Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

The achievable region approach to the optimal control of stochastic systems

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances(the achievable region) of the system of interest, and (ii) optimisingthe overall system-wide performance objective over this space. This isradically different from conventional formulations based on dynamicprogramming. The approach is explained with reference to a simpletwo-class queueing system. Powerful new methodologies due to the authorsand co-workers are deployed to analyse a general multiclass queueingsystem with parallel servers and then to develop an approach to optimalload distribution across a network of interconnected stations. Finally,the approach is used for the first time to analyse a class of intensitycontrol problems.

Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance

In this paper, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non-homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

The Limits of Discrete Time Repeated Games:Some Notes and Comments

This paper studies the limits of discrete time repeated games with public monitoring. We solve and characterize the Abreu, Milgrom and Pearce (1991) problem. We found that for the "bad" ("good") news model the lower (higher) magnitude events suggest cooperation, i.e., zero punishment probability, while the highrt (lower) magnitude events suggest defection, i.e., punishment with probability one. Public correlation is used to connect these two sets of signals and to make the enforceability to bind. The dynamic and limit behavior of the punishment probabilities for variations in ... (the discount rate) and ... (the time interval) are characterized, as well as the limit payo¤s for all these scenarios (We also introduce uncertainty in the time domain). The obtained ... limits are to the best of my knowledge, new. The obtained ... limits coincide with Fudenberg and Levine (2007) and Fudenberg and Olszewski (2011), with the exception that we clearly state the precise informational conditions that cause the limit to converge from above, to converge from below or to degenerate. JEL: C73, D82, D86. KEYWORDS: Repeated Games, Frequent Monitoring, Random Pub- lic Monitoring, Moral Hazard, Stochastic Processes.

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

Optimal feedback control rules sensitive to controlled endogenous risk-aversion

The objective of this paper is to correct and improve the results obtained by Van der Ploeg (1984a, 1984b) and utilized in the theoretical literature related to feedback stochastic optimal control sensitive to constant exogenous risk-aversion (see, Jacobson, 1973, Karp, 1987 and Whittle, 1981, 1989, 1990, among others) or to the classic context of risk-neutral decision-makers (see, Chow, 1973, 1976a, 1976b, 1977, 1978, 1981, 1993). More realistic and attractive, this new approach is placed in the context of a time-varying endogenous risk-aversion which is under the control of the decision-maker. It has strong qualitative implications on the agent's optimal policy during the entire planning horizon.

Revenue management under general discrete choice model of consumer behavior

Customer choice behavior, such as 'buy-up' and 'buy-down', is an importantphe-nomenon in a wide range of industries. Yet there are few models ormethodologies available to exploit this phenomenon within yield managementsystems. We make some progress on filling this void. Specifically, wedevelop a model of yield management in which the buyers' behavior ismodeled explicitly using a multi-nomial logit model of demand. Thecontrol problem is to decide which subset of fare classes to offer ateach point in time. The set of open fare classes then affects the purchaseprobabilities for each class. We formulate a dynamic program todetermine the optimal control policy and show that it reduces to a dynamicnested allocation policy. Thus, the optimal choice-based policy caneasily be implemented in reservation systems that use nested allocationcontrols. We also develop an estimation procedure for our model based onthe expectation-maximization (EM) method that jointly estimates arrivalrates and choice model parameters when no-purchase outcomes areunobservable. Numerical results show that this combined optimization-estimation approach may significantly improve revenue performancerelative to traditional leg-based models that do not account for choicebehavior.

Vintage capital growth theory: three breakthroughs

Vintage capital growth models have been at the heart of growth theory in the 60s. This research line collapsed in the late 60s with the so-called embodiment controversy and the technical sophisitication of the vintage models. This paper analyzes the astonishing revival of this literature in the 90s. In particular, it outlines three methodological breakthroughs explaining this resurgence: a growth accounting revolution, taking advantage of the availability of new time series, an optimal control revolution allowing to safely study vintage capital optimal growth models, and a vintage human capital revolution, along with the rise of economic demography, accounting for the vintage structure of human capital similarly to physical capital age structuring. The related literature is surveyed.

Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

On the throughput-WIP trade-off in queueing systems, diminishing returns and the threshold property: A linear programming approach

We present a new unifying framework for investigating throughput-WIP(Work-in-Process) optimal control problems in queueing systems,based on reformulating them as linear programming (LP) problems withspecial structure: We show that if a throughput-WIP performance pairin a stochastic system satisfies the Threshold Property we introducein this paper, then we can reformulate the problem of optimizing alinear objective of throughput-WIP performance as a (semi-infinite)LP problem over a polygon with special structure (a thresholdpolygon). The strong structural properties of such polygones explainthe optimality of threshold policies for optimizing linearperformance objectives: their vertices correspond to the performancepairs of threshold policies. We analyze in this framework theversatile input-output queueing intensity control model introduced byChen and Yao (1990), obtaining a variety of new results, including (a)an exact reformulation of the control problem as an LP problem over athreshold polygon; (b) an analytical characterization of the Min WIPfunction (giving the minimum WIP level required to attain a targetthroughput level); (c) an LP Value Decomposition Theorem that relatesthe objective value under an arbitrary policy with that of a giventhreshold policy (thus revealing the LP interpretation of Chen andYao's optimality conditions); (d) diminishing returns and invarianceproperties of throughput-WIP performance, which underlie thresholdoptimality; (e) a unified treatment of the time-discounted andtime-average cases.

Insurance with frequent trading

This paper looks at the dynamic management of risk in an economy with discrete time consumption and endowments and continuous trading. I study how agents in such an economy deal with all the risk in the economy and attain their Pareto optimal allocations by trading in a few natural securities: private insurance contracts and a common set of derivatives on the aggregate endowment. The parsimonious nature ofthe implied securities needed for Pareto optimality suggests that insuch contexts complete markets is a very reasonable assumption.

Nonlinear chemoconvection in the Methylene-blue-glucose system

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue¿glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

An anonymous reputation mechanism for cloud computing networks using volunteer resources

One of the major problems when using non-dedicated volunteer resources in adistributed network is the high volatility of these hosts since they can go offlineor become unavailable at any time without control. Furthermore, the use ofvolunteer resources implies some security issues due to the fact that they aregenerally anonymous entities which we know nothing about. So, how to trustin someone we do not know?.Over the last years an important number of reputation-based trust solutionshave been designed to evaluate the participants' behavior in a system.However, most of these solutions are addressed to P2P and ad-hoc mobilenetworks that may not fit well with other kinds of distributed systems thatcould take advantage of volunteer resources as recent cloud computinginfrastructures.In this paper we propose a first approach to design an anonymous reputationmechanism for CoDeS [1], a middleware for building fogs where deployingservices using volunteer resources. The participants are reputation clients(RC), a reputation authority (RA) and a certification authority (CA). Users needa valid public key certificate from the CA to register to the RA and obtain thedata needed to participate into the system, as now an opaque identifier thatwe call here pseudonym and an initial reputation value that users provide toother users when interacting together. The mechanism prevents not only themanipulation of the provided reputation values but also any disclosure of theusers' identities to any other users or authorities so the anonymity isguaranteed.

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments