State-dependent Model Research Articles

Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion

When facing a multi-period defined contribution (DC) pension plan investment problem during the accumulation phase, the risk aversion attitude of a mean-variance investor may depend on state variables. In this paper, we propose a state-dependent risk aversion model which is a linear function of the current wealth level after contribution. This risk aversion model is reasonable from both the dimensional analysis and the economic point of view. Moreover, we incorporate the wage income factor into our model. In the field of dynamic investment analysis, most studies have irrational situations in their models because of the lack of the positiveness for the wealth process. In view of it, we further improve the work of Wang and Chen by completely eliminating the irrationality of the model. Due to the time-inconsistency of the resulting stochastic control problem, we derive the explicit expressions of the equilibrium control and the corresponding equilibrium value function by adopting the game theoretic framework developed in Björk and Murgoci. Further, two special cases are discussed. Finally, using a more realistic risk aversion coefficient, we provide a series of empirical tests based on the real data from the American market and compare our results with the relevant results in the literature.

A decision support tool for bi-objective risk-based maintenance scheduling of an LNG gas sweetening unit

PurposeThe purpose of this paper is to develop a decision support tool for risk-based maintenance scheduling for a large heavily equipped gas sweetening unit in a Liquefied Natural Gas (LNG) plant. Two conflicting objectives, i.e., total maintenance cost and the reliability, are considered in the tool. The tool is tested with the real plant data and suggests several Pareto-optimal schedules for a decision maker to choose from. The financial impacts are assessed.Design/methodology/approachA bi-objective scheduling optimization model is developed for maintenance scheduling using a risk-based framework. The model is developed integrating genetic algorithm and simulation-based optimization to find Pareto-optimal schedules. The model delivered true Pareto front optimal solutions for given plant-specific data. The two conflicting objectives: the minimization of total expenditures incurred on maintenance-related activities and improving the total reliability are considered.FindingsFor large and complex processing facilities such as LNG plant, a shutdown of facility generates a significant financial impact, resulting in millions of dollars in production loss. The developed risk-based equipment selection strategy helps to minimize such an event of production loss by generating a thorough maintenance strategy for inspection, repair, overhaul or replacement schedule of the unit without initiating the shutdown. The proposed model has been successfully applied to obtain an optimize maintenance schedule for a gas sweetening unit.Research limitations/implicationsA future work may consider the state-dependent models for various failure modes that will result in obtaining a better representation of the model. The proposed scheduling can further be extended to multi-criteria scheduling including availability, resource limitation and inflationary condition. A comparative analysis with other meta-heuristic techniques such as harmony search algorithm, tabu search, and simulated annealing will further help in confirming the schedule obtained from this application.Practical implicationsMaintenance scheduling using a conventional approach for special equipment generally does not consider the conflicting objectives. This research addresses this aspect using a bi-objective model. The usefulness of risk-based method is to assist in minimizing the financial and safety risk exposure to the operating companies, but some variation in results is expected due to varying risk matrix for different organizations.Social implicationsManaging two objectives, i.e., minimizing the cost of maintenance-related activities, while at the same time maximizing the overall reliability dramatically, helps in mitigating adverse safety and financial risk due to fires, explosions, fatality and excessive maintenance cost.Originality/valueResearch develops a decision support tool for managing conflicting objectives for an LNG process. This research highlights the impact of utilizing the simulation-based approach coupled with risk-based equipment selection for complex processing unit or plant maintenance scheduling optimization.

Monetary Policy Implications of State-Dependent Prices and Wages

We study the effects of monetary shocks in a model of state-dependent price and wage adjustment based on “control costs”. Suppliers of retail goods and of labor are both monopolistic competitors that face idiosyncratic productivity shocks and nominal rigidities. Stickiness arises because precise decisions are costly, so agents choose to tolerate small errors in the timing of adjustments. Our simulations are calibrated to microdata on the size and frequency of price and wage changes. Money shocks have less persistent real effects in our state-dependent model than they would a time-dependent framework, but nonetheless we obtain sufficient monetary nonneutrality for consistency with macroeconomic evidence. Nonneutrality is primarily driven by wage rigidity, rather than price rigidity. State-dependent nominal rigidity implies a flatter Phillips curve as trend inflation declines, because nominal adjustments become less frequent, making short-run inflation less reactive to shocks.

