Standard Deviation Principle Research Articles

Determination of Micro-Insurance Premium Price for Fisheries Using Poisson-Exponential Aggregate Distribution Approach

Engaging in pond aquaculture is currently an attractive option amid the high demand for fish in the market. Entrepreneurial opportunities in the pond fish farming sector are increasingly open, although the risk of crop failure remains, both due to weather factors and the livestock process. Crop failure can have a significant financial impact on pond aquaculture cultivators. Therefore, it is necessary to have special insurance to protect against financial losses due to risks that can occur, namely Fisheries Micro Insurance. Microinsurance is a type of insurance product that is specifically designed for low-income people, offering simple, accessible, economically priced features and administration, and a fast compensation settlement process. The focus of this research is to calculate premium prices by applying an aggregate risk model approach. The data used is the number of incidents and the amount of losses due to crop failure in shrimp pond cultivation in Pandeglang Regency in the period of January 1, 2019-January 1, 2021. Data on the number of events follows the Poisson distribution, while data on the magnitude of losses follows the Exponential distribution. Furthermore, the Maximum Likelihood Estimation (MLE) method is used to calculate the parameter estimation. The average and variance estimates of the aggregate risk are used to determine the amount of premiums. The result of the premium selection in this study is IDR 42,005,600. The amount of premium reflects the collective premium resulting from the calculation based on the standard deviation principle.

Pricing of Fisheries Microinsurance Premiums using the Poisson-Exponential Aggregate Distribution Approach

Engaged in pond aquaculture is currently an attractive choice amid the high demand for fish in the market. Entrepreneurial opportunities in the pond fish farming sector are increasingly open, although the risk of crop failure remains, both due to weather factors and livestock processes. Crop failure can have a significant financial impact on pond fishery farmers. Therefore, there is a need for special insurance to protect against financial losses due to risks that can occur, namely Micro Fisheries Insurance. Microinsurance is a type of insurance product specifically designed for people with low income levels, offers features and administration that is simple, easily accessible, has an economical price, and a fast compensation settlement process. The focus of this study is to calculate premium prices by applying an aggregate risk model approach. The data used are the number of events and the magnitude of losses due to crop failure in shrimp pond cultivation in Pandeglang Regency in the period January 1, 2019-January 1, 2021. Data on the number of events follow the Poisson distribution, while data on the magnitude of losses follow the Exponential distribution. Next, it uses the Maximum Likelihood Estimation (MLE) method to calculate parameter estimation. The average and variance of aggregate risk is used to determine the size of the premium. The premium selection results in this study amounted to Rp42,005,600. The amount of the premium reflects the collective premium resulting from the calculation based on the standard deviation principle.

Pricing of Aquaculture Industry Microinsurance Premiums with Standard Deviation Principle Approach (Case Study: Tasikmalaya)

Aquaculture is a rapidly growing industry and has enormous potential to increase the income and welfare of fish farmers. The majority of aquaculture businesses in Indonesia are small-scale cultivators, low productivity and limited business accessibility. As a result, there is an aquaculture industry that does not understand the use of aquaculture-specific financial risk management tools. Therefore, an insurance instrument is needed to manage losses that occur so as to achieve financial and income benefits, namely Micro Insurance. This study aims to calculate premium prices with a standard deviation principle approach. The data used is loss data if aquaculture cultivators do not pay in accordance with the initial capital in Tasikmalaya obtained through primary data based on the results of field surveys through questionnaires. The method of analyzing the number of event data uses the Poisson distribution, while the loss data uses the Exponential distribution. Next, calculate the parameter estimation using the Maximum Likelihood Estimation method. The results of parameter estimation are used to find a collective risk model. From the calculation results in this study, a premium price of IDR was obtained.

The premium of uncertain risk based on standard deviation principle

Risk measurement and insurance pricing have always been issues of concern in actuarial science. Under the framework of uncertainty theory, this paper puts forward a new premium principle: uncertain standard deviation premium principle, proposes some of its properties about risk and compares the premiums of different risks. Based on the utility function of risk aversion, the additional premium coefficient is derived and two specific numerical examples are used to calculate the maximum premium. Furthermore, the unknown parameters of the policy with deductible are estimated by uncertain moment estimation and uncertain maximum likelihood estimation.

Spin Chaos Dynamics in Classical Random Dipolar Interactions

The stochastic nature of magnetization dynamics of dipole–dipole interactions described by the Landau–Lifshitz–Gilbert equation without considering the Gilbert damping parameter is investigated. It is shown that the occurrence of the complex dynamic states depends on the spatial anisotropy of interactions on one hand and the lattice geometry on the other. It is observed from the higher-order moments of the magnetization fluctuations that two significant dynamical regimes, regular and chaos, may be obtained depending on the perturbation strength. Relying on the Hurst exponent obtained by the standard deviation principle, the correlation and persistence of the magnetization fluctuations are analyzed. The results also exhibit a transition from an anti-correlated to a positively correlated system as the relevant parameters of the system vary.

