A Class of Non-Gaussian State Space Models With Exact Likelihood Inference

The likelihood function of a general nonlinear, non-Gaussian state space model is a high-dimensional integral with no closed-form solution. In this article, I show how to calculate the likelihood function exactly for a large class of non-Gaussian state space models that include stochastic intensity, stochastic volatility, and stochastic duration models among others. The state variables in this class follow a nonnegative stochastic process that is popular in econometrics for modeling volatility and intensities. In addition to calculating the likelihood, I also show how to perform filtering and smoothing to estimate the latent variables in the model. The procedures in this article can be used for either Bayesian or frequentist estimation of the model’s unknown parameters as well as the latent state variables. Supplementary materials for this article are available online.     

空间ZISF的估计及蒙特卡罗模拟

在随机前沿模型中引入空间效应和技术无效率项的非连续性并构建了空间零无效率随机前沿模型,使用极大似然估计和JLMS方法得出参数和技术效率的估计。蒙特卡罗模拟表明:(1)逆似然比检验能以较高的准确率识别真实模型;(2)本方法在参数估计和技术效率的估计两方面均表现较好;(3)若真实模型为空间零无效率随机前沿模型但误用了空间随机前沿模型,参数估计和技术效率的估计两方面均表现较差。空间零无效率随机前沿模型有其存在的必要性。     

Fourier-cosine method for pricing forward starting options with stochastic volatility and jumps

This article provides an efficient method for pricing forward starting options under stochastic volatility model with double exponential jumps. The forward characteristic function of the log asset price is derived and thereby forward starting options are well evaluated by Fourier-cosine technique. Based on adaptive simulated annealing algorithm, the model is calibrated to obtain the estimated parameters. Numerical results show that the pricing method is accurate and fast. Double exponential jumps have pronounced impacts on long-term forward starting options prices. Stochastic volatility model with double exponential jumps fits forward implied volatility smile pretty well in contrast to stochastic volatility model.     

Semiparametric Estimation of Stochastic Production Frontier Models

This article extends the linear stochastic frontier model proposed by Aigner, Lovell, and Schmidt to a semiparametric frontier model in which the functional form of the production frontier is unspecified and the distributions of the composite error terms are of known form. Pseudolikelihood estimators of the parameters characterizing the two error terms of the model are constructed based on kernel estimation of the conditional mean function. The Monte Carlo results show that the proposed estimators perform well in finite samples. An empirical application is presented. Extensions to a partially linear frontier function and to more flexible one-sided error distributions than the half-normal are discussed     

Asymptotic distribution of martingale estimators for a class of epidemic models

This article is a contribution to the asymptotic inference on the parameters of a quite general class of stochastic models for the spread of epidemics developing in closed populations. Various epidemic models are contained within our framework, for instance, a stochastic version of the Kermack and McKendrick model and the SIS epidemic model. Each model belonging to this class, which consists in a family of discrete-time stochastic process, contains certain parameters to be estimated by means of martingale estimators. Some particular cases defined by means of Markov chains are included in our setting. The main aim of this work is to prove consistency and asymptotic normality of these estimators. Some hypothesis tests based on the main results are also shown.     

An FFT approach for option pricing under a regime-switching stochastic interest rate model

In this article, we investigate the pricing of European-style options under a Markovian regime-switching Hull–White interest rate model. The parameters of this model, including the mean-reversion level, the volatility of the stochastic interest rate, and the volatility of an asset’s value, are modulated by an observable, continuous-time, finite-state Markov chain. A closed-form expression for the characteristic function of the logarithmic terminal asset price is derived. Then, using the fast Fourier transform, a price of a European-style option is computed. In a two-state Markov chain case, numerical examples and empirical studies are presented to illustrate the practical implementation of the model.     

Robust optimal investment and proportional reinsurance toward joint interests of the insurer and the reinsurer

In this article, we study a robust optimal investment and reinsurance problem for a general insurance company which holds shares of an insurance company and a reinsurance company. Assume that the claim process described by a Brownian motion with drift, the insurer can purchase proportional reinsurance, and both the insurer and the reinsurer can invest in a risk-free asset and a risky asset. Besides, the general insurance company’s manager is an ambiguity-averse manager (AAM) who worries about model uncertainty in model parameters. The AAM’s objective is to maximize the minimal expected exponential utility of the weighted sum surplus process of the insurer and the reinsurer. By using techniques of stochastic control theory, we first derive the closed-form expressions of the optimal strategies and the corresponding value function, and then the verification theorem is given. Finally, we present numerical examples to illustrate the effects of model parameters on the optimal investment and reinsurance strategies, and analyze utility losses from ignoring model uncertainty.     

