Stochastic Equilibrium Research Articles

Day-to-day dynamic traffic evolution in the urban traffic system with ride-sharing

The introduction of ride-sharing services has significantly diversified commuting options for urban residents. In multi-mode cities, residents select travel modes based on their perception of the costs for various available options, while these perceptions are updated daily. As a result, residents’ travel mode choices and mode-split traffic flows vary day by day. To capture the nonlinear evolution phenomenon of their mode choice behaviors and mode-split traffic flows, we focus on a linear monocentric city with the introduction of ride-sharing services and develop a deterministic discrete-time day-to-day dynamic evolution model. Our model incorporates residents’ limited perceptions to better reflect real-world scenarios. Moreover, considering one ride-sharing driver is allowed to pick up multiple passengers, specific constraints on the number of ride-sharing drivers and passengers (i.e., side constraints) are added to the model formulation. Thus, the proposed model is a discrete-time day-to-day dynamic asymmetric stochastic user equilibrium model with side constraints, which have rarely been studied. The uniqueness of optimal Lagrange multipliers corresponding to side constraints in the day-to-day dynamic evolution model is demonstrated, which makes us successfully extend related literature on static ride-sharing equilibrium to the study of dynamic stochastic ride-sharing user equilibrium problems. Furthermore, we consider the stability issue of the equilibrium and provide sufficient and necessary conditions for its asymptotic stability. Finally, numerical examples are conducted to validate the properties and effectiveness of our dynamic model.

Optimization of the power–transportation coupled power distribution network based on stochastic user equilibrium

With the increasing penetration of electric vehicles (EVs) in road traffic, the spatial and temporal stochasticity of the travel pattern and charging demand of EVs as a mode of transportation and an electrical load have generated different degrees of congestion impacts on both the power grid and the transportation network. Based on this, this paper proposes a power–transportation-coupled distribution network optimization strategy based on stochastic user traffic equilibrium theory. First, a stochastic user equilibrium-mixed traffic flow allocation model that expresses user non-completely rational path selection behavior is established, and the traffic flow equilibrium solution is obtained using an improved method of successive algorithm and mapped to charging loads. Second, a distribution network power flow optimization model under the coupled power–transportation architecture is established to optimize the operation state of the distribution network by combining distributed resources such as energy storage, demand response loads, wind power, photovoltaic, and gas turbines.

Energy and productivity-based theory of cycle and crisis: the monistic approach of Vladimir Bazarov (1874–1939)

Vladimir Bazarov (1874–1939) tried to construct a monistic theory of cycles and crises on the basis of energy. His analysis of energy principles leads him, in a second step, to put the emphasis on productive forces and labour productivity, whose behaviour plays a determining role in the manifestation of both the cycle and the crisis. Finally, in empirical and statistical terms, the dynamics of labour productivity and of most of the economic series in Bazarov’s model are considered to be the result of a moving stochastic equilibrium (different from the purely mechanic dynamic equilibrium).

A stochastic ridesharing user equilibrium model with origin-destination-based ride-matching strategy

Ridesharing, as an emerging mode of modern urban transportation, has gained widespread popularity due to its ability to improve convenience and reduce the expenses in daily travel. To capture its impact on the network-wide traffic flow pattern, this paper develops a new variational inequality (VI) formulation for modeling the stochastic ridesharing user equilibrium (SRUE) problem considering an origin–destination (O-D) -based ride-matching strategy. The proposed SRUE problem is formulated based on a hierarchical logit choice model to depict the multi-stage decision-making (i.e., role choice, ride-matching, and route choice) of the ridesharing travelers. The SRUE model also reflects a two-sided market equilibrium considering the interaction effect between the ridesharing market and the road traffic equilibrium market. The logit choice model captures the ride-matching problem between the drivers and the passengers traveling on the same/different O-D pairs. Moreover, the lower- and upper-bound constraints for a ridesharing driver picking up passengers are established at the O-D level. For solving the SRUE model with O-D-based ride-matching constraints, the Lagrangian dual method (LDM) is adopted by incorporating the Barzilai-Borwein (BB) step size to update the dual variables, which accelerates the convergence of the LDM. Three numerical examples are conducted to illustrate the features of the proposed SRUE model and demonstrate the performance of the solution algorithm.

