scholarly journals PERHITUNGAN UKURAN RISIKO UNTUK MODEL KERUGIAN AGREGAT

2020 ◽  
Vol 14 (1) ◽  
pp. 21
Author(s):  
Nadya Pratiwi ◽  
Aprida Siska Lestia ◽  
Nur Salam
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Monte Carlo Method ◽  
Value At Risk ◽  
Risk Measure ◽  
Random Variable ◽  
Insurance Companies ◽  
Loss Model ◽  
Aggregate Loss ◽  
Conditional Tail Expectation

In the case of nonlife insurance, insurance companies are very potential to get losses if claims submitted by customers (policyholders) exceeds the reserves of budgeted claims. It is the risk that have to managed properly by insurance companies . One possible disadvantage is the aggregate loss model. The aggregate loss model is a random variable that states the total of all losses incurred in an insurance policy block. This kind of loss can be modeled using a collective risk approach where the number of claims is a discrete random variable and the size of claim is a continuous random variable. The purpose of this study is to determine risk measure of standard deviation premium principle, value at risk (VaR), and conditional tail expectation (CTE) of the aggregate loss model. Standard deviation premium principle risk measure of aggregate loss model is determined analytically by substituted it expected value and varians. Meanwhile, VaR risk measure is determined using numerical method by Monte Carlo method, then the quantile value and it confidence interval for the actual value will estimate. In the CTE calculation, based on the loss data obtained in the Monte Carlo method, the CTE value is estimated by calculating the average loss that exceeds the VaR value. If the data size is large enough, the CTE value estimation will converge to the actual value.Keywords: Aggregate Loss Model, Standard Deviation Premium Principle, Value at Risk (VaR), Conditional Tail Expectation (CTE).

scholarly journals Stochastic energy-demand analyses with random input parameters for the single-family house

2021 ◽  
Author(s):  
Marcin Koniorczyk ◽  
Witold Grymin ◽  
Marcin Zygmunt ◽  
Dalia Bednarska ◽  
Alicja Wieczorek ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Energy Consumption ◽  
Monte Carlo Method ◽  
Energy Demand ◽  
Stochastic Perturbation ◽  
Random Variable ◽  
Single Family ◽  
The Monte Carlo Method ◽  
Stochastic Perturbation Method ◽  
Family House

AbstractIn the analyses of the uncertainty propagation of buildings’ energy-demand, the Monte Carlo method is commonly used. In this study we present two alternative approaches: the stochastic perturbation method and the transformed random variable method. The energy-demand analysis is performed for the representative single-family house in Poland. The investigation is focused on two independent variables, considered as uncertain, the expanded polystyrene thermal conductivity and external temperature; however the generalization on any countable number of parameters is possible. Afterwards, the propagation of the uncertainty in the calculations of the energy consumption has been investigated using two aforementioned approaches. The stochastic perturbation method is used to determine the expected value and central moments of the energy consumption, while the transformed random variable method allows to obtain the explicit form of energy consumption probability density function and further characteristic parameters like quantiles of energy consumption. The calculated data evinces a high accordance with the results obtained by means of the Monte Carlo method. The most important conclusions are related to the computational cost reduction, simplicity of the application and the appropriateness of the proposed approaches for the buildings’ energy-demand calculations.

A Simplified Software for Uncertainty Estimation Using Monte Carlo Method

2020 ◽  
Vol 12 (8) ◽  
pp. 1050-1053
Author(s):  
Jasveer Singh ◽  
L. A. Kumaraswamidhas ◽  
Neha Bura ◽  
Kapil Kaushik ◽  
Nita Dilawar Sharma
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Monte Carlo Method ◽  
Measurement Uncertainty ◽  
Standard Uncertainty ◽  
Uncertainty Estimation ◽  
End Points ◽  
The Monte Carlo Method ◽  
Adaptive Trials ◽  
Coverage Interval

The current paper discusses about the application of Monte Carlo method for the evaluation of measurement uncertainty using in-house developed program on C++ platform. The Monte Carlo method can be carried out by fixed trials as well as adaptive trials using this program. The program provides the four parameters viz. estimate of measurand, standard uncertainty in the form of standard deviation and end points of coverage interval as an output.

scholarly journals An optimal multi-layer reinsurance policy under conditional tail expectation

2017 ◽  
Vol 12 (1) ◽  
pp. 130-146
Author(s):  
Amir T. Payandeh Najafabadi ◽  
Ali Panahi Bazaz
Keyword(s):  
Optimality Criterion ◽  
Risk Measure ◽  
Insurance Companies ◽  
Total Risk ◽  
Unknown Parameters ◽  
Practical Applications ◽  
Simulation Based ◽  
Cartesian Coordinate ◽  
Stop Loss ◽  
Conditional Tail Expectation

AbstractAn usual reinsurance policy for insurance companies admits one or two layers of the payment deductions. Under optimality criterion of minimising the Conditional Tail Expectation (CTE) risk measure of the insurer’s total risk, this article generalises an optimal stop-loss reinsurance policy to an optimal multi-layer reinsurance policy. To achieve such optimal multi-layer reinsurance policy, this article starts from a given optimal stop-loss reinsurance policy f(⋅). In the first step, it cuts down the interval [0, ∞) into intervals [0, M1) and [M1, ∞). By shifting the origin of Cartesian coordinate system to (M1, f(M1)), and showing that under the CTE criteria $$f\left( x \right)I_{{[0,M_{{\rm 1}} )}} \left( x \right){\plus}\left( {f\left( {M_{{\rm 1}} } \right){\plus}f\left( {x{\minus}M_{{\rm 1}} } \right)} \right)I_{{[M_{{\rm 1}} ,{\rm }\infty)}} \left( x \right)$$ is, again, an optimal policy. This extension procedure can be repeated to obtain an optimal k-layer reinsurance policy. Finally, unknown parameters of the optimal multi-layer reinsurance policy are estimated using some additional appropriate criteria. Three simulation-based studies have been conducted to demonstrate: (1) the practical applications of our findings and (2) how one may employ other appropriate criteria to estimate unknown parameters of an optimal multi-layer contract. The multi-layer reinsurance policy, similar to the original stop-loss reinsurance policy is optimal, in a same sense. Moreover, it has some other optimal criteria which the original policy does not have. Under optimality criterion of minimising a general translative and monotone risk measure ρ(⋅) of either the insurer’s total risk or both the insurer’s and the reinsurer’s total risks, this article (in its discussion) also extends a given optimal reinsurance contract f(⋅) to a multi-layer and continuous reinsurance policy.

COLLECTIVE RISK MODELS WITH DEPENDENCE UNCERTAINTY

2017 ◽  
Vol 47 (2) ◽  
pp. 361-389 ◽  
Author(s):  
Haiyan Liu ◽  
Ruodu Wang
Keyword(s):  
Value At Risk ◽  
Random Variable ◽  
Actuarial Science ◽  
Risk Models ◽  
Worst Case ◽  
Collective Risk ◽  
Approximation Errors ◽  
Claim Frequency ◽  
Aggregate Loss ◽  
The Individual

AbstractWe bring the recently developed framework of dependence uncertainty into collective risk models, one of the most classic models in actuarial science. We study the worst-case values of the Value-at-Risk (VaR) and the Expected Shortfall (ES) of the aggregate loss in collective risk models, under two settings of dependence uncertainty: (i) the counting random variable (claim frequency) and the individual losses (claim sizes) are independent, and the dependence of the individual losses is unknown; (ii) the dependence of the counting random variable and the individual losses is unknown. Analytical results for the worst-case values of ES are obtained. For the loss from a large portfolio of insurance policies, an asymptotic equivalence of VaR and ES is established. Our results can be used to provide approximations for VaR and ES in collective risk models with unknown dependence. Approximation errors are obtained in both cases.

scholarly journals Sum of Bernoulli Mixtures: Beyond Conditional Independence

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Taehan Bae ◽  
Ian Iscoe
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Random Variable ◽  
Dependence Structure ◽  
Sample Distribution ◽  
Mixing Distribution ◽  
Bernoulli Random Variables ◽  
New Class ◽  
Bernoulli Mixtures ◽  
Conditional Tail Expectation

We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk and conditional tail expectation, are presented for a new class of models which we calldouble mixtures. Several illustrative examples with a Beta mixing distribution, are given. As well, some data from the area of credit risk are fit with the models, and comparisons are made between the new models and also the classical Beta-binomial model.

