Assessment of Seismic Loss Dependence Using Copula

The catastrophic nature of seismic risk is attributed to spatiotemporal correlation of seismic losses of buildings and infrastructure. For seismic risk management, such correlated seismic effects must be adequately taken into account, since they affect the probability distribution of aggregate seismic losses of spatially distributed structures significantly, and its upper tail behavior can be of particular importance. To investigate seismic loss dependence for two closely located portfolios of buildings, simulated seismic loss samples, which are obtained from a seismic risk model of spatially distributed buildings by taking spatiotemporally correlated ground motions into account, are employed. The characterization considers a loss frequency model that incorporates one dependent random component acting as a common shock to all buildings, and a copula‐based loss severity model, which facilitates the separate construction of marginal loss distribution functions and nonlinear copula function with upper tail dependence. The proposed method is applied to groups of wood‐frame buildings located in southwestern British Columbia. Analysis results indicate that the dependence structure of aggregate seismic losses can be adequately modeled by the right heavy tail copula or Gumbel copula, and that for the considered example, overall accuracy of the proposed method is satisfactory at probability levels of practical interest (at most 10% estimation error of fractiles of aggregate seismic loss). The developed statistical seismic loss model may be adopted in dynamic financial analysis for achieving faster evaluation with reasonable accuracy.     

Local Identification of Nonparametric and Semiparametric Models

In parametric, nonlinear structural models, a classical sufficient condition for local identification, like Fisher (1966) and Rothenberg (1971), is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We derive an analogous result for the nonparametric, nonlinear structural models, establishing conditions under which an infinite dimensional analog of the full rank condition is sufficient for local identification. Importantly, we show that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities overwhelming linear effects. We give restrictions on a neighborhood of the true value that are sufficient for local identification. We apply these results to obtain new, primitive identification conditions in several important models, including nonseparable quantile instrumental variable (IV) models and semiparametric consumption‐based asset pricing models.     

Assembly Systems with Sequential Supplier Decisions and Uncertain Demand

We consider multitier push assembly systems with sequential supplier decisions and a wholesale price contract. We show that both an Original Equipment Manufacturer (OEM)–Contract Manufacturer (CM) assembly and a modular assembly with sequential supplier decisions are mathematically equivalent to the corresponding traditional assembly. We determine that, in most cases, the first mover supplier realizes a higher profit than the second mover supplier but we also identify the sufficient conditions for the reverse to occur. We provide conditions under which the order quantity, the second mover profit, total supplier profits, and the assembler profit are either higher or lower for a multitier system with sequential suppliers compared to simultaneous suppliers. We conclude that the first mover is always better off in a three‐tier sequential system while she can be either better off or worse off in a four‐tier sequential system compared to the corresponding simultaneous systems. We also analyze the impact of information asymmetry on the supplier and assembler profits in a three‐tier sequential system. Finally, we determine the profit threshold for an independent manufacturer in a three‐tier system to become a CM in a four‐tier system and vice versa.     

Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited

A probability distribution governing the evolution of a stochastic process has infinitely many Bayesian representations of the form μ=∫μdλ(θ). Among these, a natural representation is one whose components ( μ's) are ‘learnable’ (one can approximate μ by conditioning μ on observation of the process) and ‘sufficient for prediction’ (μ's predictions are not aided by conditioning on observation of the process). We show the existence and uniqueness of such a representation under a suitable asymptotic mixing condition on the process. This representation can be obtained by conditioning on the tail-field of the process, and any learnable representation that is sufficient for prediction is asymptotically like the tail-field representation. This result is related to the celebrated de Finetti theorem, but with exchangeability weakened to an asymptotic mixing condition, and with his conclusion of a decomposition into i.i.d. component distributions weakened to components that are learnable and sufficient for prediction.     

Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices

In dynamic discrete choice analysis, controlling for unobserved heterogeneity is an important issue, and finite mixture models provide flexible ways to account for it. This paper studies nonparametric identifiability of type probabilities and type‐specific component distributions in finite mixture models of dynamic discrete choices. We derive sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work under different assumptions on the Markov property, stationarity, and type‐invariance in the transition process. Three elements emerge as the important determinants of identification: the time‐dimension of panel data, the number of values the covariates can take, and the heterogeneity of the response of different types to changes in the covariates. For example, in a simple case where the transition function is type‐invariant, a time‐dimension of T = 3 is sufficient for identification, provided that the number of values the covariates can take is no smaller than the number of types and that the changes in the covariates induce sufficiently heterogeneous variations in the choice probabilities across types. Identification is achieved even when state dependence is present if a model is stationary first‐order Markovian and the panel has a moderate time‐dimension (T 6).     