Deployment Optimization of Roadside Unit With Failure Probability Based on Stochastic Mixed Traffic Equilibrium

Deployment Optimization of Roadside Unit With Failure Probability Based on Stochastic Mixed Traffic Equilibrium

Dynamic characteristics of expectations of short-term interest rate and a generalized Vasicek model

This study's principal mathematical deduction exploits the importance of the specification of long-term equilibrium level in the mean-reversion short-term interest rate model—such as the CKLS (Chan, Karolyi, Longstaff, and Sanders) model—to describe the dynamic characteristics of future short-term interest rate expectations, especially long-horizon expectations. Therefore, we present a preferred model by introducing a stochastic long-run equilibrium level factor to extend the specifications of the Vasicek model's short-term interest rate dynamics. Using this new type of short-term interest rate as a driver we develop a two-factor affine arbitrage-free model of term structure, the generalized Vasicek mode. The empirical results show that the model not only has a good sample fitting ability to the Chinese government bond yield curve, but also has better performance in capturing the dynamic characteristics of short-term interest rates and short-term interest rate expectations. This study provides not only a promising avenue for future research on improving interest rate modeling techniques and their practical applications in the financial industry but also a new literature base for accurately identifying public expectations and explaining the underlying mechanisms of expectation changes.

ANALYTICALLY PRICING EUROPEAN OPTIONS UNDER A TWO-FACTOR STOCHASTIC INTEREST RATE MODEL WITH A STOCHASTIC LONG-RUN EQUILIBRIUM LEVEL

AbstractWe construct a new stochastic interest rate model with two stochastic factors, by introducing a stochastic long-run equilibrium level into the Vasicek interest rate model which follows another Ornstein–Uhlenbeck process. With the interest rate under the Black–Scholes model being assumed to follow the newly proposed model, a closed-form representation of European option prices is successfully presented, when the analytical characteristic function of the underlying log-price under a forward measure is derived. To assess the model performance, a preliminary empirical study is conducted using S&P 500 index and its options, with the Vasicek model and an alternative two-factor Vasicek model taken as benchmarks.

Stochastic Modeling of Star Formation Histories. III. Constraints from Physically Motivated Gaussian Processes

Galaxy formation and evolution involve a variety of effectively stochastic processes that operate over different timescales. The extended regulator model provides an analytic framework for the resulting variability (or “burstiness”) in galaxy-wide star formation due to these processes. It does this by relating the variability in Fourier space to the effective timescales of stochastic gas inflow, equilibrium, and dynamical processes influencing giant molecular clouds' creation and destruction using the power spectral density (PSD) formalism. We use the connection between the PSD and autocovariance function for general stochastic processes to reformulate this model as an autocovariance function, which we use to model variability in galaxy star formation histories (SFHs) using physically motivated Gaussian processes in log star formation rate (SFR) space. Using stellar population synthesis models, we then explore how changes in model stochasticity can affect spectral signatures across galaxy populations with properties similar to the Milky Way and present-day dwarfs, as well as at higher redshifts. We find that, even at fixed scatter, perturbations to the stochasticity model (changing timescales vs. overall variability) leave unique spectral signatures across both idealized and more realistic galaxy populations. Distributions of spectral features including Hα and UV-based SFR indicators, Hδ and Ca H and K absorption-line strengths, D n (4000), and broadband colors provide testable predictions for galaxy populations from present and upcoming surveys with the Hubble Space Telescope, James Webb Space Telescope, and Nancy Grace Roman Space Telescope. The Gaussian process SFH framework provides a fast, flexible implementation of physical covariance models for the next generation of spectral energy distribution modeling tools. Code to reproduce our results can be found at https://github.com/kartheikiyer/GP-SFH.

Congestion Risk, Transmission Rights, and Investment Equilibria in Electricity Markets

Financial instruments that help provide revenue certainty are fundamental for project finance in liberalized electricity markets. Improved management of locational risk caused by network congestion is becoming increasingly important with a growing share of production from geographically remote renewable resources. Nodal markets have financial transmission rights (FTRs) to enable participants to manage locational risk, but there is no evidence that FTRs have been used to support project finance. Through a stochastic equilibrium model in which market participants invest in production assets and trade risk, we show that long-term FTRs promote surplus-maximizing generation investments and reduce the cost of capital. Investors pair them with energy price hedges and thus protect themselves against both types of risk. Our results suggest that altering the definition and allocation of FTRs to match the needs of project finance, e.g., by enabling new generators to procure a long-term right at the time of interconnection, could help ensure a complete risk market and encourage efficient investments.

