scholarly journals Permutation Monotone Functions of Random Vectors with Applications in Financial and Actuarial Risk Management

2015 ◽  
Vol 47 (1) ◽  
pp. 270-291 ◽  
Author(s):  
Xiaohu Li ◽  
Yinping You
Keyword(s):  
Financial Engineering ◽  
Capital Allocation ◽  
Portfolio Allocation ◽  
Monotone Functions ◽  
Insurance Policy ◽  
Actuarial Science ◽  
Unified Approach ◽  
Actuarial Risk ◽  
Increasing Functions ◽  
Theoretical Results

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.

scholarly journals Permutation Monotone Functions of Random Vectors with Applications in Financial and Actuarial Risk Management

2015 ◽  
Vol 47 (01) ◽  
pp. 270-291 ◽  
Author(s):  
Xiaohu Li ◽  
Yinping You
Keyword(s):  
Financial Engineering ◽  
Capital Allocation ◽  
Portfolio Allocation ◽  
Monotone Functions ◽  
Insurance Policy ◽  
Actuarial Science ◽  
Unified Approach ◽  
Actuarial Risk ◽  
Increasing Functions ◽  
Theoretical Results

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.

Charge transfer in the presence of a radiation field

1998 ◽  
Vol 76 (3) ◽  
pp. 245-250 ◽  
Author(s):  
S -M Li ◽  
J -G Khou ◽  
Z -F Zhou ◽  
J Chen ◽  
Y -Y Liu
Keyword(s):  
Charge Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Born Approximation ◽  
Atomic Hydrogen ◽  
Capture Cross ◽  
Exchange Collision ◽  
Increasing Functions ◽  
Theoretical Results ◽  
Capture Cross Sections

In the first Born approximation, the dressing modification in laser-assisted charge exchange collision is investigated. The crosssections for electron capture by a proton from dressed atomic hydrogen and dressed helium targets are calculated within awide energy range. Theoretical results show that with impact energy increasing, the dressing effect leads to increasingly significant cross-section modifications. The modified capture cross sections are increasing functions of the ratio of laser strength to frequency. PACS Nos.: 34.50.Rk; 34.70.+e; 32.80.Wr; and 34.90.+q

Failure rate — a unified approach

1976 ◽  
Vol 13 (01) ◽  
pp. 176-182
Author(s):  
Larry Lee ◽  
W. A. Thompson
Keyword(s):  
Failure Rate ◽  
Continuous Time ◽  
Mechanical Systems ◽  
Failure Rates ◽  
Actuarial Science ◽  
Unified Approach

Aging, of biological and mechanical systems, is well described as ‘deterioration of the power to withstand destruction.’ The failure-rate concept is the mathematical way of describing aging. Failure rates have been defined for discrete and continuous time and used extensively, particularly in actuarial science and reliability. This paper assumes an arbitrary scale on which an object encounters stress, and develops a theory of failure rate with respect to ‘stress-time’ in analogy with the discrete- and continuous-time cases.

DISTORTION RISKMETRICS ON GENERAL SPACES

2020 ◽  
Vol 50 (3) ◽  
pp. 827-851 ◽  
Author(s):  
Qiuqi Wang ◽  
Ruodu Wang ◽  
Yunran Wei
Keyword(s):  
General Model ◽  
Risk Measures ◽  
Actuarial Science ◽  
Model Spaces ◽  
Choquet Integrals ◽  
Theoretical Results ◽  
Distortion Risk Measures

AbstractThe class of distortion riskmetrics is defined through signed Choquet integrals, and it includes many classic risk measures, deviation measures, and other functionals in the literature of finance and actuarial science. We obtain characterization, finiteness, convexity, and continuity results on general model spaces, extending various results in the existing literature on distortion risk measures and signed Choquet integrals. This paper offers a comprehensive toolkit of theoretical results on distortion riskmetrics which are ready for use in applications.

scholarly journals Credit Portfolios, Credibility Theory, and Dynamic Empirical Bayes

2012 ◽  
Vol 2012 ◽  
pp. 1-42 ◽  
Author(s):  
Tze Leung Lai
Keyword(s):  
Credit Risk ◽  
Empirical Bayes ◽  
Credit Derivatives ◽  
Credibility Theory ◽  
Actuarial Science ◽  
Unified Approach ◽  
Insurance Contracts ◽  
Insurance Rate ◽  
Pricing Theory ◽  
Similarities And Differences