Modelling and Analysis of a Host‐Parasitoid Impulsive Ecosystem under Resource Limitation

With a long history of theoretical development, biological model has focused on the interaction of a parasitoid and its host. In this paper, two Nicholson‐Bailey models with a nonlinear pulse control strategy are proposed and analyzed to examine how limited resource affects the pest control. For a fixed‐time discrete impulsive model, the existence and stability of the host‐free periodic solution are derived. Threshold analysis suggests that it is critical to release parasitoid in an optimal number in case of the happening of the intra‐specific competition, which will seriously affect the pest control. Bifurcation analysis reveals that the model exists complex dynamics including period doubling, chaotic solutions, coexistence of multiple attractors, and so on. For a state‐dependent discrete impulsive model, the numerical simulations for bifurcation analysis are studied, the results show that how the key parameters and the initial densities of both populations affect the pest outbreaks, and consequently the relative biological implications with respect to pest control are discussed.

Monetary Policy Implications of State-Dependent Prices and Wages

This paper studies the dynamic general equilibrium effects of monetary shocks in a control cost model of state-dependent retail price adjustment and state-dependent wage adjustment. Suppliers of retail goods and of labor are both monopolistic competitors that face idiosyncratic productivity shocks and nominal rigidities. Stickiness arises because precise choice is costly: decision-makers tolerate errors both in the timing of adjustments, and in the new level at which the price or wage is set, because making these choices with perfect precision would be excessively costly. The model is calibrated to microdata on the size and frequency of price and wage changes. We find that the impact multiplier of a money growth shock on consumption and labor in our calibrated state-dependent model is similar to that in a Calvo model with the same adjustment frequencies, though the response is less persistent than it would be under the Calvo mechanism. Wage rigidity accounts for most of the nonneutrality that occurs in a model where both prices and wages are sticky; hence, a model with both rigidities produces substantially larger real effects of monetary shocks than does a model with sticky prices only. We find that the state-dependence of nominal rigidity strongly decreases the slope of the Phillips curve as trend inflation declines. This result is not driven by downward wage rigidity; adjustment costs are symmetric in our model. Here, instead, price- and wage-setters prefer to adjust less frequently when trend inflation is low, making short-run inflation less reactive to shocks.

A state dependent mandatory lane-changing model for urban arterials with hidden markov model method

The inherent intention and decision process of lane changes are complex. Though the external environment and traffic conditions are changing along the traveling direction, the drivers’ characteristics and preferences may lead to persistence of preferable lane choice. The lane-changing decision process is commonly separated into two steps after the decision to consider a lane change: lane choices and acceptance of available gaps, while the outcome of first step is unobservable. To better represent the mandatory lane-changing behaviors on arterials, a two-stage lane-changing model with Hidden Markov Model (HMM) method is proposed. The proposed model is estimated and validated using detail Next Generation Simulation (NGSIM) vehicle trajectory data from an urban arterial. Comparison between generated lane position sequences and original trajectories validated the model’s capability of representing mandatory lane changes.

Prediction of shear fracture in multi-stage deep drawing process including ironing process for Al3003 sheet

To predict fracture caused by both tensile and shearing stresses, we applied the GISSMO (generalized incremental stress state-dependent model) in conjunction with the TFD (triaxiality failure diagram) in the finite element (FE) software LS-DYNA. Required damage parameters were determined by fitting to the load-displacement curves from tensile tests necessary to set up the TFD those obtained by corresponding FE analyses. Curve fitting was performed using the optimum design tool LS-OPT. For validation, the obtained GISSMO damage parameters were applied to the problem of rectangular cup forming for Al3003 material. Good agreement between the numerically obtained fracture locus and that observed in real forming shows that accurate shear fracture prediction is possible with the presented GISSMO-based approach.

A state-dependent soil model and its application to principal stress rotation simulations

The plastic strain caused by principal stress rotation is one of the most important factors contributing to substantial deformation under earthquake, wave or traffic loading. The original Pastor–Zienkiewicz Mark III model, a well-known model for the analysis of the dynamic response under cyclic loading, is unable to consider the effects of principal stress orientation as well as state-dependent dilatancy. In this article, a new constitutive model for sand is developed to consider both aforementioned effects based on the original Pastor–Zienkiewicz Mark III model. There are 14 model parameters in total for the static condition and three extra parameters for cyclic loading, and a corresponding calibration method of model parameters is proposed. The predictive capability of the proposed model is verified with the results of a series of experiments on sand, including undrained monotonic tests in different fixed principal stress orientations and undrained cyclic rotational shear tests. The comparisons indicate that the proposed model can effectively incorporate the effects of principal stress orientation and state-dependent dilatancy.