Stochastic equilibrium solution for a debt management problem with currency devaluation

Stochastic equilibrium solution for a debt management problem with currency devaluation

Analytical formulae for variance and volatility swaps with stochastic volatility, stochastic equilibrium level and regime switching

<p>The CIR stochastic volatility model is modified to introduce nonlinear mean reversion, with the long-run volatility average as a random variable controlled by two parts being modeled through a Brownian motion and a Markov chain, respectively. This model still possesses an analytical formulation of the forward characteristic function, from which we establish variance swap prices as well as volatility swap ones with a nonlinear payoff in closed form. The numerical implementation of the two formulae demonstrates the significant impact of regime switching.</p>

Container shipping: A market equilibrium perspective on freight rates formation post-Covid-19

The unprecedented container shipping freight rate levels post-Covid-19 are studied in a stochastic dynamic partial equilibrium framework. The proposed container marked model is calibrated on annual aggregate data from the two recent decades. The observed freight rate levels in 2021 and 2022 match a switch of competitive equilibria from Bertrand to Cournot competition. Whereas increased costs and reduced productivity play a role in explaining freight rates, these factors alone appear not to be able to justify the high post-Covid-19 freight rate levels.

Spatial stochastic D-RBA and limit equilibrium analysis of unreinforced masonry pier-spandrel structures

This study investigates the effect of spatially varying material properties on the in-plane seismic behaviour and capacity of an unreinforced pier-spandrel masonry system. The discontinuous nature of masonry is represented via a system of rigid blocks that can mechanically interact with each other along their boundaries. In the discontinuous modelling strategy, denoted as discrete rigid block analysis (D-RBA), deformations are lumped at the joints, and masonry units are replicated using two rigid blocks with a potential crack plane using the discrete element method (DEM). The obtained collapse mechanisms are automatically classified into two main categories via an algorithm processing the results of D-RBA. The adopted methodology offers a robust and time-efficient categorization of different collapse modes obtained from the computational model, which is required for better understanding the possible mechanisms developing in pier-spandrel structures and their occurrence rate. Accordingly, the most recurrent failure mechanisms are further investigated via upper- and lower-bound theorems of limit equilibrium analysis (LEA) by adopting an ad hoc coded optimization algorithm to ensure the solution's uniqueness. The results show that the DEM-based modelling approach provides a comprehensive understanding of the structural behaviour and capacity of pier-spandrel systems subjected to in-plane lateral loads. Further, the proposed probabilistic assessment workflow offers a broader perspective than deterministic analysis.

Static homotopy response analysis of structure with random variables of arbitrary distributions by minimizing stochastic residual error

The modelling of realistic engineering structures with uncertainties often involves various probabilistic distribution types, which bring forward higher requirements for the generality of stochastic analysis methods. This paper proposes a novel stochastic homotopy method to evaluate the static response of the structure with random variables of arbitrary distributions. In this method, a homotopy series expansion is used to approximate the stochastic static response, and the optimal form of the expansion can be determined by minimizing the residual error about the stochastic static equilibrium equation regardless of distribution types of random variables. The numerical results of a logarithmic function and a thin plate show that the new method exhibits excellent accuracy and stability compared to the homotopy stochastic finite element method depending on the sample selection. Compared with the arbitrary polynomial chaos method (aPC), the proposed method is more efficient under equivalent accuracy. On the other hand, as the expansion order increases, this new method shows better convergence than the aPC method and the perturbation stochastic finite element method in the case of non-Gaussian distributed random variables of large fluctuation. In addition, a cable-stayed bridge example illustrates the application of the proposed method on the large-scale structure.

Beyond capacity: Contractual form in electricity reliability obligations

Liberalized electricity markets often include resource adequacy mechanisms that require consumers to contract with generation resources well in advance of real-time operations. While administratively defined mechanisms have most commonly taken the form of a capacity obligation, efficient markets would feature a broad array of arrangements adapted to the risk profiles and appetites of market participants. This article considers how the financial hedge embedded in alternative resource adequacy contract designs can induce different responses from risk-averse investors, with consequences for the resource mix and market structure. We construct a stochastic equilibrium model describing a competitive market with incomplete risk trading and compute investment equilibria under different contracting regimes. Two policy recommendations result. First, to avoid creating inefficiency by crowding out other forms of risk sharing, system operators should allow resources contracted through other means to opt out of mandatory capacity mechanisms, with their contribution to those requirements subtracted from administratively defined demand curves. Second, if they wish to promote a single contractual form, regulators should consider replacing existing option-like capacity mechanisms with a shaped forward contract for energy. Beyond these recommendations, we discuss the tension that liberalized systems face in seeking to promote both reliability and competitive outcomes.

