Asset prices in affine real business cycle models

I describe a tractable way to study macroeconomic quantities and asset prices in a large class of dynamic stochastic general equilibrium models. The proposed approximate solution is analytical, log-linear, and adjusted for risk. Therefore, it is well suited to investigate economic mechanisms, describe the time series properties or estimate the model, and deal with stochastic volatility. I explain the pitfalls encountered by previous attempts to use simple approximation techniques, in particular with models featuring recursive preferences. Finally, I show the theoretical relationship between my solution and higher-order perturbation methods.     

Inequalities for the De Pril approximation to the distribution of the number of policies with claims

In the present paper, we give sufficient conditions for an ordering of De Pril approximations of the distribution of the number of claims in an insurance portfolio of independent policies. Possible extensions are discussed, both for the De Pril approximation and the Kornya approximation. A numerical example is given.     

Solving dynamic public insurance games with endogenous agent distributions: Theory and computational approximation

We make two contributions in this paper. First, we extend the characterization of equilibrium payoff correspondences in history-dependent dynamic policy games to a class with endogenously heterogeneous private agents. In contrast to policy games involving representative agents, this extension has interesting consequences as it implies additional nonlinearity (i.e., bilinearity) between the game states (distributions) and continuation/promised values in the policymaker’s objective and incentive constraints. The second contribution of our paper is in addressing the computational challenges arising from this payoff-relevant nonlinearity. Exploiting the game’s structure, we propose implementable approximate bilinear programming formulations to construct estimates of the equilibrium value correspondence. Our approximation method respects the property of upper hemicontinuity in the target correspondence. We provide small-scale computational examples as proofs of concept.     

Estimating demand with distance functions: Parameterization in the primal and dual

Our purpose is to investigate the ability of different parametric forms to ‘correctly’ estimate consumer demands based on distance functions using Monte Carlo methods. Our approach combines economic theory, econometrics and quadratic approximation. We begin by deriving parameterizations for transformed quadratic functions which are linear in parameters and characterized by either homogeneity or which satisfy the translation property. Homogeneity is typical of Shephard distance functions and expenditure functions, whereas translation is characteristic of benefit/shortage or directional distance functions. The functional forms which satisfy these conditions and include both first- and second-order terms are the translog and quadratic forms, respectively. We then derive a primal characterization which is homogeneous and parameterized as translog and a dual model which satisfies the translation property and is specified as quadratic. We assess functional form performance by focusing on empirical violations of the regularity conditions. Our analysis corroborates results from earlier Monte Carlo studies on the production side suggesting that the quadratic form more closely approximates the ‘true’ technology or in our context consumer preferences than the translog.     

Spanning with indexes

This paper presents several approximation theorems of a general contingent claim in terms of index options. We demonstrate that any contingent claim on the primitive securities in an infinite state economy can be approximated arbitrarily close by a portfolio of index options. In addition, these index options are associated with the same payout function, which belongs to a large and explicit class of one-variable measurable functions. I also characterize the layer structure of a general contingent claim.     

Heuristic Approximation to Cramér-von Mises Type Statistics

We derive a formal expansion for a distribution in terms of another distribution. As a particular case we get the formal Edgeworth expansion. The heuristic procedure that we present is used to obtain approximations for distribution functions of the Cramér-von Mises and Watson goodness-of-fit statistics. Finally we compare our results with some obtained in the literature.     

Approximation approach for the performance analysis of production lines under a kanban discipline

In a JIT production environment, pull-type control systems are usually implemented to reduce the lead time and to synchronize the production rate with the demand rate. The design of an effective production control system requires easy and reliable approaches for evaluating the effect of the major system parameters on its performance.In this paper we model the kanban control system of a manufacturing line as a Markov process. In addition, we develop an approximation approach to the model that permits reliable evaluation of manufacturing system performance in terms of throughput time and work-in-process. The validation of the approach is implemented by comparing the exact results (based on discrete event simulation) and the approximated results.A good approximation is observed for a large range of conditions.     

约略现象探析--对精确数字的模糊理解的思考

何自然(2000)将精确数字的模糊理解这类特殊的模糊现象称为“约略”,而该文章以国内外学者在这方面的研究为基础,从抽象与具体、深层与表层的相对立和联系的角度出发,将约略放在模糊的连续统内来加以考虑,提出了数字在抽象的系统层面无模糊、而在人类认知的经验内作为认知参考点精确性都具有相对性的观点；从模糊限制语的模糊连续性出发,提出了用空模糊限制语来代替“约略”的设想。     

Johnson's algorithm: A key to solve optimally or approximately flow shop scheduling problems with unavailability periods

Johnson's algorithm (JA) is perhaps the most classical algorithm in the scheduling area. JA gives the optimal solution to the two machine flow shop to minimize the makespan in polynomial time. Researchers have tried to extend this notorious result to obtain polynomial time algorithms for more general cases. Such importance motivated us to devote this paper to JA applied to three flow shop problems with unavailability periods to minimize the makespan. First we focus on the optimality condition of JA. Then we propose a modification of JA. After we calculate new performances of JA as a heuristic. Last we deal with an extension of JA.     

On irregular functionals of SDEs and the Euler scheme

We prove a sharp upper bound for the error $\mathbb {E}|g(X)-g(\hat{X})|^{p}We prove a sharp upper bound for the error in terms of moments of , where X and are random variables and the function g is a function of bounded variation. We apply the results to the approximation of a solution to a stochastic differential equation at time T by the Euler scheme, and show that the approximation of the payoff of the binary option has asymptotically sharp strong convergence rate 1/2. This has consequences for multilevel Monte Carlo methods. The author was supported by the Finnish Graduate School in Stochastics and Statistics, the Ellen and Artturi Nyyss?nen Foundation, and the Academy of Finland, project #110599.