Determination of Earthquake Insurance Premium Based on Great Physical and Economic Loss Using the Bayesian Method

Indonesia is an area prone to earthquakes because it is traversed by the meeting point of 3 tectonic plates, namely: the Indo-Australian plate, the Eurasian plate and the Pacific plate. An earthquake is an event where the earth vibrates due to a sudden restraint of energy in the earth which is characterized by the breaking of rock layers in the earth's crust. Almost all regions in Indonesia are at risk of being exposed to earthquakes. To anticipate the risk of natural disasters, earthquakes are advised to join the insurance program provided by the insurance company. This study aims to determine earthquake insurance premiums based on large physical and economic losses. The method used is the Bayesian method. This method produces each estimated loss value which is then used to calculate the combined estimated loss value. After that, the combined estimated loss value is used to calculate the premium value. The result of this research is the premium which is calculated based on the principle of expected value and standard deviation principle. The premium resulting from the expected value principle is lower than the premium resulting from the standard deviation principle.

Determining the Price of Fisherman Micro Insurance Premiums Using the Aggregate Risk Model Approach in Cirebon Regency

Catastrophe such as hurricanes, heavy rains, and similar occurrence pose serious threats and risks to fishermen's livelihoods as well as losses from damage to their assets. Therefore, it is necessary to have special insurance to protect the fishermen's assets from financial losses due to the risks that can occur, namely Fisherman Micro Insurance. Micro-insurance is an insurance product that is intended for low-income people with features and administration that are simple, easy to obtain, economical prices and immediately in the completion of the provision of compensation. Fisherman's micro insurance guarantees assets in the form of fishing equipment in the occurrence of a risk of an accident causing damage, this insurance product protects against worries without a large premium burden. This study aims to calculate the premium price with an aggregate risk model approach. The data used is data on fisherman’s losses if they did not go to sea which obtained by surveys. The occurrence data follows the Poisson distribution, and the loss data follows the Exponential distribution. Parameter Estimation was carried out using the Maximum Likelihood Estimation. The estimation results from numbers of occurrence and the amount of losses are used to estimate the collective risk model. Estimators of the average and variance of the aggregate risk are used to determine the premium. The results of the premium selection in this study amounted to IDR 153.861.958.00. The premium amount is a collective premium which is the result of a calculation based on the standard deviation principle.

Determination of the natural disaster insurance premiums by considering the mitigation fund reserve decisions: An application of collective risk model

In Indonesia, natural disasters cases have significantly increased from time to time and have the largest impact on economic losses. To avoid losses in the future due to natural disasters, the insurance company needs to estimate the risk and determine the rate of premium that would be charged to the policyholder. In conjunction with the present issue, this study seeks to determine the premium rate and estimate the size claim of insurance by considering the mitigation fund reserve decisions using The Collective Risk Model (CRM). The data was analyzed using the Poisson process with Weibull distribution to determine the natural disaster frequency and losses. The distribution of losses is estimated using Maximum Likelihood Estimation (MLE), and the magnitude of losses was estimated using the CRM. Also, the mean and variance estimators of the aggregate risk were used to estimate the premium charged. The results indicated that expectation and variance of the frequency of incident claims have the same value, i.e., 2562. Also, the loss claims follow the Weibull distribution with the expected value and variance of 5.81309×1010 and 2.5301×1022, respectively. The mean and variance of the aggregate (collective) claims are 148,931,365,800,000 and 7.35×1025, respectively. In conclusion, this study has successfully determined the efficient pure premium model through the Standard Deviation Principle (SDP). SDP provides a much cheaper premium than the Expected Value Principle with the same loading factor. In addition, SDP considers the standard deviation of the collective risk of natural disasters. The implications of the results of the premium determination are expected to be the basis for decision-making for insurance companies and the government in determining insurance policies for natural disaster mitigation.

Uncertain multi-objective dynamic weapon-target allocation problem based on uncertainty theory

<abstract><p>The weapon-target allocation (WTA) problem is a fundamental subject of defense-related applications research, and previous studies assume that the parameters in the model are determinate. For the real battlefield, asymmetric information usually leads to the failure of the above assumption, and there are uncertain factors whose frequency is hard to pinpoint. Based on uncertainty theory, we study a WTA problem in indeterminate battlefield in this paper. First, we analyze the uncertain factors in indeterminate battlefield and their influence on WTA problem. Then, considering the target threat value, the protected asset value and the extra cost of interception as uncertain variables, the uncertain multi-objective dynamic WTA (UMDWTA) model is established, where three indices including the value of destruction of targets, the value of surviving assets and the cost of operation are regarded as objective functions, and on this basis, an equivalent transformation is presented to convert the UMDWTA model into a determinate multi-objective programming (MOP) problem by expected value and standard deviation principle. To solve the proposed model efficiently, an improved multi-objective evolutionary algorithm based on decomposition (MOEA/D) is designed, which employs three new evolutionary operators and the weight vectors adaptation mechanism to improve the convergence and uniformity of the Pareto front obtained. Finally, a case of the UMDWTA problem is carried out to be solved by the designed algorithm, and the results verify the feasibility of the proposed model.</p></abstract>

