Arbitrary Horizon Research Articles

Proof of the generalized second law for rapidly changing fields and arbitrary horizon slices

The generalized second law is proven for semiclassical quantum fields falling across a causal horizon, minimally coupled to general relativity. The proof is much more general than previous proofs in that it permits the quantum fields to be rapidly changing with time, and shows that entropy increases when comparing any slice of the horizon to any earlier slice. The proof requires the existence of an algebra of observables restricted to the horizon, satisfying certain axioms (determinism, ultralocality, local Lorentz invariance, and stability). These axioms are explicitly verified in the case of free fields of various spins, as well as $1+1$ conformal field theories. The validity of the axioms for other interacting theories is discussed.

Insurance risk capital for the Sparre Andersen model with geometric Lévy stochastic returns

Some multi-period insurance risk economic capital models that include the effects of heavy-tail claims and random returns are considered. They are based on the Sparre Andersen risk model with geometric Levy stochastic returns. The random accumulated surplus over an arbitrary finite time horizon is decomposed into insurance risk, market risk and future profit components. A protection against the solvency risk of the policyholders is obtained by applying the VaR (CVaR) measure to the insurance risk component and defines a multi-period insurance risk VaR (CVaR) economic capital. A classical asymptotic result by Resnick and Willekens [28] on the tail probability of moving averages with random coefficients is applied to the accumulated aggregate claims random variable for claim size distributions with regularly varying tail to derive asymptotic formulas for these multi-period insurance risk economic capitals. Numerical examples with a Pareto claim size distribution reveal interesting features and differences between these two solvency rules. Since the preceding results exclude the log-normal and the heavy-tailed Weibull claim size distributions, we consider also an extension to sub-exponential claim sizes for the compound Poisson model with constant force of interest, which is based on Hao and Tang [12]. The obtained results are compared with the standard Solvency II specification of the non-life insurance risk.

Online planning for multi-agent systems with bounded communication

We propose an online algorithm for planning under uncertainty in multi-agent settings modeled as DEC-POMDPs. The algorithm helps overcome the high computational complexity of solving such problems offline. The key challenges in decentralized operation are to maintain coordinated behavior with little or no communication and, when communication is allowed, to optimize value with minimal communication. The algorithm addresses these challenges by generating identical conditional plans based on common knowledge and communicating only when history inconsistency is detected, allowing communication to be postponed when necessary. To be suitable for online operation, the algorithm computes good local policies using a new and fast local search method implemented using linear programming. Moreover, it bounds the amount of memory used at each step and can be applied to problems with arbitrary horizons. The experimental results confirm that the algorithm can solve problems that are too large for the best existing offline planning algorithms and it outperforms the best online method, producing much higher value with much less communication in most cases. The algorithm also proves to be effective when the communication channel is imperfect (periodically unavailable). These results contribute to the scalability of decision-theoretic planning in multi-agent settings.

No-hair theorems for black holes in the Abelian Higgs model

Motivated by the study of holographic superconductors, we generalize no-hair theorems for minimally coupled scalar fields charged under an Abelian gauge field, in arbitrary dimensions and with arbitrary horizon topology. We first present a straightforward generalization of no-hair theorems for neutral scalar hair. We then consider the existence of extremal black holes with scalar hair, and in the case of horizons with zero or positive curvature, provide a bound on the mass and charge of the scalar field that are necessary for the scalar hair to develop.

Multi-Agent Online Planning with Communication

We propose an online algorithm for planning under uncertainty in multi-agent settings modeled as DEC-POMDPs. The algorithm helps overcome the high computational complexity of solving such problems off-line. The key challenge is to produce coordinated behavior using little or no communication. When communication is allowed but constrained, the challenge is to produce high value with minimal communication. The algorithm addresses these challenges by communicating only when history inconsistency is detected, allowing communication to be postponed if necessary. Moreover, it bounds the memory usage at each step and can be applied to problems with arbitrary horizons. The experimental results confirm that the algorithm can solve problems that are too large for the best existing off-line planning algorithms and it outperforms the best online method, producing higher value with much less communication in most cases.

Analysis of Thermal Energy Storage for a Pharmaceutical CompanyAnalyse eines thermischen Energiespeichers für ein pharmazeutisches Unternehmen

Abstract A pharmaceutical facility located in Southern Germany is experiencing a trend of growing cooling loads to be met by the chilled water plant composed of ten chillers of greatly varying cost effectiveness. With a capacity shortfall inevitable, the question arises whether to install an additional chiller or improve the utilization of the existing chillers, in particular those with low operating costs per unit cooling, through the addition of a chilled water thermal energy storage (TES) system. To provide decision support in this matter, an optimization environment was developed and validated that adopts mixed integer programming as the approach to optimizing the chiller dispatch for any load condition, while an overarching dynamic programming based optimization approach optimizes the charge/discharge strategy of the TES system. In this fashion, the chilled water plant optimization is decoupled but embedded in the TES control optimization. The approach was selected to allow for arbitrary constraints and optimization horizons, while ensuring a global optimum to the problem. The results show that a relatively small TES tank provides significant economic and operational benefits. Yet, in order to facilitate long-term supply security, a larger TES tank capacity was decided on and the TES system was constructed in 2008.