Dynamics of a stage-structured single population model with state-dependent delay

In this paper, a novel stage-structured single population model with state-dependent maturity delay is formulated and analyzed. The delay is related to the size of population and taken as a non-decreasing differentiable bounded function. The model is quite different from previous state-dependent delay models in the sense that a correction term, 1-tau'(z(t))dot{z}(t), is included in the maturity rate. Firstly, positivity and boundedness of solutions are proved without additional conditions. Secondly, existence of all equilibria and uniqueness of a positive equilibrium are discussed. Thirdly, local stabilities of the equilibria are obtained. Finally, permanence of the system is analyzed, and explicit bounds for the eventual behaviors of the immature and mature populations are established.

Formability enhancement of EN AW-5182 H18 aluminum alloy sheet metal parts in a flash forming process: testing, calibration and evaluation of fracture models

Currently, it is state of the art to use precipitation hardening 6000-series aluminum alloys to manufacture high-strength aluminum automotive parts by extrusion or in a cold forming process. Alternatively, it is also possible to produce such parts by the use of non-precipitation hardening 5000-series aluminum alloys in a work-hardened condition. Therefore, BENTELER Automobiltechnik GmbH developed a special sheet forming process, henceforth referred to as “flash forming process”. The application of the flash forming process, consisting of a rapid heat treatment and a subsequent cold die stamping, increases the forming capability of the work-hardened 5000-series aluminum sheets and results in high-strength parts with a very good ductility and weldability. In addition, this thermal assisted forming process allows a cost-saving production of such high-strength aluminum parts due to lower material costs of 5000-series aluminum alloys than those of a 6000-series material. Furthermore, the weight-saving effects of “flash formed” parts can be higher compared to extruded or cold formed 6000-series aluminum alloys. The suitability of the process is evaluated by forming a commercial AW-5182 H18 aluminum sheet to a crash-relevant automotive part. However, to accurately simulate the flash forming process itself, a temperature dependent fracture model is necessary. Investigations on a coupon basis also showed that the effect of adiabatic heating due to plastic work cannot be neglected. In cooperation with Paderborn University, a detailed mechanical testing, aided by digital image correlation (DIC) and thermal imaging, is carried out to characterize the yield, hardening and fracture behavior at elevated temperatures. The experimental tests are followed by the calibration of a FLD and an incremental stress state dependent fracture model in LS-DYNA. Finally, the simulation models are validated on a cross die deep drawn cup.

A state-dependent model for assessing the population consequences of disturbance on income-breeding mammals

Human activities continue to expand in marine and terrestrial environments, leading to increased interactions with wildlife that can have negative impacts on population dynamics. Approaches for quantifying how these interactions translate to population-level effects are therefore crucial for effective management practices and balancing human-wildlife tradeoffs. We developed a method using state-dependent behavioral theory implemented via Stochastic Dynamic Programming (SDP) for predicting the population consequences of disturbance on the physiology and reproductive behavior of an income-breeding mammal, using California sea lions (Zalophus californianus) as a motivating species. Emergent properties of the model included reproductive characteristics associated with long-lived species, such as variation in the age at first reproduction, early termination of pregnancy, and skipped breeding. In undisturbed model simulations, reproductive rates and the average wean date were consistent with empirically-derived estimates from sea lions and other marine mammals, highlighting the utility of this model for quantifying fecundity estimates of data-deficient species and addressing fundamental ecological processes. In disturbed model simulations, exposure to prolonged, repetitive disturbances negatively impacted population growth; in addition, short, infrequent disturbances had the potential for adverse effects depending on the behavioral response of sea lions and the probability of being disturbed. The adverse effect of disturbance on population dynamics was due to a combination of reduced pup recruitment (survival to age one) resulting from a lower wean mass and increased abortion rates that led to skipped reproductive years, both of which have been documented for marine mammal populations experiencing natural fluctuations in prey availability. The derivation of state- and time-dependent reproductive decisions using an SDP model is an effective approach that links behavioral and energetic effects at the individual level to changes at the population level, and one that serves a dual purpose in the ability to quantify basic biological parameters and address ecological questions irrespective of disturbance.

