THE DESIGN OF AN OPTIMAL RETROSPECTIVE RATING PLAN

2015 ◽  
Vol 46 (1) ◽  
pp. 141-163
Author(s):  
Xinxiang Chen ◽  
Yichun Chi ◽  
Ken Seng Tan
Keyword(s):  
Value At Risk ◽  
Conversion Factor ◽  
Insurance Premium ◽  
Conditional Value At Risk ◽  
Insurance Policy ◽  
Stop Loss ◽  
The Cost ◽  
The Relationship ◽  
Insurance Agreement ◽  
Actual Loss

AbstractA retrospective rating plan, whose insurance premium depends upon an insured's actual loss during the policy period, is a special insurance agreement widely used in liability insurance. In this paper, the design of an optimal retrospective rating plan is analyzed from the perspective of the insured who seeks to minimize its risk exposure in the sense of convex order. In order to reduce the moral hazard, we assume that both the insured and the insurer are obligated to pay more for a larger realization of the loss. Under the further assumptions that the minimum premium is zero, the maximum premium is proportional to the expected indemnity, and the basic premium is the only free parameter in the formula for retrospective premium given by Meyers (2004) and that the basic premium is determined in such a way that the expected retrospective premium equates to the expected indemnity with a positive safety loading, we formally establish the relationship that the insured will suffer more risk for a larger loss conversion factor or a higher maximum premium. These findings suggest that the insured prefers an insurance policy with the expected value premium principle, which is a special retrospective premium principle with zero loss conversion factor. In addition, we show that any admissible retrospective rating plan is dominated by a stop-loss insurance policy. Finally, the optimal retention of a stop-loss insurance is derived numerically under the criterion of minimizing the risk-adjusted value of the insured's liability where the liability valuation is carried out using the cost-of-capital approach based on the conditional value at risk.

OPTIMAL REINSURANCE WITH LIMITED CEDED RISK: A STOCHASTIC DOMINANCE APPROACH

2013 ◽  
Vol 44 (1) ◽  
pp. 103-126 ◽  
Author(s):  
Yichun Chi ◽  
X. Sheldon Lin
Keyword(s):  
Stochastic Dominance ◽  
Value At Risk ◽  
Piecewise Linear ◽  
Optimization Criterion ◽  
Conditional Value At Risk ◽  
Convex Order ◽  
Optimal Reinsurance ◽  
Reinsurance Treaty ◽  
Stop Loss ◽  
The Cost

AbstractAn optimal reinsurance problem from the perspective of an insurer is studied in this paper, where an upper limit is imposed on a reinsurer's expected loss over a prescribed level. In order to reduce the moral hazard, we assume that both the insurer and the reinsurer are obligated to pay more as the amount of loss increases in a typical reinsurance treaty. We further assume that the optimization criterion preserves the convex order. Such a criterion is very general as most of the criteria for optimal reinsurance problems in the literature preserve the convex order. When the reinsurance premium is calculated as a function of the actuarial value of coverage, we show via a stochastic dominance approach that any admissible reinsurance policy is dominated by a stop-loss reinsurance or a two-layer reinsurance, depending upon the amount of the reinsurance premium. Moreover, we obtain a similar result to Mossin's Theorem and find that it is optimal for the insurer to cede a loss as much as possible under the net premium principle. To further examine the reinsurance premium for the optimal piecewise linear reinsurance policy, we assume the expected value premium principle and derive the optimal reinsurance explicitly under (1) the criterion of minimizing the variance of the insurer's risk exposure, and (2) the criterion of minimizing the risk-adjusted value of the insurer's liability where the liability valuation is carried out using the cost-of-capital approach based on the conditional value at risk.

scholarly journals Analytical Bounds for two Value-at-Risk Functionals

2002 ◽  
Vol 32 (2) ◽  
pp. 235-265 ◽  
Author(s):  
Werner Hürlimann
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Decision Makers ◽  
Conditional Value At Risk ◽  
General Interest ◽  
Dominance Order ◽  
Risk Capital ◽  
Time Period ◽  
Aggregate Loss ◽  
Stop Loss

AbstractBased on the notions of value-at-risk and conditional value-at-risk, we consider two functionals, abbreviated VaR and CVaR, which represent the economic risk capital required to operate a risky business over some time period when only a small probability of loss is tolerated. These functionals are consistent with the risk preferences of profit-seeking (and risk averse) decision makers and preserve the stochastic dominance order (and the stop-loss order). This result is used to bound the VaR and CVaR functionals by determining their maximal values over the set of all loss and profit functions with fixed first few moments. The evaluation of CVaR for the aggregate loss of portfolios is also discussed. The results of VaR and CVaR calculations are illustrated and compared at some typical situations of general interest.

