

Model uncertainty is ubiquitous and plays an important role in insurance and financial modeling. While a substantial effort has been given to studying optimal consumption, portfolio selection and investment problems in the presence of model uncertainty, relatively little attention is given to investigating optimal payout policies taking account of the impacts of model uncertainty. As one of the early attempts, this paper studies the optimal payout control problem under the classical risk model taking into account of model uncertainty about the claims arrival intensity. We aim to provide insights into understanding optimal decisions incorporating model uncertainty and to examine key impact of model uncertainty. We find that the optimal strategy robust to model uncertainty is of a band type. However, the presence of the model uncertainty alters the qualitative behavior of the optimal strategy in the sense that the optimal robust policy is no longer a barrier strategy for some particular cases. We provide numerical examples to illustrate the theoretical results and examine the impact of model uncertainty on optimal payout policies. We also provide examples that use real insurance data for calibration. We discover that the decision maker takes more conservative strategies under model uncertainty, which is consistent with the findings in the economic field and has not been addressed in the existing optimal payout problems without model uncertainty.

Optimal annuitization and asset allocation under linear habit formation

This paper studies the optimal consumption-investment-annuitization problem for a retiree with linear consumption habits. We explore the effect of consumption habits on the decision to annuitize when annuities are purchased as a lump sum. The problem is formulated as a combined stopping-control problem. We derive optimal annuitization time, investment, and consumption strategies by a generalized dual method and habit reduction method. We investigate the influence of various factors on the annuitization time and derive optimal annuitization time, which is a barrier strategy. The numerical simulations reveal several interesting results. Our results demonstrate that risk aversion, subjective hazard rate, and consumption habits all play a role in shaping annuitization decisions. Furthermore, we offer a new explanation for the rarity of voluntary annuitization among retirees.

Barrier Strategy for Strain-Free Encapsulation of Perovskite Solar Cells.

The performance loss caused by encapsulation has been an obstacle to guarantee the excellent power conversion efficiency of perovskite solar cells (PSCs) in practical application. This work revealed that the encapsulation-induced performance loss is highly related to the tensile strains imposed on the functional layers of the device when the PSC is exposed directly to the deformed encapsulant. A barrier strategy is developed by employing a nonadhesive barrier layer to isolate the deformed encapsulant from the PSC functional layer, achieving a strain-free encapsulation of the PSCs. The encapsulated device with a barrier layer effectively reduced the relative performance loss from 21.4% to 5.7% and dramatically improved the stability of the device under double 85 environment conditions. This work provides an effective strategy to mitigate the negative impact of encapsulation on the performance of PSCs as well as insight into the underlying mechanism of the accelerated degradation of PSCs under external strains.

Optimal periodic dividends with penalty payments under a diffusion model

In this work, we examine the optimal periodic dividend problem with penalty payments for a diffusion model, where dividends are only paid at Poisson arrival times. Moreover, we assume that (observed) ruin or bankruptcy does not occur even if the surplus is negative, but the penalty payments happen. The goal is to seek an optimal periodic dividend strategy to maximize the expectation of the difference between the present value of dividends and penalty payments. We demonstrate that the optimal strategy is a periodic barrier strategy. For the exponential penalty function, the optimal periodic barrier and the explicit expression for the value function are determined. Several numerical instances are also presented.

Equilibrium reporting strategy: Two rate classes and full insurance

AbstractWe propose a multiperiod insurance model under a bonus–malus system with two rate classes and consider an insured who has purchased full insurance for her losses. To explore the potential advantage of underreporting her insurable losses, the insured follows a barrier strategy and only reports lossses above the barrier to the insurer. We obtain a unique equilibrium declaration strategy in closed form for a risk‐neutral insured who maximizes her expected wealth, and in semiclosed form for a risk‐averse insured who maximizes her expected exponential utility of wealth, both over an exogenous random horizon. We find that the equilibrium barriers for the two classes are equal and strictly greater than zero, offering a theoretical explanation for the underreporting of insurable losses, a form of ex post moral hazard. Finally, we consider the case of three rate classes and show, through numerical examples, that the equilibrium barriers are not equal.

An LMI adaptive-barrier function global sliding mode control of uncertain nonlinear systems with input saturation

This paper proposes a barrier function-based adaptive control strategy with a nonlinear sliding surface for a class of uncertain dynamic systems with input saturation. Its main objectives are to ensure robustness to parametric and non-parametric uncertainties whilst eliminating the reaching phase. A global nonlinear switching surface is defined and an adaptive barrier function sliding mode control approach is derived. The barrier strategy is adopted to ensure the convergence of the states to the desired values without overestimating the control gains. System stability is analyzed using the Lyapunov stability theory. The control parameters are obtained using the linear matrix inequality (LMI) approach. The control law is designed to remove the reaching phase. The effectiveness of the proposed approach was validated using a simulation study. The proposed control approach can easily be implemented to various nonlinear uncertain systems.

