(2003). Comparison Methods for Stochastic Models and Risks. Technometrics: Vol. 45, No. 4, pp. 370-371.

Comparison Methods for Stochastic Models and Risks

(2007). Stochastic Ageing and Dependence for Reliability. Technometrics: Vol. 49, No. 2, pp. 222-222.

Stochastic Ageing and Dependence for Reliability

A class of bivariate distributions that generalize Marshall-Olkin's one is characterized through a functional equation which involves two associative operations. The obtained distributions concentrate positive mass on the linex=y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function.

Characterization of a Marshall-Olkin type class of distributions

Dependence structures of multiple risks play an important role in optimal allocation problems for insurance, quantitative risk management, and finance. However, in many existing studies on these problems, risks or losses are often assumed to be independent or comonotonic or exchangeable. In this paper, we propose several new notions of dependence to model dependent risks and give their characterizations through the probability measures or distributions of the risks or through the expectations of the transformed risks. These characterizations are related to the properties of arrangement increasing functions and the proposed notions of dependence incorporate many typical dependence structures studied in the literature for optimal allocation problems. We also develop the properties of these dependence structures. We illustrate the applications of these notions in the optimal allocation problems of deductibles and policy limits and in capital reserves problems. These applications extend many existing researches to more general dependent risks.

Some new notions of dependence with applications in optimal allocation problems

Likelihood ratio order of sample minimum from heterogeneous Weibull random variables

This paper studies k-out-of-n redundant systems with component lifetimes having lower tail permutation decreasing probability density. For matched redundancies with stochastic arrangement increasing lifetimes, the allocation of a more reliable component to a weaker component is proved to enhance system reliability. For redundancies with independent and identically distributed lifetimes, more allocations to a weaker component are shown to stochastically increase the system lifetime. In addition, using a real data set, we illustrate the statistical aspects of developing lifetimes with lower tail permutation decreasing density. Copyright © 2016 John Wiley & Sons, Ltd.

Allocating active redundancies to k-out-of-n reliability systems with permutation monotone component lifetimes

In this paper we develop two permutation theorems on argument increasing functions of a multivariate random vector and a real parameter vector. We use the unified approach of our two theorems to provide some important theoretical results on the capital allocation in actuarial science, the deductible and upper limit allocations in insurance policy, and portfolio allocation in financial engineering. Our results successfully improve or extend the corresponding works in the literature.

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Permutation monotone functions of random vectors with applications in financial and actuarial risk management

For two components in series and one redundancy with their lifetimes following the proportional hazard models, we build the likelihood ratio order and the hazard rate order for lifetimes of the redundant systems. Also, for k-out-of- n system with components' lifetimes having the arrangement increasing joint density and the redundancies having identically distributed lifetimes, allocating more redundancies to weaker components is shown to help improve the system's reliability. Copyright © 2014 John Wiley & Sons, Ltd.

On allocating redundancies to k-out-of- n reliability systems

This paper further studies the capital allocation concerning mutually interdependent random risks. In the context of exchangeable random risks, we establish that risk-averse insurers incline to evenly distribute the total capital among multiple risks. For risk-averse insurers with decreasing convex loss functions, we prove that more capital should be allocated to the risk with the larger reversed hazard rate when risks are coupled by an Archimedean copula. Also, sufficient conditions are developed to exclude the worst capital allocations for random risks with some specific Archimedean copulas.

Optimal capital allocations to interdependent actuarial risks

For the weighted k-out-of-n system with statistically dependent component lifetimes, we have a discussion on the system performance through investigating the ordering properties of the total system weight with respect to component weight vector. Applications of the present ordering results to signature of coherent systems are presented as well.

Yinping You

Papers

Allocating active redundancies to k-out-of-n reliability systems with permutation monotone component lifetimes

Permutation monotone functions of random vectors with applications in financial and actuarial risk management

On allocating redundancies to k-out-of- n reliability systems

Optimal capital allocations to interdependent actuarial risks

On weighted k-out-of-n systems with statistically dependent component lifetimes