Cross‐Section Regression with Common Shocks

This paper considers regression models for cross‐section data that exhibit cross‐section dependence due to common shocks, such as macroeconomic shocks. The paper analyzes the properties of least squares (LS) estimators in this context. The results of the paper allow for any form of cross‐section dependence and heterogeneity across population units. The probability limits of the LS estimators are determined, and necessary and sufficient conditions are given for consistency. The asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling. The t, Wald, and F statistics are found to have asymptotic standard normal, χ², and scaled χ² distributions, respectively, under the null hypothesis when the conditions required for consistency of the parameter under test hold. However, the absolute values of t, Wald, and F statistics are found to diverge to infinity under the null hypothesis when these conditions fail. Confidence intervals exhibit similarly dichotomous behavior. Hence, common shocks are found to be innocuous in some circumstances, but quite problematic in others. Models with factor structures for errors and regressors are considered. Using the general results, conditions are determined under which consistency of the LS estimators holds and fails in models with factor structures. The results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units.     

Changing default risk dependencies during the subprime crisis: DJ iTraxx subindices and goodness-of-fit-testing for copulas

This paper tests whether (and to what extent) default risk dependencies changed during the subprime crisis in 2007 and 2008. This is done by applying a Goodness-of-fit test, based on the Rosenblatt transformation, to test various null hypotheses with respect to the copula function that describes the stochastic dependence between daily returns of six sector-specific subindices of the Dow Jones iTraxx Credit Default Swap index for Europe. Overall, the results suggest that in the bivariate case, the t-copula is a better approximation to the true copula of returns of DJ iTraxx subindices than the normal copula or the generalized Clayton copula. On average, the number of degrees of freedom of the bivariate t-copula tends to decrease during the crisis. As expected, the correlation between the returns of the subindices increases significantly during the crisis. However, the multivariate analysis reveals that it is only before the crisis that the null hypothesis of a six-dimensional t-copula is not rejected. During the crisis, the multivariate stochastic dependence between the sector-specific DJ iTraxx subindices seems to change in such a complex way that it is no longer sufficiently described by a multivariate t-copula.     

Semi‐Nonparametric IV Estimation of Shape‐Invariant Engel Curves

This paper studies a shape‐invariant Engel curve system with endogenous total expenditure, in which the shape‐invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric Engel curves. We focus on the identification and estimation of both the nonparametric shapes of the Engel curves and the parametric specification of the demographic scaling parameters. The identification condition relates to the bounded completeness and the estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions, allowing for endogeneity. We establish a new root mean squared convergence rate for the nonparametric instrumental variable regression when the endogenous regressor could have unbounded support. Root‐n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of “low‐level” sufficient conditions. Our empirical application using the U.K. Family Expenditure Survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of Engel curves.     

Modeling Correlated Discrete Uncertainties in Event Trees with Copulas

Modeling the dependence between uncertainties in decision and risk analyses is an important part of the problem structuring process. We focus on situations where correlated uncertainties are discrete, and extend the concept of the copula‐based approach for modeling correlated continuous uncertainties to the representation of correlated discrete uncertainties. This approach reduces the required number of probability assessments significantly compared to approaches requiring direct estimates of conditional probabilities. It also allows the use of multiple dependence measures, including product moment correlation, rank order correlation and tail dependence, and parametric families of copulas such as normal copulas, t‐copulas, and Archimedean copulas. This approach can be extended to model the dependence between discrete and continuous uncertainties in the same event tree.     

