Aim: Actuaries are financial engineers who construct arrays of risk models combining mathematical techniques in order to carry out required actuarial calculations, such as reserve valuation and pricing. The main purpo...Aim: Actuaries are financial engineers who construct arrays of risk models combining mathematical techniques in order to carry out required actuarial calculations, such as reserve valuation and pricing. The main purpose is to identify some reliable models which price risk factors embedded in insurance products. Health insurance products which are very different in nature from life insurance products must be examined and priced carefully. This paper discusses predominantly two risks. Excess claims ratio and Rectangularisation risks. Background: The first author, Dr. S. Jayaprakash was responsible for Enterprise Risk Management with MetLife India. He was earlier associated with Life Insurance Corporation of India & Oracle Financial Services. Dr. P. K. Dinakar, the second author, qualified as Fellow of the Institute of Actuaries of India, was Chief Actuary of MetLife India Insurance. He was earlier associated with Life Insurance Corporation of India & Birla Sunlife. The third author, Dr. Michael Ha, FSA, MAAA, CFA, CPA (Australia), FRM, PRM, LLM, was Vice President of Strategic Business Initiatives Units at ING Life Insurance in its Taiwan operation. He started his actuarial career at MetLife, Canada. Earlier, the first and third authors worked on a research paper titled “Modeling Policyholder Behavior through Insurance Resonant Marts for Pricing Options and Guarantees” [1] which was presented at the 5th World Congress on Engineering and Technology. The seven authors decided to collaborate on the current research paper for health insurance design and financing purposes.展开更多
We derive higher-order expansions of L-statistics of independent risks X1,..., Xn under conditions on the underlying distribution function F. The new results are applied to derive the asymptotic expansions of ratios o...We derive higher-order expansions of L-statistics of independent risks X1,..., Xn under conditions on the underlying distribution function F. The new results are applied to derive the asymptotic expansions of ratios of two kinds of risk measures, stop-loss premium and excess return on capital, respectively. Several examples and a Monte Carlo simulation study show the efficiency of our novel asymptotic expansions. Keywords smoothly varying condition, second-order regular variation, tail asymptotics, value-at-risk, con- ditional tail expectation, largest claims reinsurance, ratio of risk measure, excess return on capital展开更多
文摘Aim: Actuaries are financial engineers who construct arrays of risk models combining mathematical techniques in order to carry out required actuarial calculations, such as reserve valuation and pricing. The main purpose is to identify some reliable models which price risk factors embedded in insurance products. Health insurance products which are very different in nature from life insurance products must be examined and priced carefully. This paper discusses predominantly two risks. Excess claims ratio and Rectangularisation risks. Background: The first author, Dr. S. Jayaprakash was responsible for Enterprise Risk Management with MetLife India. He was earlier associated with Life Insurance Corporation of India & Oracle Financial Services. Dr. P. K. Dinakar, the second author, qualified as Fellow of the Institute of Actuaries of India, was Chief Actuary of MetLife India Insurance. He was earlier associated with Life Insurance Corporation of India & Birla Sunlife. The third author, Dr. Michael Ha, FSA, MAAA, CFA, CPA (Australia), FRM, PRM, LLM, was Vice President of Strategic Business Initiatives Units at ING Life Insurance in its Taiwan operation. He started his actuarial career at MetLife, Canada. Earlier, the first and third authors worked on a research paper titled “Modeling Policyholder Behavior through Insurance Resonant Marts for Pricing Options and Guarantees” [1] which was presented at the 5th World Congress on Engineering and Technology. The seven authors decided to collaborate on the current research paper for health insurance design and financing purposes.
基金supported by the Swiss National Science Foundation(Grant Nos.2000211401633/1,200021-134785 and 200021-1401633/1)Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme(Grant No.RARE-318984)+1 种基金National Natural Science Foundation of China(Grant No.11171275)the Natural Science Foundation Project of Chongqing(Grant No.cstc2012jjA00029)
文摘We derive higher-order expansions of L-statistics of independent risks X1,..., Xn under conditions on the underlying distribution function F. The new results are applied to derive the asymptotic expansions of ratios of two kinds of risk measures, stop-loss premium and excess return on capital, respectively. Several examples and a Monte Carlo simulation study show the efficiency of our novel asymptotic expansions. Keywords smoothly varying condition, second-order regular variation, tail asymptotics, value-at-risk, con- ditional tail expectation, largest claims reinsurance, ratio of risk measure, excess return on capital