Treatment effect models with strategic interaction in treatment decisions

This study considers treatment effect models in which others’ treatment decisions can affect both one’s own treatment and outcome. Focusing on the case of two-player interactions, we formulate treatment decision behavior as a complete information game with multiple equilibria. Using a latent index framework and assuming a stochastic equilibrium selection, we prove that the marginal treatment effect from one’s own treatment and that from the partner are identifiable on the conditional supports of certain threshold variables determined through the game model. Based on our constructive identification results, we propose a two-step semiparametric procedure for estimating the marginal treatment effects using series approximation. We show that the proposed estimator is uniformly consistent and asymptotically normally distributed. As an empirical illustration, we investigate the impacts of risky behaviors on adolescents’ academic performance.

Contaminated water and the Food Safety Modernization Act

AbstractWe develop a theoretical framework and present a corresponding empirical analysis of the Food and Drug Administration’s irrigation water quality regulatory standard under the Food Safety Modernization Act using lettuce as a case study. We develop a stochastic price endogenous partial equilibrium model with recourse to examine the standard’s efficacy under various scenarios of foodborne illness severity, standard implementation, demand response to foodborne outbreaks, and irrigation costs. The stringency of regulation is evaluated with endogenous producer response to regulatory requirements and corresponding implications for economic surplus. The baseline results show that in the case of the lettuce market, the proposed microbial irrigation water quality regulation in the Food Safety Modernization Act (FSMA) is not cost effective relative to the existing Leafy-Greens Marketing Agreements relying on water treatment for mitigation of microbial contamination. However, FSMA can be cost effective if water treatment is sufficiently expensive.

A climate–economy model in a stochastic differential equilibrium with fractional Brownian motions and Poisson jumps

A climate–economy model in a stochastic differential equilibrium with fractional Brownian motions and Poisson jumps

A recursive stochastic transit equilibrium model estimated using passive data from Santiago, Chile

A strategic public transport equilibrium model is developed that considers each user's trip decision, covering the choices of access stop, mode and line, alighting stop, and transfer or egress. At each stage, these choices are considered to be stochastic and made under capacity constraints resulting in waiting time increases at stops and stations due to demand levels and/or arriving vehicle loads. The modeling strategy is based on the hyper-path concept, but rather than evaluate user strategies, the approach models transitions at all individual nodes, thus facilitating computational efficiency. In this approach, we develop a recursive method different from resolving explicitly a recursion based on Bellman´s equation, which is suitable for large and dense transit networks. A method is presented for estimating the model parameters, which was applied to the real case of the Santiago, Chile transit system based on passive transaction datasets generated by users’ smart cards and GPS technology aboard the system's buses. These data were used to estimate alighting stops and an exhaustive and disaggregate reconstruction of all user trips. Once calibrated, the model proved able to predict the trip assignments observed in the calibration dataset as well as datasets from later periods, making predictions that closely fit the observations and adapting well to changes in network topology, operating patterns, and user demand. Therefore, the model should have considerable potential as a powerful, flexible, and highly useful tool for system regulators and operators who define public transport structures, operations, and policies.

Integrated deployment of dedicated lane and roadside unit considering uncertain road capacity under the mixed-autonomy traffic environment

The rapid development of automated vehicle (AV) technologies enables us to explore how to update the urban road infrastructure to cater for the upcoming mixed-autonomy traffic with both AVs and human-driven vehicles (HVs). In this study, we aim to seek an optimal solution to integrate the deployment of AV-dedicated lane and roadside unit assisting automated driving subject to a limited budget by considering the route choice behaviors of AVs and HVs. An AV-dedicated lane segregates AVs from the mixed traffic to create a fully automated driving environment and eliminate disturbances from HVs. The deployment of roadside units assisting automated driving could overcome the connectivity gap for AVs and lower their headway when they follow an HV. We seek to develop a robust and optimal integrated deployment solution that accommodates the uncertain road capacity caused by the stochastic mixed AV and HV fleet sequence. We first establish the stochastic network equilibrium conditions for the mixed traffic, and formulate the integrated deployment problem as a mathematical program with complementarity constraints (MPCC). The MPCC is approximated by a mixed-integer linear programing (MILP) model, which allows existing algorithms for its global optimum. We further develop two interesting strategies, including domain reduction and breakpoint selection, to enhance the effectiveness of the MILP model. Numerical experiments are finally carried out to evaluate the feasibility of research methodology proposed in this study and find some valuable insights.