Oriented Fibers Cooperate with DFO to Prevent Tendon Adhesions by Improving the Repair Microenvironment

AbstractTo solve the problem of tendon adhesion after an operation, an anti‐adhesion membrane is designed, which can inhibit the exogenous healing of tendons and promote endogenous healing. Here, poly[3(S)‐methyl‐morpholine‐2,5‐dione‐co‐lactic acid] P(MMD‐co‐LA) containing alanine units is obtained by melt ring‐opening polymerization (ROP). It can effectively reduce the production of acidic degradation products that cause aseptic inflammation. Then a kind of oriented P(MMD‐co‐LA)/deferoxamine (DFO) anti‐adhesion membrane with good mechanical properties, cell adhesion properties, and induced macrophage polarization properties is constructed by electrospinning. In vitro and in vivo studies have shown that oriented fibrous membranes can down‐regulate the expression of inflammatory cytokines. In addition, the fibrous membrane can up‐regulate the expression of angiogenesis‐related genes, namely HIF1‐α, SDF‐1α, and VEGF, by releasing DFO in situ, thus promoting the revascularization of tendon defects and providing nutritional support for endogenous tendon healing. This method provides a new barrier strategy to reduce tendon adhesion through anti‐inflammation combined with vascularization to inhibit exogenous tendon healing while promoting tendon endogenous healing. The results provide essential insights into the corresponding regulation of the tendon healing microenvironment.

On the bailout dividend problem with periodic dividend payments for spectrally negative Markov additive processes

This paper studies the bailout optimal dividend problem with regime switching under the constraint that dividend payments can be made only at the arrival times of an independent Poisson process while capital can be injected continuously in time. We show the optimality of the regime-modulated Parisian-classical reflection strategy when the underlying risk model follows a general spectrally negative Markov additive process. In order to verify the optimality, first we study an auxiliary problem driven by a single spectrally negative Lévy process with a final payoff at an exponential terminal time and characterize the optimal dividend strategy. Then, we use the dynamic programming principle to transform the global regime-switching problem into an equivalent local optimization problem with a final payoff up to the first regime switching time. The optimality of the regime modulated Parisian-classical barrier strategy can be proven by using the results from the auxiliary problem and approximations via recursive iterations.

On Singular Control for Lévy Processes

We revisit the classical singular control problem of minimizing running and controlling costs. Existing studies have shown the optimality of a barrier strategy when driven by Brownian motion or Lévy processes with one-sided jumps. Under the assumption that the running cost function is convex, we show the optimality of a barrier strategy for a general class of Lévy processes. Funding: This work was supported by the Japan Society for the Promotion of Science [Grants 18J12680, 19H01791, 20K035758, 21K13807, and JPJSBP120209921] and a University of Queensland start-up grant.

A Surface Diffusion Barrier Strategy toward Water-Resistant Photonic Materials for Accurate Detection of Ethanol.

Photonic materials that enable visual detection of chemicals have shown great potential for wide applications in chemical, environmental, biotechnological, and food industries, but until now, using hydrophilic photonic materials for tracing water-soluble chemicals remains a major challenge due to the strong water interference. Here, we demonstrate a two-step co-assembly and subsequent surface coating strategy to develop an ethanol-sensitive and anti-water interference photonic crystal film. By using citric acid as a co-assembly phase, high ethanol sensing is realized because of the strong intermolecular affinity. By controlling the thickness of the outer polyvinyl butyral layer, selective ethanol penetration but a water barrier is enabled. Notably, the composite photonic films are free-standing, highly flexible, and controllably structurally colored. We further present using the composite film to quantitatively trace ethanol/water mixtures and potentially track drunk driving as a colorimetric sensor. The heuristic two-step modification strategy proposed in this work not only overcomes the limitation of water interference for hydrophilic colorimetric sensors but also provides references to develop more new photonic materials with water resistance that need to be applied in water/humid environments.

Infinite series expansion of some finite-time dividend and ruin related functions

In this paper, we consider some finite-time dividend and ruin problems in a class of risk models under the constant dividend barrier strategy. This class of risk models includes Brownian motion risk model and the compound Poisson model with and without diffusion. By using Laguerre series expansion, we derive infinite series expansion formulas for the time T-deferred Laplace transform of the ruin time and time T-deferred expected present valued of dividend payments until ruin.