A system of state-dependent delay differential equation modeling forest growth I: semiflow properties

In this article, we investigate the semiflow properties of a class of state-dependent delay differential equations which is motivated by some models describing the dynamics of the number of adult trees in forests. We investigate the existence and uniqueness of a semiflow in the space of Lipschitz and $$C^1$$ weighted functions. We obtain a blow-up result when the time approaches the maximal time of existence. We conclude the paper with an application of a spatially structured forest model.

Functional connectivity in ruminants: A generalized state-dependent modelling approach.

Animal behaviour is increasingly seen as an important component in maintaining functional connectivity between patches in fragmented landscapes. However, models that explicitly incorporate behavioural trade-offs are rarely applied to landscape planning problems like connectivity. The aim of this study was to explore how state-dependent behaviour influenced functional connectivity between patches from a theoretical perspective. We investigated how inter-patch distances influenced functional connectivity using a dynamic state variable model framework. The decision making process of an individual ruminant facing fitness trade-offs in staying in its patch of origin or moving to another patch at various distances were explicitly modelled. We incorporated energetic costs and predation costs of feeding, ruminating, and resting while in the patch and for transit between patches based on inter-patch distance. Functional connectivity was maintained with isolated patches when they offered high intake and the inactivity of rumination associated with rapid gut fill resulted in reduced predation risk. Nevertheless, individuals in high energetic state often would forgo moving to another patch, whereas individuals in poor energetic states were forced to accept the cost of movement to best meet their requirements in the distant patch. The inclusion of state-dependent behavioural models provides important insights into functional connectivity in fragmented landscapes and helps integrate animal behaviour into landscape planning. We discuss the consequences of our findings for landscape planning to show how the approach provides a heuristic tool to assess alternative scenarios for restoring landscape functional connectivity.

State-dependent Dilatancy Theory and Numerical Modelling of Rockfills

The dilatancy behavior of rockfills is relate to the stress level, the initial state and particle breakage. In this paper, based on the critical state theory, the state-dependent dilatancy theory of rockfills is established, and it is introduced into the state-dependent constitutive model of coarse materials, so the state-dependent constitutive model of rockfills is formulated. According to the large-scale triaxial testing results, using the Fortran program modelling the experimental results, then, comparing the test results and simulation results, only one set parameters of state-dependent constitutive model of rockfills can reflect the strain softening and dilatancy properties of rockfills under the condition of different density, gradation and confining pressure. Therefore, the rationality of the state-dependent constitutive model of rockfills is verified.

Implementation of state-dependent plasticity model in strain wedge model for laterally loaded piles in sand

ABSTRACTThe strain wedge model effectively performs nonlinear analyses of the lateral response of piles by using a nonlinear stress-strain relationship to describe soil behavior in the strain wedge. In this study, a state-dependent plasticity model has been implemented in the strain wedge model to calculate the stress-strain relationship for sand in the strain wedge. To complement this implementation, the effect of dilatancy on the shear strain is considered in the strain wedge. A full-scale test and a 45 g centrifuge model test on laterally loaded piles are used to validate the proposed method. The results show that the deflections and moments predicted by the proposed method accord well with those measured from full-scale and centrifugal model pile tests. Moreover, the combination of the state-dependent plasticity model and the strain wedge model allows for analyzing the lateral response of single piles using a unique set of model parameters for different relative densities of sands. In addtion, the stress-strain response in the strain wedge, not the dilatancy, dominates the soil resistance in the strain wedge and thus the lateral response of piles.

Ecological opportunity may facilitate diversification in Palearctic freshwater organisms: a case study on hydrobiid gastropods