融资融券制度对尾部系统风险的非对称影响——基于A股市场极值相关性的研究

融资融券交易制度的推出能否有效降低个股随市场暴涨暴跌的概率是广泛关注的问题.文章利用Patton提出的SJC Copula函数, 估计了个股与大市尾部相关性, 并使用双重差分法分析了融资融券交易制度推出的政策处置效应, 发现融资融券制度降低了标的个股左尾 (下跌) 极值相关性, 但加剧了右尾 (上涨) 极值相关性.进一步分析表明, 上述结果来源于融资融券交易对极值相关性的非对称影响.具体而言, 融资交易对左尾极值相关性影响不显著, 但加剧了右尾极值相关性, 融券交易则同时显著降低了左尾和右尾极值相关性.由于融券交易规模远小于融资交易, 融资融券交易对左尾极值相关性的总体影响为负, 对右尾总体影响为正.研究结论认为, 融资交易追涨模式导致个股跟随大盘暴涨, 而融券交易将悲观交易者信息纳入股价, 有利于抑制股价过度上涨, 而逆向平仓也适当降低了个股暴跌概率.因此, 监管者应灵活控制融资交易杠杆, 完善融券交易机制以发挥其股价稳定器功能.     

Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain

We develop results for the use of Lasso and post‐Lasso methods to form first‐stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post‐Lasso in the first stage is root‐n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well‐approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic “beta‐min” conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso‐based IV estimator with a data‐driven penalty performs well compared to recently advocated many‐instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso‐based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post‐Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non‐Gaussian, heteroscedastic disturbances that uses a data‐weighted ℓ₁‐penalty function. By innovatively using moderate deviation theory for self‐normalized sums, we provide convergence rates for the resulting Lasso and post‐Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that logp = o(n^1/3). We also provide a data‐driven method for choosing the penalty level that must be specified in obtaining Lasso and post‐Lasso estimates and establish its asymptotic validity under non‐Gaussian, heteroscedastic disturbances.     

国际油气价格与汇率动态相依关系研究:基于一种新的时变最优Copula模型

本文提出一个新的时变最优Copula模型,可以准确识别二元时间序列任意时点最优的相依结构。该模型构造了半旋转copula以刻画非对称的反向相依关系,并引入独立性的无分布检验证实相依关系的存在性。同时,我们对能源商品市场（原油、天然气）、外汇市场间动态相依关系进行了实证分析,实证结果表明跨市场相依结构类型确实是时变的,突发事件往往是相依结构突变的主因。另外,时变最优Copula模型的主要优势在于不仅能够捕捉相依方向和相依强度的动态性,还能有效捕捉相依结构类型的动态性。     

Strong Duality for a Multiple‐Good Monopolist

We characterize optimal mechanisms for the multiple‐good monopoly problem and provide a framework to find them. We show that a mechanism is optimal if and only if a measure μ derived from the buyer's type distribution satisfies certain stochastic dominance conditions. This measure expresses the marginal change in the seller's revenue under marginal changes in the rent paid to subsets of buyer types. As a corollary, we characterize the optimality of grand‐bundling mechanisms, strengthening several results in the literature, where only sufficient optimality conditions have been derived. As an application, we show that the optimal mechanism for n independent uniform items each supported on [c,c+1] is a grand‐bundling mechanism, as long as c is sufficiently large, extending Pavlov's result for two items Pavlov, 2011. At the same time, our characterization also implies that, for all c and for all sufficiently large n, the optimal mechanism for n independent uniform items supported on [c,c+1] is not a grand‐bundling mechanism.     

Route vs. Segment: An Experiment on Real‐Time Travel Information in Congestible Networks

We report the results of an experimental study of route choice in congestible networks with a common origin and common destination. In one condition, in each round of play network users independently committed themselves at the origin to a three‐segment route; in the other condition, they chose route segments sequentially at each network junction upon receiving en route information. At the end of each round, players received ex‐post complete information about the distribution of the route choices. Although the complexity of the network defies analysis by common users, traffic patterns in both conditions converged rapidly to the equilibrium solution. We account for the observed results by a Markov adaptive learning model postulating regret minimization and inertia. We find that subjects' learning behavior was similar across conditions, except that they exhibited more inertia in the condition with en route information.     