空间误差自相关随机前沿模型及其估计

将空间计量经济学的思想引入随机前沿分析，构建了基于横截面数据的空间误差自相关随机前沿模型，推导出模型的似然函数以求得参数估计，并给出了各生产单元技术效率的估计。     

A Generalized Stochastic Restricted Ridge Regression Estimator

In this article, we introduce a new stochastic restricted estimator for the unknown vector parameter in the linear regression model when stochastic linear restrictions on the parameters hold. We show that the new estimator is a generalization of the ordinary mixed estimator (OME), Liu estimator (LE), ordinary ridge estimator (ORR), (k-d) class estimator, stochastic restricted Liu estimator (SRLE), and stochastic restricted ridge estimator (SRRE). Performance of the new estimator in comparison to other estimators in terms of the mean squares error matrix (MMSE) is examined. Numerical example from literature have been given to illustrate the results.     

Random-Time Aggregation in Partial Adjustment Models

Structural econometric auction models with explicit game-theoretic modeling of bidding strategies have been quite a challenge from a methodological perspective, especially within the common value framework. We develop a Bayesian analysis of the hierarchical Gaussian common value model with stochastic entry introduced by Bajari and Hortaçsu. A key component of our approach is an accurate and easily interpretable analytical approximation of the equilibrium bid function, resulting in a fast and numerically stable evaluation of the likelihood function. We extend the analysis to situations with positive valuations using a hierarchical gamma model. We use a Bayesian variable selection algorithm that simultaneously samples the posterior distribution of the model parameters and does inference on the choice of covariates. The methodology is applied to simulated data and to a newly collected dataset from eBay with bids and covariates from 1000 coin auctions. We demonstrate that the Bayesian algorithm is very efficient and that the approximation error in the bid function has virtually no effect on the model inference. Both models fit the data well, but the Gaussian model outperforms the gamma model in an out-of-sample forecasting evaluation of auction prices. This article has supplementary material online.     

Topp–Leone normal distribution with application to increasing failure rate data

In this article, we proposed a new three-parameter probability distribution, called Topp–Leone normal, for modelling increasing failure rate data. The distribution is obtained by using Topp–Leone-X family of distributions with normal as a baseline model. The basic properties including moments, quantile function, stochastic ordering and order statistics are derived here. The estimation of unknown parameters is approached by the method of maximum likelihood, least squares, weighted least squares and maximum product spacings. An extensive simulation study is carried out to compare the long-run performance of the estimators. Applicability of the distribution is illustrated by means of three real data analyses over existing distributions.     

Non parametric estimation of the structural expectation of a stochastic increasing function

This article introduces a non parametric warping model for functional data. When the outcome of an experiment is a sample of curves, data can be seen as realizations of a stochastic process, which takes into account the variations between the different observed curves. The aim of this work is to define a mean pattern which represents the main behaviour of the set of all the realizations. So, we define the structural expectation of the underlying stochastic function. Then, we provide empirical estimators of this structural expectation and of each individual warping function. Consistency and asymptotic normality for such estimators are proved.     

Optimal investment and consumption with unknown parameters

An investment and consumption problem is formulated and its optimal strategy is investigated. We assume the basic binary model, but with unknown parameters. We apply the parametric Bayesian approach to formulate the problem as a sequential stochastic optimization model and use the technique of dynamic programming to characterize the optimal strategy. It is discovered that despite unknown parameters, when the power and logarithmic utility functions are treated, the optimal value function is of the same form of the utility function. The random finite horizon model is formulated as an infinite horizon model. Our results are similar to the ones in the literature having different return functions with constant relative risk aversion.     

Robust Inference for Inverse Stochastic Dominance

The notion of inverse stochastic dominance is gaining increasing support in risk, inequality, and welfare analysis as a relevant criterion for ranking distributions, which is alternative to the standard stochastic dominance approach. Its implementation rests on comparisons of two distributions’ quantile functions, or of their multiple partial integrals, at fixed population proportions. This article develops a novel statistical inference model for inverse stochastic dominance that is based on the influence function approach. The proposed method allows model-free evaluations that are limitedly affected by contamination in the data. Asymptotic normality of the estimators allows to derive tests for the restrictions implied by various forms of inverse stochastic dominance. Monte Carlo experiments and an application promote the qualities of the influence function estimator when compared with alternative dominance criteria.     