PRODUCTIVITY OF FIRST CALVING COWS UKRAINIAN BLACK-AND-WHITE DAIRY BREED DEPENDING ON WEIGHT GROWTH OF HEIFERS

The productivity of cows with the first calving depending on live weight and average daily gains of heifers during rearing studied. The data of animals of Ukrainian Black-and-White dairy breed of Kyiv factory type used for the research. Every three months, from birth to 18 months of age, heifers were determined live weight and average daily gain. According to the indicators of weight growth, the heifers divided into 5 groups of the standard deviation principle from the mean. In animals included in these groups studied the performance of the first lactation. It found that obtaining a live weight of 3-month-old heifers over 127 kg can significantly reduce the age of the first calving. The advantage over animals belonging to the groups with less weight is 2.7-3.5 months. Increasing the live weight of heifers at 12 and 15 months also allows reducing the age of the first calving. Moderate (less than 722 g per day) growth of heifers at the age of 6-9 months also has a positive effect on the reduction of the age of the first calving. The weight of newborns heifers during lactation was associated with first calving cow’s milk yield. Heifers born with the lowest live weight (less than 28 kg) had after the first calving milk yield per lactation 145… 1956 kg more than in other groups. The live weight of 3-month-old heifers is of the greatest importance for the formation of high milk productivity of cows. Obtaining live weight of heifers of this age 117-127 kg with an average daily gain of 902-1037 g provided in first the lactation the largest milk yield with an advantage over animals of other groups up to 3119 kg. In older age periods, the influence of growing heifers on the formation of milk productivity is less pronounced, and the optimal live weight and growth rate was at the level of the average size of the herd. The research results can used to optimize the growth plans of heifers and their selection.

FDOST-Based Fault Classification Scheme for Fixed Series Compensated Transmission System

This paper proposes a new method for diagnosis of fault type and faulty phase of a series compensated transmission line. The standard deviation (SD) principle together with the fast discrete orthonormal s-transform (FDOST) and the decision tree (DT) is applied for the purpose of fault classification. The FDOST, as an efficient signal processing tool, is used for extracting the features from a half cycle window of voltage and current signals sampled from one end of the power system network. Finally, the SD of a half cycle post-fault samples of the FDOST coefficients is calculated to form the input feature vector for the DT-based classifier. The features are processed by the DT to classify faults. The practicability of the proposed method is validated by modified Western System Coordinating Council 3-machine 9-bus system simulated in the PSCAD/EMTDC software and field fault data captured from a real transmission network of Chhattisgarh state, India. The results confirm that the proposed method reliably classifies all types of faults with high efficacy.

Optimal Reinsurance Design: A Mean-Variance Approach

In this article, we study an optimal reinsurance model from the perspective of an insurer who has a general mean-variance preference. In order to reduce ex post moral hazard, we assume that both parties in a reinsurance contract are obligated to pay more for a larger realization of loss. We further assume that the reinsurance premium is calculated only based on the mean and variance of the indemnity. This class of premium principles is quite general in the sense that it includes many widely used premium principles such as expected value, mean value, variance, and standard deviation principles. Moreover, to protect the insurer's profit, a lower bound is imposed on its expected return. We show that any admissible reinsurance policy is dominated by a change-loss reinsurance or a dual change-loss reinsurance, depending upon the coefficient of variation of the ceded loss. Further, the change-loss reinsurance is shown to be optimal if the premium loading increases in the actuarial value of the coverage; while it becomes decreasing, the optimal reinsurance policy is in the form of dual change loss. As a result, the quota-share reinsurance is always optimal for any variance-related reinsurance premium principle. Finally, some numerical examples are applied to illustrate the applicability of the theoretical results.

Multivariate reinsurance designs for minimizing an insurer’s capital requirement

This paper investigates optimal reinsurance strategies for an insurer with multiple lines of business under the criterion of minimizing its total capital requirement calculated based on the multivariate lower-orthant Value-at-Risk. The reinsurance is purchased by the insurer for each line of business separately. The premium principles used to compute the reinsurance premiums are allowed to differ from one line of business to another, but they all satisfy three mild conditions: distribution invariance, risk loading and preserving the convex order, which are satisfied by many popular premium principles. Our results show that an optimal strategy for the insurer is to buy a two-layer reinsurance policy for each line of business, and it reduces to be a one-layer reinsurance contract for premium principles satisfying some additional mild conditions, which are met by the expected value principle, standard deviation principle and Wang’s principle among many others. In the end of this paper, some numerical examples are presented to illustrate the effects of marginal distributions, risk dependence structure and reinsurance premium principles on the optimal layer reinsurance.