Interface barrier strategy for perovskite solar cells realized by In-situ synthesized polyionic layer

The harmonious coordination between the perovskite and the charge transport layer is the prerequisite for the high efficiency and stability of perovskite solar cells (PSCs). The excellent photoelectric and solution processable SnO2 electron transport material opens the most commercial potential of planar PSCs. However, SnO2 has rich surface activity and photocatalytic properties, which will deteriorate perovskite after absorbing UV light and seriously affect the stability and efficiency of PSCs. Here, the interface barrier strategy is introduced to insert an anchored-then-rinsed lead polystyrene sulfonate (ARPSS-Pb) polyionic layer between SnO2 and perovskite via in-situ synthesis method to construct a new stable interface, which can effectively block the phase transition of perovskite driven by photocatalytic SnO2. In addition, ARPSS-Pb also has the functions of passivating interfacial defects, relaxing interfacial stress and guiding crystallization of perovskite. PSCs based on ARPSS-Pb achieved a power conversion efficiency (PCE) of 22.26%, much higher than 19.60% of the control devices. More importantly, after 1000 h of storage under continuous humidity conditions, up to 96.32% of the initial PCE is maintained. A high open circuit voltage (VOC) as high as 1.190 V has been obtained for ARPSS-Pb based devices. To our best knowledge, this is the highest VOC achieved in the system of perovskite with 1.56 eV energy gap.

On Itô’s formula for semimartingales with jumps and non-[formula omitted]2 functions

This paper considers a variant of Itô’s formula for discontinuous semimartingales and non-C2 functions. This result is particularly helpful for insurance control problems with Markov-modulated components. An example of a dividend barrier strategy for a Brownian risk model with Markov-switching illustrates the result.

Competitive dynamics of strategic groups in the Portuguese banking industry

The objective of this paper is to analyse the retail banking behaviour in Portugal (2008–2010, 2011–2013 and 2014–2016), by taking into account the financial and economic assistance programme (FEAP) – monitored by the European Commission, the European Central Bank and the International Monetary Fund – that Portugal went through and that started in 2011. With competitive dynamics it is possible to understand the evolution of competitive strategies of the institutions of a strategic group within a given time horizon. Data were collected after consultation of reports and accounts of Banks from Banco de Portugal database. The results were analysed and discussed in light of the theory of strategic groups and their competitive dynamics allows us to conclude that: Banks implemented different competitive strategies; Strategic groups have dissimilar resources; and Strategic groups display different strategies. The 2008–2010 period can be considered as a ‘deregulated’ period, the 2011–2013 as a period of ‘imposed regulation’, and the 2014–2016 as a period of ‘strategic consolidation’ with strategic changes that have prompted strategic groupings of the various institutions as consequence of a low mobility barrier strategy.

Optimal Dividend Strategy Under Parisian Ruin with Affine Penalty

In this paper, we investigate the optimal dividend problem under Parisian ruin with affine penalty payments at Parisian ruin time. The underlying risk process is assumed to be a spectrally negative Levy risk process. With the help of the dynamic programming principle, we prove that the value function associated to our optimal control problem is the smallest solution with certain characteristics to the corresponding Hamilton–Jacobi–Bellman (HJB) equation. In addition, the form of the performance function under barrier dividend strategy is expressed in terms of various extended scale functions. Then we identify a condition under which the performance function under certain barrier strategy is also a solution to the HJB equation, which in turn illustrates the optimalilty of such barrier dividend strategy among all admissible strategies. Various numerical examples are also given when the underlying risk process is compound Poisson process, Brownian motion with drift and jump-diffusion process.

An oxidative stress-responsive electrospun polyester membrane capable of releasing anti-bacterial and anti-inflammatory agents for postoperative anti-adhesion

Peritendinous adhesion, secondary to the repair surgery of tendon rupture or injury, is one of the most common causes of reoperation, owing to the proliferation of fibrous tissue and excessive collagen synthesis caused by the residing inflammatory cells. In this study, a smart oxidative stress-responsive electrospun polyester membrane (EPM) was fabricated as both physical barrier and reservoir of curcumin/celecoxib (CUR/CEL) to prevent peritendinous adhesion. The multicomponent EPM was designed to release the encapsulated drugs in response to oxidative stress of the local microenvironment induced by inflammation. Specifically, sulfides in the EPM were able to react with reactive oxygen species (ROS) and become hydrophilic sulfoxide or sulfone to accelerate the release rate of drugs and regulate oxidative stress level in the inflammatory site intelligently. The oxidation-sensitive multicomponent EPM loaded with CUR and CEL was tested for anti-adhesion capacity in vitro and in vivo. An excellent ROS-sensitive degradation behavior and good cytocompatibility with cell viability of above 85% were presented with the fabricated EPM. The CUR- or CEL-loaded EPM possessed a better anti-adhesion ability compared with EPM without the drugs. Nevertheless, they were inferior to the EPM simultaneously loaded with both drugs, where the adhesion rate and fibrous adhesion number in the EPM+CUR/CEL group were close to extremely low values of about zero, demonstrating that CUR and CEL could synergistically prevent peritendinous adhesion. More interestingly, the multicomponent EPM was able to react with the local oxidative stress, leading to a smart and sustained behavior of releasing approximately 80% of the drug within 20days. Overall, the smart multicomponent EPM offers a promising barrier strategy to prevent peritendinous adhesion.