Applied Stochastic Models in Business and Industry最新文献

Since Lotfi Zadeh introduced fuzzy logic and fuzzy sets, this theory characterizing the uncertainty of classification has a proven record in fields of computation and engineering. These successful applications, however, have been falsely interpreted as competition or replacement of probability theory by those in many statistical and mathematical communities. Such misconceptions are the result of a lack of understanding about types of uncertainties, and anchored attitudes clinging to the past. Nozer Singpurwalla, among other statisticians, came to the realization that probability and fuzzy set theory can and should work in concert (i.e., not in competition) to accommodate two different types of uncertainty present within a problem or system. The authors had the honor to collaborate with Nozer; those works are featured as successful applications of the probability measure of fuzzy sets in reliability where respective uncertainties of the outcome of events and of classification exist. This paper features those works which embody the use of Bayesian analysis and the subjective interpretation of probability.

Our paper explores a discrete-time risk model with time-varying premiums, investigating two types of correlated claims: main claims and by-claims. Settlement of the by-claims can be delayed for up to two time periods, representing real-world insurance practices. We examine a premium principle based on reported claims, using recursively computable finite-time ruin probabilities to evaluate the performance of time-varying premiums. Our findings suggest that, under specific assumptions, a higher probability of by-claim settlement delays leads to lower ruin probabilities. Moreover, a stronger correlation between main claims and their associated by-claims results in higher ruin probabilities.

This study employs finite-horizon dynamic programming to examine markets with imitative and habit-forming (IH) customers. Our findings indicate that optimal pricing and base demand increase as the number of customers who exhibit imitative and habit-forming behaviors grows. Additionally, we analyze the impact of various stochastic parameters on optimal pricing, revealing that retailers should reduce prices when the variability among IH customers increases and raise prices when the average number of such customers rises. Notably, we challenge the conventional belief that greater uncertainty reduces profits, demonstrating that higher additive variability among IH customers can unexpectedly enhance profitability. These findings offer valuable insights for retailers into optimal pricing strategies for markets with imitative and habit-forming customers, potentially aiding businesses in achieving growth and profitability.

The knowledge of the number of customers is the pillar of retail business analytics. In our setting, we assume that a portion of customers is monitored and easily counted due to the loyalty program while the rest is not monitored. The behavior of customers in both groups may significantly differ making the estimation of the number of unmonitored customers a nontrivial task. We identify shopping patterns of several customer segments which allows us to estimate the distribution of customers without the loyalty card using the maximum likelihood method. In a simulation study, we find that the proposed approach is quite precise even when the data sample is very small and its assumptions are violated to a certain degree. When a major violation is suspected, we suggest an interval approach. In an empirical study of a drugstore chain, we validate and illustrate the proposed approach in practice. The actual number of customers estimated by the proposed method is much higher than the number suggested by the naive estimate assuming the constant customer distribution. The proposed method can also be utilized to determine penetration of the loyalty program in the individual customer segments.

Identifying the start and end dates of past oil price super cycles attracts significant attention in the literature. However, there are limited attempts to construct a formal methodology for determining the duration and maximum drawdown of a typical oil price super cycle. This paper aims to fill this gap by identifying the pricing and duration properties of a super cycle using a fractional Brownian motion model (fBm). We calibrate the fBm and conduct simulations using data from January 1996 to September 2020. The simulation results indicate that the maximum drawdown is expected to last 124 months. This result implies that the last oil price super-cycle ended in September 2018. In other words, our findings imply that oil prices are currently in a bull market. The findings carry significant policy implications for policymakers in both oil-exporting and -importing countries, as well as financial market players.

The classical Bühlmann model employs a least squared loss criterion that penalizes pricing errors equally across all risk classes. In contrast, this paper develops a new credibility theory based on the least squared relative loss (LSRL) function to address scenarios where the classical approach may fall short. We derive explicit expressions of LSRL-based credibility estimators, including non-parametric versions and Bühlmann–Straub extensions. Through a comparative study, we illustrate the real-world applicability of the LSRL estimator across different scenarios, highlighting its advantages and limitations in comparison to the classical model. Additionally, we explore different LSRL formulations to provide deeper insights into their practical viability.

In this paper, we are the first to consider the combination of the minimal repair with the defined better than minimal repair. With a given probability, each failure of a repairable system is minimally repaired and with complementary probability it is better than minimally repaired. The latter can be interpreted in terms of a reliability growth model when a defect of a system is eliminated on each failure. It turns out that the better than minimal repair can be even better than a perfect one if a perfect repair is understood as a replacement of the whole system or stochastically equivalent operation. We provide stochastic description of the failure/repair process by introducing and describing the corresponding bivariate point process via the concept of stochastic intensity. Distributions for the number of failures for the pooled and marginal processes are derived along with their expected values. The latter can describe the process of reliability growth in applications. Some meaningful special cases are discussed.