Application of Portfolio Theory Based on CVaR in Determining Optimal Spinning Reserve with Consideration of Load and Wind Power Uncertainties

2013 ◽  
Vol 724-725 ◽  
pp. 649-654
Author(s):  
Jun Li Wu ◽  
Bu Han Zhang ◽  
Zhen Yin Xiao ◽  
Kui Wang
Keyword(s):  
Power System ◽  
Wind Power ◽  
Value At Risk ◽  
Efficient Frontier ◽  
Portfolio Theory ◽  
Conditional Value At Risk ◽  
Power Prediction ◽  
Spinning Reserve ◽  
The Cost ◽  
Installed Capacity

With the increased installed capacity of wind power in power system, determining optimal spinning reserve capacity is one of the most important problems in operation of electricity power system. CVaR (conditional value at risk) is introduced to calculate the risk of the cost associated with load shed and abandoning wind power with the consideration of load and wind power prediction uncertainties. Portfolio theory based on CVaR is used to build the Cost-CVaR model. Efficient frontier, which can support the system operators (SO) with the decision of optimal spinning reserve, can be obtained by solving the Cost-CVaR model. The analysis of RTS example can demonstrate the usefulness and efficiency of the model.

Robust bi-level risk-based optimal scheduling of microgrid operation against uncertainty

2020 ◽  
Vol 54 (4) ◽  
pp. 993-1012 ◽  
Author(s):  
Hêriș Golpîra ◽  
Salah Bahramara ◽  
Syed Abdul Rehman Khan ◽  
Yu Zhang
Keyword(s):  
Risk Aversion ◽  
Value At Risk ◽  
Goodness Of Fit ◽  
Distribution Functions ◽  
Optimal Scheduling ◽  
Conditional Value At Risk ◽  
Optimization Approach ◽  
Goodness Of Fit Tests ◽  
The Cost ◽  
Initial Objective

The model introduced in this paper is the first to propose a decentralized robust optimal scheduling of MG operation under uncertainty and risk. The power trading of the MG with the main grid is the first stage variable and power generation of DGs and power charging/discharging of the battery are the second stage variables. The uncertain term of the initial objective function is transformed into a constraint using robust optimization approach. Addressing the Decision Maker’s (DMs) risk aversion level through Conditional Value at Risk (CVaR) leads to a bi-level programming problem using a data-driven approach. The model is then transformed into a robust single-level using Karush–Kahn–Tucker (KKT) conditions. To investigate the effectiveness of the model and its solution methodology, it is applied on a MG. The results clearly demonstrate the robustness of the model and indicate a strong almost linear relationship between cost and the DMs various levels of risk aversion. The analysis also outlines original characterization of the cost and the MGs behavior using three well-known goodness-of-fit tests on various Probability Distribution Functions (PDFs), Beta, Gumbel Max, Normal, Weibull, and Cauchy. The Gumbel Max and Normal PDFs, respectively, exhibit the most promising goodness-of-fit for the cost, while the power purchased from the grid are well fitted by Weibull, Beta, and Normal PDFs, respectively. At the same time, the power sold to the grid is well fitted by the Cauchy PDF.

scholarly journals A Bi-Objective Portfolio Optimization with Conditional Value-at-Risk

2010 ◽  
Vol 4 (2) ◽  
pp. 47-69 ◽  
Author(s):  
Bartosz Sawik
Keyword(s):  
Value At Risk ◽  
Stock Exchange ◽  
Risk Measure ◽  
Performance Measure ◽  
Conditional Value At Risk ◽  
Programming Approach ◽  
Expected Return ◽  
Worst Case ◽  
Warsaw Stock Exchange ◽  
The Relationship

This paper presents a bi-objective portfolio model with the expected return as a performance measure and the expected worst-case return as a risk measure. The problems are formulated as a bi-objective linear program. Numerical examples based on 1000, 3500 and 4020 historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided. The computational experiments prove that the proposed linear programming approach provides the decision maker with a simple tool for evaluating the relationship between the expected and the worst-case portfolio return.

scholarly journals Portfolio Optimization Using Conditional Sharpe Ratio

2015 ◽  
Vol 53 ◽  
pp. 130-136 ◽  
Author(s):  
Meena Baweja ◽  
Ratnesh R. Saxena ◽  
Deepak Sehgal
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Fitness Function ◽  
Sharpe Ratio ◽  
Conditional Value At Risk ◽  
Case Scenario ◽  
Optimal Portfolio Selection ◽  
Dynamic Portfolio ◽  
Portfolio Optimization Model ◽  
The Relationship