scholarly journals VALUE-AT-RISK (VaR) FOR LQ – 45 COMPANIES

2011 ◽  
Vol 3 (2) ◽  
pp. 93-108
Author(s):  
Rangga Handika
Keyword(s):  
At Risk ◽  
Standard Deviation ◽  
Normal Distribution ◽  
Analytical Methods ◽  
Value At Risk ◽  
Stock Exchange ◽  
Risk Measure ◽  
Percent Level ◽  
Level Of Confidence

This paper offers a new measurement of risk, Value-at-Risk (VaR) for LQ-45 index in Indonesian Stock Exchange (ISX). Basic finance uses standard deviation in measuring and quantifying the risks. This paper uses VaR as a risk measure by using historical and analytical methods. This study uses the data containing all LQ-45 weekly data from January 1st, 2005 to December, 31st 2010. Moreover, this paper also calculates VaR of three indices (IHSG, Dow Jones, and S&P 500) for benchmarking purpose. This study finds that LQ-45 companies have VaR ranging from -5.30 to -41.05 percent with 95 percent level of confidence. It means that we can expect to suffer a minimum weekly loss between 5.30 to 41.05 percent in 5 percent probability when we invest in the LQ-45 companies stocks individually. Furthermore, this study finds that individual LQ-45 stock is riskier than indices based on VaR measure. This paper also concludes that individual LQ-45 stock tends not to follow normal distribution while index tends to follow by comparing their historical and analytical VaR calculation.

scholarly journals Analysis of the Accuracy of the Calculation of the Diaphragm Area by the Monte Carlo Method

2020 ◽  
pp. 22-26
Author(s):  
O. D. Kupko
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Monte Carlo Method ◽  
Probability Distribution ◽  
Circular Aperture ◽  
The Monte Carlo Method ◽  
Relative Standard ◽  
Uniform Probability Distribution ◽  
Standard Deviations ◽  
The Difference

The process of measuring the area of a circular diaphragm using a device that determines the coordinates of the boundary of the diaphragm is theoretically considered. The Monte Carlo method with a small number of implementations was used. The procedure for calculating the area is described in detail. We considered a circular aperture with a precisely known radius. On the circumference of the diaphragm, the coordinate measuring points vibrated through 0.1, 0.3, 0.6, and π/2 radians vibrated. To simulate random deviations (uncertainties) when measuring coordinates, random additives were used with a uniform probability distribution and a given standard deviation. For each case, the areas were calculated in accordance with the proposed procedure. The difference in the results of calculating the area from the true area depending on the number of measurement points and the standard deviation of random additives is analyzed. It is shown that the ratio of the relative standard deviations of the area to the relative standard deviations of the coordinates is approximately the same for each number of measurements. The dependence of this relationship on the number of measurements is determined. The results obtained are analyzed.

Exit Condition for Probabilistic Assessment Using Monte Carlo Method

2010 ◽  
Vol 10 (1) ◽  
pp. 1-9
Author(s):  
Jakub Valihrach ◽  
Petr Konečný
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Optimization Design ◽  
Random Variable ◽  
Probability Of Failure ◽  
Probabilistic Assessment ◽  
Theoretical Derivation ◽  
The Monte Carlo Method ◽  
The Relationship

Exit Condition for Probabilistic Assessment Using Monte Carlo Method This paper introduces a condition used to exit a probabilistic assessment using the Monte Carlo simulation, and to evaluate it with regard to the relationship between the computed estimate of the probability of failure and the target design probability. The estimation of probability of failure is treated as a random variable, considering its variance that is dependent on the number of performed Monte Carlo simulation steps. After theoretical derivation of the decision condition, it is tested numerically with regard to its accuracy and computational efficiency. The condition is suitable for optimization design using the Monte Carlo method.

scholarly journals Quantifying and Correcting the Bias in Estimated Risk Measures

2007 ◽  
Vol 37 (2) ◽  
pp. 365-386 ◽  
Author(s):  
Joseph Hyun Tae Kim ◽  
Mary R. Hardy
Keyword(s):  
At Risk ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value At Risk ◽  
Risk Measures ◽  
Bootstrap Techniques ◽  
Practical Guideline ◽  
Estimated Risk ◽  
Conditional Tail Expectation

In this paper we explore the bias in the estimation of the Value at Risk and Conditional Tail Expectation risk measures using Monte Carlo simulation. We assess the use of bootstrap techniques to correct the bias for a number of different examples. In the case of the Conditional Tail Expectation, we show that application of the exact bootstrap can improve estimates, and we develop a practical guideline for assessing when to use the exact bootstrap.

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