Bayesian beta nonlinear models with constrained parameters to describe ruminal degradation kinetics

The models used to describe the kinetics of ruminal degradation are usually nonlinear models where the dependent variable is the proportion of degraded food. The method of least squares is the standard approach used to estimate the unknown parameters but this method can lead to unacceptable predictions. To solve this issue, a beta nonlinear model and the Bayesian perspective is proposed in this article. The application of standard methodologies to obtain prior distributions, such as the Jeffreys prior or the reference priors, involves serious difficulties here because this model is a nonlinear non-normal regression model, and the constrained parameters appear in the log-likelihood function through the Gamma function. This paper proposes an objective method to obtain the prior distribution, which can be applied to other models with similar complexity, can be easily implemented in OpenBUGS, and solves the problem of unacceptable predictions. The model is generalized to a larger class of models. The methodology was applied to real data with three models that were compared using the Deviance Information Criterion and the root mean square prediction error. A simulation study was performed to evaluate the coverage of the credible intervals.     

Bayesian Time Series Analysis of Structural Changes in Level and Trend

In this article we consider the problem of detecting changes in level and trend in time series model in which the number of change-points is unknown. The approach of Bayesian stochastic search model selection is introduced to detect the configuration of changes in a time series. The number and positions of change-points are determined by a sequence of change-dependent parameters. The sequence is estimated by its posterior distribution via the maximum a posteriori (MAP) estimation. Markov chain Monte Carlo (MCMC) method is used to estimate posterior distributions of parameters. Some actual data examples including a time series of traffic accidents and two hydrological time series are analyzed.     

Efficient Regularization Parameter Selection Via Information Criteria

In a nonlinear regression model based on a regularization method, selection of appropriate regularization parameters is crucial. Information criteria such as generalized information criterion (GIC) and generalized Bayesian information criterion (GBIC) are useful for selecting the optimal regularization parameters. However, the optimal parameter is often determined by calculating information criterion for all candidate regularization parameters, and so the computational cost is high. One simple method by which to accomplish this is to regard GIC or GBIC as a function of the regularization parameters and to find a value minimizing GIC or GBIC. However, it is unclear how to solve the optimization problem. In the present article, we propose an efficient Newton–Raphson type iterative method for selecting optimal regularization parameters with respect to GIC or GBIC in a nonlinear regression model based on basis expansions. This method reduces the computational time remarkably compared to the grid search and can select more suitable regularization parameters. The effectiveness of the method is illustrated through real data examples.     

Optimal investment strategy for a DC pension plan with mispricing under the Heston model

Abstract

In this article, we consider the optimal investment problem for a defined contribution (DC) pension plan with mispricing. We assume that the pension funds are allowed to invest in a risk-free asset, a market index, and a risky asset with mispricing, i.e. the prices are inconsistent in different financial markets. Assuming that the price process of the risky asset follows the Heston model, the manager of the pension fund aims to maximize the expected utility for the power utility function of terminal wealth. By applying stochastic control theory, we establish the corresponding Hamilton-Jacobi-Bellman (HJB) equation. And the optimal investment strategy is obtained for the power utility function explicitly. Finally, numerical examples are provided to analyze effects of parameters on the optimal strategy.     

Statistical Properties of Generalized Method-of-Moments Estimators of Structural Parameters Obtained From Financial Market Data

The article examines the properties of generalized method of moments GMM estimators of utility function parameters. The research strategy is to apply the GMM procedure to generated data on asset returns from stochastic exchange economies; discrete methods and Markov chain models are used to approximate the solutions to the integral equations for the asset prices. The findings are as follows: (a) There is variance/bias trade-off regarding the number of lags used to form instruments; with short lags, the estimates of utility function parameters are nearly asymptotically optimal, but with longer lags the estimates concentrate around biased values and confidence intervals become misleading, (b) The test of the overidentifying restrictions performs well in small samples; if anything, the test is biased toward acceptance of the null hypothesis.     

Likelihood-free stochastic approximation EM for inference in complex models

A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function of model parameters. While SAEM is best suited for models having a tractable “complete likelihood” function, its application to moderately complex models is a difficult or even impossible task. We show how to construct a likelihood-free version of SAEM by using the “synthetic likelihood” paradigm. Our method is completely plug-and-play, requires almost no tuning and can be applied to both static and dynamic models.