BackgroundDifferences in species richness among phylogenetic clades are attributed to clade age and/or variation in diversification rates. Access to ecological opportunity may trigger a temporary increase in diversification rates and ecomorphological variation. In addition, lower body temperatures in poikilothermic animals may result in decreasing speciation rates as proposed by the metabolic theory of ecology. For strictly freshwater organisms, environmental gradients within a river continuum, linked to elevation and temperature, might promote access to ecological opportunity and alter metabolic rates, eventually influencing speciation and extinction processes. To test these hypotheses, we investigated the influence of environmental temperature and elevation, as proxies for body temperature and ecological opportunity, respectively, on speciation rates and ecomorphological divergence. As model systems served two closely related gastropod genera with unequal species richness and habitat preferences – Pseudamnicola and Corrosella.ResultsLineage-through-time plots and Bayesian macroevolutionary modeling evidenced that Pseudamnicola species, which typically live in lower reaches of rivers, displayed significantly elevated speciation rates in comparison to the ‘headwater genus’ Corrosella. Moreover, state-dependent speciation models suggested that the speciation rate increased with decreasing elevation, supporting the ecological opportunity hypothesis. In contrast, a significant effect of environmental temperature, as proposed by the metabolic theory of ecology, could not be observed. Disparity-through-time plots, models of ecomorphological evolution, and ancestral habitat estimation showed for Pseudamnicola species rapid morphological divergence shortly after periods of elevational and habitat divergence. In contrast, Corrosella species did not deviate from null models of drift-like evolution.ConclusionOur finding that speciation rates are correlated with elevation and ecomorphological disparity but not with environmental temperatures suggests that differences in ecological opportunity may have played a key role in Corrosella and Pseudamnicola diversifications. We propose that Pseudamnicola lineages experienced higher ecological opportunity through dispersal to new locations or habitats in lowlands, which may explain the increase in speciation rates and morphological change. In contrast, the evolution of Corrosella in headwaters is likely less facilitated by the environment and more by non-ecological processes.

Extended State Dependent Parameter modelling with a Data-Based Mechanistic approach to nonlinear model structure identification

A unified approach to Multiple and single State Dependent Parameter modelling, termed Extended State Dependent Parameters (ESDP) modelling, of nonlinear dynamic systems described by time-varying dynamic models applied to ARX or transfer-function model structures. Crucially, the approach proposes an effective model structure identification method using a novel Information Criterion (IC) taking into account model complexity in terms of the number of states involved. In ESDP, model structure involves not only the model orders, but also selection of the states driving the parameters, which effectively prevents the use of most current IC. This leads to a powerful methodology for investigating nonlinear systems building on the Data-Based Mechanistic (DBM) philosophy of Young and expanding the applications of the existing DBM methods. The methodologies presented are tested and demonstrated on both simulated data and on high frequency hydrological observations, showing how structure identification leads to discovery of dynamic relationships between system variables.

Time-Consistent Portfolio Policy for Asset-Liability Mean-Variance Model with State-Dependent Risk Aversion

In reality, when facing a multi-period asset-liability portfolio selection problem, the risk aversion attitude of a mean-variance investor may depend on the wealth level and liability level. Thus, in this paper, we propose a state-dependent risk aversion model for the investor, in which risk aversion is a linear function of current wealth level and current liability level. Due to the time inconsistency of the resulting multi-period asset-liability mean-variance model, we investigate its time-consistent portfolio policy by solving a nested mean-variance game formulation. We derive the analytical time-consistent portfolio policy, which takes a linear form of current wealth level and current liability level. We also analyze the influence of the risk aversion coefficients on the time-consistent portfolio policy and the investment performance via a numerical example.

State-dependent stochastic models: A general stochastic framework for modeling deteriorating engineering systems considering multiple deterioration processes and their interactions

For performance analysis of deteriorating engineering systems, it is critical to model and incorporate the various deterioration processes and associated uncertainties. This paper proposes state-dependent stochastic models (SDSMs) for modeling the impact of deterioration on the performance of engineering systems. Within the stochastic framework, the change of the system state variables due to different deterioration processes and their interaction is modeled explicitly. As a candidate model to be used in the framework, a new general age and state dependent stochastic model for gradual deterioration is proposed, and its calibration based on data is also discussed. Once the time-variant system state variables are modeled, proper capacity and demand models that take them as inputs can be adopted to fully capture the impact of deterioration processes on the capacity, demand, and other system performances. The proposed framework is first demonstrated through a simple example, and then is used to model the deterioration of an example reinforced concrete (RC) bridge considering deterioration caused by both corrosion and earthquake including their interaction. The results show the importance of modeling the interaction between different deterioration processes, and also verify the advantages of the proposed framework.

The Stochastic Queue Core problem, evacuation networks, and state-dependent queues

In this paper, we present the Stochastic Queue Core (SQC) model for network evacuation problems incorporating state-dependent queue roadway links. The roadway links are used to evacuate occupants so that the average travel time of the evacuation and the operating costs are minimized. Several algorithms are developed when there is blocking and where there is none. If there is significant blocking during the evacuation time, then the capacities of the roadway links are improved so as to alleviate the blocking. The computational complexity of the algorithms and numerical results are shown. We also compare and contrast the performance of the state dependent models with two well-known formulas for calculating the travel time of a vehicle along a network.