We begin with a review of (a) the pricing theory of multiname credit derivatives to hedge the credit risk of a portfolio of corporate bonds and (b) current approaches to modeling correlated default intensities. We then consider pricing of insurance contracts using credibility theory in actuarial science. After a brief discussion of the similarities and differences of both pricing theories, we propose a new unified approach, which uses recent advances in dynamic empirical Bayes modeling, to evolutionary credibility in insurance rate-making and default modeling of credit portfolios.

Failure rate — a unified approach

1976 ◽  
Vol 13 (1) ◽  
pp. 176-182 ◽  
Author(s):  
Larry Lee ◽  
W. A. Thompson
Keyword(s):  
Failure Rate ◽  
Continuous Time ◽  
Mechanical Systems ◽  
Failure Rates ◽  
Actuarial Science ◽  
Unified Approach

Aging, of biological and mechanical systems, is well described as ‘deterioration of the power to withstand destruction.’ The failure-rate concept is the mathematical way of describing aging. Failure rates have been defined for discrete and continuous time and used extensively, particularly in actuarial science and reliability. This paper assumes an arbitrary scale on which an object encounters stress, and develops a theory of failure rate with respect to ‘stress-time’ in analogy with the discrete- and continuous-time cases.

Exact simulation of Ornstein–Uhlenbeck tempered stable processes

2021 ◽  
Vol 58 (2) ◽  
pp. 347-371
Author(s):  
Yan Qu ◽  
Angelos Dassios ◽  
Hongbiao Zhao
Keyword(s):  
Stochastic Processes ◽  
Financial Engineering ◽  
Numerical Experiments ◽  
Stable Processes ◽  
Simulation Algorithm ◽  
Inverse Gaussian ◽  
Unified Approach ◽  
Important Special Case ◽  
Exact Simulation ◽  
Special Case

AbstractThere are two types of tempered stable (TS) based Ornstein–Uhlenbeck (OU) processes: (i) the OU-TS process, the OU process driven by a TS subordinator, and (ii) the TS-OU process, the OU process with TS marginal law. They have various applications in financial engineering and econometrics. In the literature, only the second type under the stationary assumption has an exact simulation algorithm. In this paper we develop a unified approach to exactly simulate both types without the stationary assumption. It is mainly based on the distributional decomposition of stochastic processes with the aid of an acceptance–rejection scheme. As the inverse Gaussian distribution is an important special case of TS distribution, we also provide tailored algorithms for the corresponding OU processes. Numerical experiments and tests are reported to demonstrate the accuracy and effectiveness of our algorithms, and some further extensions are also discussed.

scholarly journals A Population Genetic Study of the Evolution of SINEs. II. Sequence Evolution Under the Master Copy Model

Genetics ◽  
1996 ◽  
Vol 143 (2) ◽  
pp. 1033-1042
Author(s):  
Hidenori Tachida
Keyword(s):  
Population Genetic ◽  
Genetic Model ◽  
Sequence Evolution ◽  
Population Genetic Study ◽  
Monotone Functions ◽  
Transient Population ◽  
Mean And Variance ◽  
Element Evolution ◽  
Theoretical Results ◽  
Expansion Period

Abstract A transient population genetic model of SINE (short interspersed repetitive element) evolution assuming the master copy model is theoretically investigated. Means and variances of consensus frequency of nucleotides, nucleotide homozygosity, and the number of shared differences that are considered to have caused by mutations occurring in the master copy lineages are computed. All quantities investigated are shown to be monotone functions of the duration of the expansion period. Thus, they can be used to estimate the expansion period although their sampling variances are generally large. Using the theoretical results, the Sb subfamily of human Alu sequences is analyzed. First, the expansion period is estimated from the observed mean and variance of homozygosity. The expansion period is shown to be short compared to the time since the end of the expansion of the subfamily. However, the observed number of the shared differences is more than twice that expected under the master copy model with the estimated expansion period. Alternative models including that with multiple master copy loci to explain this observation are discussed.

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