The Farsighted Stable Set

Harsanyi (1974) criticized the von Neumann–Morgenstern (vNM) stable set for its presumption that coalitions are myopic about their prospects. He proposed a new dominance relation incorporating farsightedness, but retained another feature of the stable set: that a coalition S can impose any imputation as long as its restriction to S is feasible for it. This implicitly gives an objecting coalition complete power to arrange the payoffs of players elsewhere, which is clearly unsatisfactory. While this assumption is largely innocuous for myopic dominance, it is of crucial significance for its farsighted counterpart. Our modification of the Harsanyi set respects “coalitional sovereignty.” The resulting farsighted stable set is very different from both the Harsanyi and the vNM sets. We provide a necessary and sufficient condition for the existence of a farsighted stable set containing just a single‐payoff allocation. This condition roughly establishes an equivalence between core allocations and the union of allocations over all single‐payoff farsighted stable sets. We then conduct a comprehensive analysis of the existence and structure of farsighted stable sets in simple games. This last exercise throws light on both single‐payoff and multi‐payoff stable sets, and suggests that they do not coexist.     

Strategic Liquidity Provision in Limit Order Markets

We characterize and prove the existence of Nash equilibrium in a limit order market with a finite number of risk‐neutral liquidity providers. We show that if there is sufficient adverse selection, then pointwise optimization (maximizing in p for each q) in a certain nonlinear pricing game produces a Nash equilibrium in the limit order market. The need for a sufficient degree of adverse selection does not vanish as the number of liquidity providers increases. Our formulation of the nonlinear pricing game encompasses various specifications of informed and liquidity trading, including the case in which nature chooses whether the market‐order trader is informed or a liquidity trader. We solve for an equilibrium analytically in various examples and also present examples in which the first‐order condition for pointwise optimization does not define an equilibrium, because the amount of adverse selection is insufficient.     

典型事实、混合Copula函数与金融市场相依结构研究

运用ARFIMA-FIAPARCH-skst模型对沪深300指数和香港恒生指数建立收益-波动模型, 然后结合估计的参数对模型进行修正以确立最终模型, 排除金融市场典型事实对相依关系的影响, 进而运用由Clayton、Frank和Gumbel组成的混合copula模型对相依结构进行建模。研究结果表明:内地市场和香港市场均未观察到显著的杠杆效应;由Clayton、Frank和Gumbel组成的混合Copula模型能够准确地描述两个市场之间的相依结构, 且两个市场下尾相依关系要强于上尾的相依关系, 通过动态混合copula也验证了这一明显的非对称关系。     

Myopic Analysis for Multi‐Echelon Inventory Systems with Batch Ordering and Nonstationary/Time‐Correlated Demands

We provide an exact myopic analysis for an N‐stage serial inventory system with batch ordering, linear ordering costs, and nonstationary demands under a finite planning horizon. We characterize the optimality conditions of the myopic nested batching newsvendor (NBN) policy and the myopic independent batching newsvendor (IBN) policy, which is a single‐stage approximation. We show that echelon reorder levels under the NBN policy are upper bounds of the counterparts under both the optimal policy and the IBN policy. In particular, we find that the IBN policy has bounded deviations from the optimal policy. We further extend our results to systems with martingale model of forecast evolution (MMFE) and advance demand information. Moreover, we provide a recursive computing procedure and optimality conditions for both heuristics which dramatically reduces computational complexity. We also find that the NBN problem under the MMFE faced by one stage has one more dimension for the forecast demand than the one faced by its downstream stage and that the NBN policy is optimal for systems with advance demand information and stationary problem data. Numerical studies demonstrate that the IBN policy outperforms on average the NBN policy over all tested instances when their optimality conditions are violated.     

Inferential Theory for Factor Models of Large Dimensions

This paper develops an inferential theory for factor models of large dimensions. The principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator (if normality is assumed). We derive the rate of convergence and the limiting distributions of the estimated factors, factor loadings, and common components. The theory is developed within the framework of large cross sections (N) and a large time dimension (T), to which classical factor analysis does not apply. We show that the estimated common components are asymptotically normal with a convergence rate equal to the minimum of the square roots of N and T. The estimated factors and their loadings are generally normal, although not always so. The convergence rate of the estimated factors and factor loadings can be faster than that of the estimated common components. These results are obtained under general conditions that allow for correlations and heteroskedasticities in both dimensions. Stronger results are obtained when the idiosyncratic errors are serially uncorrelated and homoskedastic. A necessary and sufficient condition for consistency is derived for large N but fixed T.