Ambient Air Quality Assessment via Comprehensive Evaluation through Automatic Weight Determining

A mathematical model is built for air quality evaluation, which has taken PM2.5, PM10, SO2, NO2, CO and O3 six parameters into consideration. The comprehensive air quality evaluation is carried out via standard deviation method and principle component analysis method; automatic weight determining has been discussed. Correlations of the factors are considered and a preprocess procedure is issued to eliminate the effects. Ambient air quality data of eleven cities are taken as an example and the comprehensive evaluation results are compared, which shows the mathematical model provides a viable approach to environmental assessment.

Risk Classiification for Claim Counts and Losses Using Generalized Additive Models for Location, Scale and Shape

This paper presents and compares different risk classification models for the number and the costs of claims employing generalized additive models for location, scale and shape. The difference between these models is analyzed through the mean and the variance of the annual number of claims and the costs of claims of the insureds, who belong to different risk classes and interesting results about claiming behavior are obtained. Furthermore, the resulting a priori premiums rates are calculated via the expected value and standard deviation principles with independence between the claim frequency and severity components assumed.

Optimal reinsurance under the standard deviation principle

This paper concerns how to purchase the reinsurance to minimize both the insurer and the reinsurers risk fluctuation under the standard deviation principle. Sufficient conditions for the optimal reinsurance contract are obtained in the restricted class of admissible contracts. Assume that the reinsurers risk is less than a threshold, and then wefind out the optimal reinsurance contract that minimizes the insurers risk. Here the insurer company can take three general and useful risk measures.

Optimal reinsurance under the general mixture risk measures

This paper concerns the problem of how to purchase the reinsurance in order to make the insurer and the reinsurer’s total risk least under the standard deviation principle. Sufficient conditions for optimality of reinsurance contract are given within the restricted class of admissible contracts. Here, the insurer and reinsurance company can take arbitrary risk measures, respectively. Further, we give the explicit forms of optimal reinsurance contract under special risk measures. We also give the method to decide the parameters.

Hedging with a correlated asset: Solution of a nonlinear pricing PDE

Hedging a contingent claim with an asset which is not perfectly correlated with the underlying asset results in unhedgeable residual risk. Even if the residual risk is considered diversifiable, the option writer is faced with the problem of uncertainty in the estimation of the drift rates of the underlying and the hedging instrument. If the residual risk is not considered diversifiable, then this risk can be priced using an actuarial standard deviation principle in infinitesimal time. In both cases, these models result in the same nonlinear partial differential equation (PDE). A fully implicit, monotone discretization method is developed for solution of this pricing PDE. This method is shown to converge to the viscosity solution. Certain grid conditions are required to guarantee monotonicity. An algorithm is derived which, given an initial grid, inserts a finite number of nodes in the grid to ensure that the monotonicity condition is satisfied. At each timestep, the nonlinear discretized algebraic equations are solved using an iterative algorithm, which is shown to be globally convergent. Monte Carlo hedging examples are given to illustrate the profit and loss distribution at the expiry of the option.

Indifference pricing of insurance contracts in a product space model

The financial variance and standard deviation principles of Schweizer (2001b) are applied for the valuation of insurance contracts. These principles are financial transformations of the classical actuarial variance and standard deviation principles and take into consideration the possibilities of hedging on financial markets. We focus on the role of the information available to the insurer and study its impact on the fair premiums and the optimal trading strategies for insurance claims with financial risk. The presentation is kept within a product space model, a construction which is discussed in detail. Via a projection argument for Hilbert spaces, we show that the variance of the so-called non-hedgeable part of an insurance claim increases when the information is restricted from one filtration to a smaller filtration. By considering two extreme filtrations for the pure insurance risk, we arrive at simple upper and lower bounds for the fair premiums.

Indifference pricing of insurance contracts in a product space model: applications

This paper determines fair premiums and optimal strategies under the financial variance and standard deviation principles of Schweizer [Insur.: Math. Econ. 28 (2001b) 31] for some insurance contracts with financial risk. Examples considered include unit-linked pure endowment contracts and integrated risk management solutions such as stop-loss contracts with barrier and financial stop-loss contracts. In each example we illustrate how the amount of information available to the reinsurer affects premiums and investment strategies. In addition, we determine the simple upper and lower bounds for the fair premiums that were obtained in [Finan. Stochast., in press].