Planning Horizon Procedures for Machine Replacement Models

This paper develops efficient forward algorithms and planning horizon results for several machine replacement models under an improving technological environment over time. The models are that of cost minimization, profit maximization, and cost minimization with probabilistic breakdowns. The conditions of the improving technological environment are stated in terms of operating costs, incremental profits, and expected operating costs, respectively, for these models. The state of technology can be assumed to improve every period or every so many periods. The conditions are fairly general and are likely to be satisfied by most improving technologies. What is shown, specifically, is that there exists a forecast horizon T such that the optimal replacement decision for the first machine (new or existing) based on the forecast of machine technology until period T remains optimal for any longer (than T) horizon, and for that matter, the infinite horizon problem. In particular, it is possible to decide whether it is optimal to replace an existing machine at the beginning of a period or keep it at least one more period with much less information than the entire future forecast of technology. It should be noted that the forecasts become less precise farther into the future and that requiring an infinite horizon forecast for decision-making would be unrealistic. Because the planning horizon results obtained in this paper free the solution from an arbitrary horizon and ascertain the optimality of the first period decision or the first few periods decisions based on the forecast of technology only up to some finite period T, these results represent a major advance in the machine replacement literature. These planning horizon results also enable us to develop a computationally highly efficient forward algorithm for the models under consideration. The algorithm is illustrated with a numerical example. Another important corollary of the planning horizon results is that the optimal number of machine replacements cannot decrease as the length of the horizon (planning period) increases. Planning horizon procedures are shown to be easily extendable to the existing machine case as well as the case when machine lives are constrained within a prespecified finite interval. The paper concludes with various suggestions for future research efforts.

News - Good or Bad - and its Impact Over Multiple Horizons

It is difficult to define news, and many definitions are model-based since part of what is announced is anticipated. Therefore, news is typically defined as a residual within the context of some type of prediction model, and the prediction model locks in the sampling frequency that is the reference time scale for analyzing propagation mechanisms. We try to accomplish two goals: (1) characterize news as much as possible as a model-free observation, and (2) measure the impact of news over any arbitrary horizon of interest. We revisit the concept of news impact curves introduced by Engle and Ng (1993), in the current high frequency data environment of financial market time series. Instead of taking a single horizon fixed parametric specification, we recast many of the original ideas in a very flexible multi-horizon semi-parametric setting. Technically speaking we introduce semi-parametric MIDAS regressions and study their asymptotic properties. The analysis relates to and extends recent work by Linton and Mammen (2005). In addition we also introduce various new parametric models. We find that moderately good (intra-daily) news reduces volatility (the next day), while both very good news (unusual high positive returns) and bad news (negative returns) increase volatility, with the latter having a more severe impact. The asymmetries we find have profound implications for current volatility prediction models that are based on in-sample asymptotic analysis developed over recent years. In this context we discuss the link between diffusions and news impact curves.

Conditions for optimality of Naïve quantized finite horizon control

This paper presents properties of a control law which quantizes the unconstrained solution to a unitary horizon quadratic programme. This naïve quantized control law underlies many popular algorithms, such as ΣΔ-converters and decision feedback equalities, and is easily shown to be globally optimal for horizon one. However, the question arises as to whether it is also globally optimal for horizons greater than one, i.e. whether it solves a finite horizon quadratic programme, where decision variables are restricted to belonging to a quantized set. By using dynamic programming, we develop sufficient conditions for this to hold. The present analysis is restricted to first order plants. However, this case already raises a number of highly non-trivial issues. The results can be applied to arbitrary horizons and quantized sets, which may contain a finite or an infinite (though countable) number of elements.

Solution of the input-constrained LQR problem using dynamic programming

The input-constrained LQR problem is addressed in this paper; i.e., the problem of finding the optimal control law for a linear system such that a quadratic cost functional is minimised over a horizon of length N subject to the satisfaction of input constraints. A global solution (i.e., valid in the entire state space) for this problem, and for arbitrary horizon N, is derived analytically by using dynamic programming. The scalar input case is considered in this paper. Solutions to this problem (and to more general problems: state constraints, multiple inputs) have been reported recently in the literature, for example, approaches that use the geometric structure of the underlying quadratic programming problem and approaches that use multi-parametric quadratic programming techniques. The solution by dynamic programming proposed in the present paper coincides with the ones obtained by the aforementioned approaches. However, being derived using a different approach that exploits the dynamic nature of the constrained optimisation problem to obtain an analytical solution, the present result complements the previous methods and reveals additional insights into the intrinsic structure of the optimal solution.