In this paper we propose a portfolio optimization model that selects the portfolio with the largest worse-case-scenario sharpe ratio with a given confidence level. We highlight the relationship between conditional value-atrisk based sharpe ratio and standard deviation based sharpe ratio proposed in literature. By utilizing the results of Rockafellar and Uryasev [5], we evaluate conditional value- at- risk for each portfolio. Our model is expected to enlarge the application area of practical investment problems for which the original sharpe ratio is not suitable, however should device effective computational methods to solve optimal portfolio selection problems with large number of investment opportunities. Here conditional sharpe ratio is defined as the ratio of expected excess return to the expected shortfall. This optimization considers both risk and return, of which changes will effect the sharpe ratio. That is the fitness function for dynamic portfolio is the objective function of the model.

scholarly journals Viable Medical Waste Chain Network Design by Considering Risk and Robustness

2021 ◽  
Author(s):  
Reza Lotfi ◽  
Bahareh Kargar ◽  
Alireza Gharehbaghi ◽  
Gerhard-Wilhelm Weber
Keyword(s):  
Network Design ◽  
Cost Function ◽  
Value At Risk ◽  
Medical Waste ◽  
Conditional Value At Risk ◽  
Production Cycle ◽  
Recovery Coefficient ◽  
Energy And Environment ◽  
Increasing Demand ◽  
The Cost

Abstract Medical Waste Management (MWM) is an important and necessary problem in the COVID-19 situation for treatment staff. When the number of infectious patients grows up and amount of MWMs increases day by day. We present Medical Waste Chain Network Design (MWMCND) that contains Health Center (HC), Waste Segregation (WS), Waste Purchase Contractor (WPC) and landfill. We propose to locate WS to decrease waste and recover them and send them to the WPC. Recovering medical waste like metal and plastic can help the environment and return to the production cycle. Therefore, we proposed a novel Viable MWCND by a novel two-stage robust stochastic programming that considers resiliency (flexibility and network complexity) and sustainable (energy and environment) requirements. Therefore, we try to consider risks by Conditional Value at Risk (CVaR) and improve robustness and agility to demand fluctuation and network. We utilize and solve it by GAMS CPLEX solver. The results show that by increasing the conservative coefficient, the confidence level of CVaR and waste recovery coefficient increases cost function and population risk. Moreover, increasing demand and scale of the problem make to increase the cost function.

Assessing the Impact of Suicide Exclusion Periods on Life Insurance

Crisis ◽  
2010 ◽  
Vol 31 (4) ◽  
pp. 217-223 ◽  
Author(s):  
Paul Yip ◽  
David Pitt ◽  
Yan Wang ◽  
Xueyuan Wu ◽  
Ray Watson ◽  
...  
Keyword(s):  
Life Insurance ◽  
Accidental Death ◽  
Insurance Policy ◽  
Death Rates ◽  
Insurance Policies ◽  
Suicidal Death ◽  
Insured Individual ◽  
The Impact ◽  
Insurance Data ◽  
The Relationship

Background: We study the impact of suicide-exclusion periods, common in life insurance policies in Australia, on suicide and accidental death rates for life-insured individuals. If a life-insured individual dies by suicide during the period of suicide exclusion, commonly 13 months, the sum insured is not paid. Aims: We examine whether a suicide-exclusion period affects the timing of suicides. We also analyze whether accidental deaths are more prevalent during the suicide-exclusion period as life-insured individuals disguise their death by suicide. We assess the relationship between the insured sum and suicidal death rates. Methods: Crude and age-standardized rates of suicide, accidental death, and overall death, split by duration since the insured first bought their insurance policy, were computed. Results: There were significantly fewer suicides and no significant spike in the number of accidental deaths in the exclusion period for Australian life insurance data. More suicides, however, were detected for the first 2 years after the exclusion period. Higher insured sums are associated with higher rates of suicide. Conclusions: Adverse selection in Australian life insurance is exacerbated by including a suicide-exclusion period. Extension of the suicide-exclusion period to 3 years may prevent some “insurance-induced” suicides – a rationale for this conclusion is given.

The Awareness Level of the Safety and Health of the Operational Level

2017 ◽  
Vol 3 (1) ◽  
pp. 42
Author(s):  
Roshanira Che Mohd Noor ◽  
Nur Atiqah Rochin Demong
Keyword(s):  
Health And Safety ◽  
Health Conditions ◽  
Effective Strategies ◽  
Operational Level ◽  
Safety And Health ◽  
Health Factors ◽  
The Cost ◽  
The Relationship ◽  
Awareness Level

Providing a safe and healthy workplace is one of the most effective strategies in for holding down the cost of doing construction business. It was a part of the overall management system to facilitate themanagement of the occupational health and safety risk that are associated with the business of the organization. Factors affected the awareness level inclusive of safety and health conditions, dangerous working area, long wait care and services and lack of emergency communication werethe contributed factors to the awareness level for the operational level. Total of 122 incidents happened at Telekom Malaysia Berhad as compared to year 2015 only 86 cases. Thus, the main objective of this study was to determine the relationship between safety and health factors and the awareness level among operational workers.The determination of this research was to increase the awareness level among the operational level workerswho committing to safety and health environment.

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