Jeffrey Pai

An algorithm for estimating parameters of state-space models

We describe an algorithm for estimating the parameters of time-series models expressed in state-space form. The algorithm is based on the EM algorithm, and generalizes an algorithm given by Shumway and Stoffer (1982)

Bayesian analysis of autoregressive fractionally integrated moving-average processes

For the autoregressive fractionally integrated moving‐average (ARFIMA) processes which characterize both long‐memory and short‐memory behavior in time series, we formulate Bayesian inference using Markov chain Monte Carlo methods. We derive a form for the joint posterior distribution of the parameters that is computationally feasible for repetitive evaluation within a modified Gibbs sampling algorithm that we employ. We illustrate our approach through two examples.

Crop Insurance Principles and Risk Implications for China

ABSTRACT Firms within various sectors of an economy are often faced with a number of risks. These risks can be relatively sudden and large, especially if they are weather related. In agriculture, risk often has natural causes such as weather, and therefore losses can be large and costly in particular years. Crop insurance has been commercially available in many developed countries for a number of decades, though it is only now starting to become more commercially available in a number of developing countries such as China. When facing these risks without crop insurance, farmers may use fewer inputs and invest less in crop production, resulting in lower yields and lower production. As well, lenders may be reluctant to extend credit to farmers, if farmers have not purchased crop insurance. Crop insurance has been one of the most successful risk management and longest running stabilization programs for farmers in many parts of the world. The purpose of this article is to explain the main principles underlying crop insurance, with implications for China. Challenges for crop insurance development are also pointed out, along with some possible solutions. Some North American experience with crop insurance is also discussed, including the case of Canada.

Factors affecting crop insurance purchases in China: the Inner Mongolia region

Purpose - The purpose of this paper is to explain the factors affecting crop insurance purchases by farmers in Inner Mongolia, China. Design/methodology/approach - A survey of farmers in Inner Mongolia, China, is undertaken. Selected variables are used to explain crop insurance purchases, and a probit regression model is used for the analysis. Findings - Results show that a number of variables explain crop insurance purchases by farmers in Inner Mongolia. Of the eight variables in the model, seven are statistically significant. The eight variables used to explain crop insurance purchases are: knowledge of crop insurance, previous purchases of crop insurance, trust of the crop insurance company, amount of risk taken on by the farmer, importance of low crop insurance premium, government as the main information source for crop insurance, role of head of village, and number of family members working in the city. Research limitations/implications - A possible limitation of the study is that data includes only one geographic area, Inner Mongolia, China, and so results may not always fully generalize to all regions of China, for all situations. Practical implications - Crop insurance has been recently expanded in China, and the information from this study should be useful for insurance companies and government policy makers that are attempting to increase the adoption rate of crop insurance in China. Social implications - Crop insurance may be a useful approach for stabilizing the agricultural sector, and for increasing agricultural production and food security in China. Originality/value - This is the first study to quantitatively model the factors affecting crop insurance purchases by farmers in Inner Mongolia, China.

Bayesian analysis of compound loss distributions

Abstract Bayesian analysis is performed to scrutinize the compound loss distribution using sampling based methods. Both the number and the size of the losses are treated in a stochastic manner. Model selection, forecasting and reinsurance are studied from the predictive distribution. Model uncertainty is incorporated in forecasting through the use of posterior probabilities. The variation of the aggregate claim amount is analyzed under different reinsurance treaties. The methodology for modeling collective distributions of insurance losses is illustrated by an example.

Bayesian modelling of ARFIMA processes by Markov chain Monte Carlo methods

This article describes Bayesian inference for autoregressive fractionally integrated moving average (ARFIMA) models using Markov chain Monte Carlo methods. The posterior distribution of the model parameters, corresponding to the exact likelihood function is obtained through the partial linear regression coefficients of the ARFIMA process. A Metropolis-Rao-Blackwellizallization approach is used for implementing sampling-based Bayesian inference. Bayesian model selection is discussed and implemented.

On the nth stop-loss transform order of ruin probability☆

Abstract The concept of the nth stop-loss order is generalized to the class of general nonnegative monotone decreasing functions. The nth stop-loss transform of the first deficit below its initial level is expressed in terms of the nth stop-loss transform of the claim amount random variable. We study the stop-loss ordering of ruin probability through the maximal aggregate loss and obtain a result relating the stop-loss ordering of ruin probabilities to the stop-loss ordering of severities.

Exact Likelihood Function Forms for an ARFIMA Process

We present four closed form expressions for the exact likelihood function for a Gaussian ARFIMA process, which is useful in modeling time series with long memory and short memory behavior. Use is made of the relationship between the ARFIMA process and the corresponding fractional Gaussian noise process. Application to the simpler short memory ARMA process is illustrated.

Insurance Premium Calculation Using Credibility Analysis: An Example from Livestock Mortality Insurance

A major problem facing livestock producers is animal mortality risk. Livestock mortality insurance is still at the initial stages, and premium computation approaches are still relatively new and will require more research. This study seeks to provide a first step for developing a better understanding of livestock insurance as a solution to mortality risk, as it explores improved methods for livestock mortality insurance modeling procedures, and premium computation, using credibility analysis. The purpose of this study is to develop improved estimates for livestock mortality insurance premiums for Canada under a credibility framework. We illustrate our approach through one example using livestock data from 1999 to 2007.

Bayes Inference for Technological Substitution Data with Data‐based Transformation

Bayesian inference via Gibbs sampling is studied for forecasting technological substitutions. The Box‐Cox transformation is applied to the time series AR(1) data to enhance the linear model fit. We compute Bayes point and interval estimates for each of the parameters from the Gibbs sampler. The unknown parameters are the regression coeAcients, the power in the Box‐Cox transformation, the serial correlation coeAcient, and the variance of the disturbance terms. In addition, we forecast the future technological substitution rate and its interval. Model validation and model choice issues are also addressed. Two numerical examples with real data sets are given.