Modeling Expected Loss with Unobservable Heterogeneity

In this paper we model the expected loss over multi-year horizons. Investors usually have only incomplete information about the true state of a firm. To model this form of unobservable heterogeneity, we introduce a latent non-negative random variable into the model specification of the probability of default and the recovery rate. To estimate the expected loss over arbitrary horizons, we estimate the coefficients for the stochastic processes describing the covariates for the probability of default for each obligor and the loss given default. We provide an analysis of both in and out of sample performance of our estimates of the probability of default and the loss given default.

THE ROBUSTNESS OF INPUT CONSTRAINED MODEL PREDICTIVE CONTROL TO INFINITY-NORM BOUND MODEL UNCERTAINTY

The nonlinearity that arises in constrained MPC (model predictive control) satisfies an IQC (integral quadratic constraint), provided zero is feasible. It is thus possible to construct a robust stability test against any model uncertainty that also satisfies an IQC. In particular the test may be applied to structured and unstructured infinity-norm bound uncertainty. The test may be applied with predictive controllers of arbitrary horizon. The test is illustrated for several simple MPC schemes and simulation results are shown for a two-input two-output plant with left matrix fraction uncertainty.

Planning Horizon Procedures for Machine Replacement Models

This paper develops efficient forward algorithms and planning horizon results for several machine replacement models under an improving technological environment over time. The models are that of cost minimization, profit maximization, and cost minimization with probabilistic breakdowns. The conditions of the improving technological environment are stated in terms of operating costs, incremental profits, and expected operating costs, respectively, for these models. The state of technology can be assumed to improve every period or every so many periods. The conditions are fairly general and are likely to be satisfied by most improving technologies. What is shown, specifically, is that there exists a forecast horizon T such mat the optimal replacement decision for the first machine (new or existing) based on the forecast of machine technology until period T remains optimal for any longer (than T) horizon, and for that matter, the infinite horizon problem. In particular, it is possible to decide whether it is optimal to replace an existing machine at the beginning of a period or keep it at least one more period with much less information than the entire future forecast of technology. It should be noted that the forecasts become less precise farther into the future and that requiring an infinite horizon forecast for decision-making would be unrealistic. Because the planning horizon results obtained in this paper free the solution from an arbitrary horizon and ascertain the optimality of the first period decision or the first few periods decisions based on the forecast of technology only up to some finite period T, these results represent a major advance in the machine replacement literature. These planning horizon results also enable us to develop a computationally highly efficient forward algorithm for the models under consideration. The algorithm is illustrated with a numerical example. Another important corollary of the planning horizon results is that the optimal number of machine replacements cannot decrease as the length of the horizon (planning period) increases. Planning horizon procedures are shown to be easily extendable to the existing machine case as well as the case when machine lives are constrained within a prespecified finite interval. The paper concludes with various suggestions for future research efforts.

Selection and use of representative sites in a large neutron moisture meter network

The assessment of the representivity of individual sites in a large neutron moisture meter (NMM) network, and the errors incurred by selecting subsets of various sizes, and using different methods to estimate the full set value from the subsets, is described. Soil water data collected over 13 months from the NMM network (240 sites, divided into eight strata) were analysed to determine the relationship between individual sites and their stratum means. Relationships were assessed using the following four methods: (1) root mean square of the discrepancy; (2) linear regression; (3) quadratic regression; (4) power curve regression. Sites best related to their stratum means were then included in various size subsets, and estimates based on these subsets were compared with the respective full stratum means using 24 months' data. The best estimates of stratum means were obtained by using quadratic regressions and c. eight sites per subset. Using this method, the root mean square discrepancy between estimates of profile water content and observed full stratum means averaged 2.1 mm when the total profile was estimated directly and 2.5 mm when the profile water content was computed as the sum of individual estimates for four arbitrary horizons within the profile. Daily readings of one group of selected subsets indicated the potential of frequent NMM readings at key sites to indicate short-term changes in the soil water content of an area. The performance of the selected subsets has been monitored for a further 12 months as an independent check on their representivity. The root mean square discrepancy of estimates during that period was 2.7 mm. Subsequently only the selected eight sites in each stratum of the field study are being read on a routine basis.

Future Generations and the Social Rate of Discount

This paper reexamines the case for discounting for time in public investment appraisal where long-term or irreversible effects on future generations are involved. It is concluded that—while, in the short-term, considerations of equity reinforce the commonly advocated case for discounting for time—in evaluating long-term or irreversible effects, current discounting procedures require the doubtful assumption of perpetual exponential growth of real income. However, if discounting were abandoned, use of the standard cost—benefit-analysis framework would require the forecasting of shadow prices for all future dates, unless an arbitrary time horizon is adopted. Thus cost—benefit analysis does not appear to be a satisfactory method for evaluating effects on future generations.

Wealden petrology : The Top Ashdown Pebble Bed and the Top Ashdown Sandstone

Wealden petrology : The Top Ashdown Pebble Bed and the Top Ashdown Sandstone