scholarly journals The Expected Utility Insurance Premium Principle with Fourth-Order Statistics: Does It Make a Difference?

Algorithms ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 116
Author(s):  
Alessandro Mazzoccoli ◽  
Maurizio Naldi
Keyword(s):  
Order Statistics ◽  
Fourth Order ◽  
Expected Utility ◽  
Value At Risk ◽  
Order Approximation ◽  
Insurance Premium ◽  
Second Order ◽  
Accurate Approximation ◽  
Increased Risk ◽  
The Impact

The expected utility principle is often used to compute the insurance premium through a second-order approximation of the expected value of the utility of losses. We investigate the impact of using a more accurate approximation based on the fourth-order statistics of the expected loss and derive the premium under this expectedly more accurate approximation. The comparison between the two approximation levels shows that the second-order-based premium is always lower (i.e., an underestimate of the correct one) for the commonest loss distributions encountered in insurance. The comparison is also carried out for real cases, considering the loss parameters values estimated in the literature. The increased risk of the insurer is assessed through the Value-at-Risk.

scholarly journals Beyond second-order convergence in simulations of magnetized binary neutron stars with realistic microphysics

2019 ◽  
Vol 490 (3) ◽  
pp. 3588-3600 ◽  
Author(s):  
E R Most ◽  
L Jens Papenfort ◽  
L Rezzolla
Keyword(s):  
Neutron Stars ◽  
Fourth Order ◽  
Finite Temperature ◽  
Equations Of State ◽  
Magnetic Energy ◽  
Second Order ◽  
Conservative Finite Difference Scheme ◽  
Order Scheme ◽  
Convergence Orders ◽  
The Impact

ABSTRACT We investigate the impact of using high-order numerical methods to study the merger of magnetized neutron stars with finite-temperature microphysics and neutrino cooling in full general relativity. By implementing a fourth-order accurate conservative finite-difference scheme we model the inspiral together with the early post-merger and highlight the differences to traditional second-order approaches at the various stages of the simulation. We find that even for finite-temperature equations of state, convergence orders higher than second order can be achieved in the inspiral and post-merger for the gravitational-wave phase. We further demonstrate that the second-order scheme overestimates the amount of proton-rich shock-heated ejecta, which can have an impact on the modelling of the dynamical part of the kilonova emission. Finally, we show that already at low resolution the growth rate of the magnetic energy is consistently resolved by using a fourth-order scheme.

Measuring the Welfare Loss of Pension Mandates: A Methodology and Example

1985 ◽  
Vol 13 (1) ◽  
pp. 47-62
Author(s):  
Kathy Hayes ◽  
Shawna Grosskopf
Keyword(s):  
Approximation Method ◽  
Local Governments ◽  
Order Approximation ◽  
Second Order ◽  
Welfare Loss ◽  
Compensating Variation ◽  
Second Order Approximation ◽  
Price Distortion ◽  
Recent Advances ◽  
The Impact

In this article we employ recent advances in measuring consumer's surplus (and the related Hicksian compensation measures) to measure the impact of state mandates requiring local governments to establish minimum pensions for their employees. We measure the Hicksian compensating variation of the price distortion caused by such mandates and compare those losses to those calculated using a Harberger-type second-order approximation method.

scholarly journals Understanding the impact of Light cone effect on the EoR/CD 21-cm power spectrum

2017 ◽  
Vol 12 (S333) ◽  
pp. 12-17
Author(s):  
Kanan K. Datta ◽  
Rajesh Mondal ◽  
Raghunath Ghara ◽  
Somnath Bharadwaj ◽  
T. Roy Choudhury
Keyword(s):  
Power Spectrum ◽  
Order Statistics ◽  
Light Cone ◽  
Second Order ◽  
Line Of Sight ◽  
Periodic Signal ◽  
Angular Power Spectrum ◽  
Second Order Statistics ◽  
The Impact

AbstractRedshifted HI 21-cm signal from the cosmic dawn and epoch of reionization evolve considerably along the LoS. We study the impact of this evolution (so called the light cone effect) on the HI 21-cm power spectrum. It is found that the LC effect has a significant impact on the 3D power spectrum and the change could be up to a factor of few. The LC effect is particularly strong during the cosmic dawn near the ‘peaks’ and ‘dips’ in the power spectrum when plotted with redshift. We also show that the 3D power spectrum, which could fully describe ergodic and periodic signal, losses out some information regarding the second order statistics of the signal as the EoR/CD 21-cm signal is non-ergodic and non-periodic along the line of sight. We show that the multi-frequency angular power spectrum (MAPS)${\mathcal {C}}_{\ell }(\nu _1, \nu _2)$captures all the information regarding the second order statistics of the signal even in the presence of the LC effect.

scholarly journals OPTIMAL PROPORTIONAL REINSURANCE UNDER TWO CRITERIA: MAXIMIZING THE EXPECTED UTILITY AND MINIMIZING THE VALUE AT RISK

2010 ◽  
Vol 51 (4) ◽  
pp. 449-463 ◽  
Author(s):  
ZHIBIN LIANG ◽  
JUNYI GUO
Keyword(s):  
At Risk ◽  
Expected Utility ◽  
Value At Risk ◽  
Optimal Solution ◽  
Optimal Strategies ◽  
Pareto Optimal Solution ◽  
Model Parameters ◽  
Pareto Optimal ◽  
Proportional Reinsurance ◽  
The Impact

AbstractWe consider the optimal proportional reinsurance from an insurer’s point of view to maximize the expected utility and minimize the value at risk. Under the general premium principle, we prove the existence and uniqueness of the optimal strategies and Pareto optimal solution, and give the relationship between the optimal strategies. Furthermore, we study the optimization problem with the variance premium principle. When the total claim sizes are normally distributed, explicit expressions for the optimal strategies and Pareto optimal solution are obtained. Finally, some numerical examples are presented to show the impact of the major model parameters on the optimal results.

A Practical Fourth Order Finite-Difference Time-Domain Algorithm for the Solution of Maxwell’s Equations

2021 ◽  
Vol 35 (11) ◽  
pp. 1422-1423
Author(s):  
Antonio Thomson ◽  
Atef Elsherbeni ◽  
Mohammed Hadi
Keyword(s):  
Finite Difference ◽  
Fourth Order ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Order Approximation ◽  
Second Order ◽  
Dipole Antennas ◽  
Simulation Accuracy ◽  
Space Formulation ◽  
Difference Time

Implementing a practical fourth order accurate in time and second order accurate in space finite difference time domain simulation using MATLAB is the goal of this paper. The formulation presented for the fourth order approximation is simple to integrate into an existing second order accurate in time and second order accurate in space formulation and well-established code. The fourth order formulation has been verified and simulation accuracy is confirmed through the application of radiation from a single and an array of dipole antennas.

Principal domains of the trispectrum, signal bandwidth, and implications for deconvolution

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 958-969 ◽  
Author(s):  
Lisa A. Pflug
Keyword(s):  
Order Statistics ◽  
Fourth Order ◽  
Gaussian Noise ◽  
Second Order ◽  
Second Order Statistics ◽  
Mathematical Properties ◽  
Existence Conditions ◽  
Non Gaussian ◽  
The Individual ◽  
The Relationship

Fourth‐order statistics can be useful in many signal processing applications, offering advantages over or supplementing second‐order statistical techniques. One reason is that fourth‐order statistics can discriminate between non‐Gaussian signals and Gaussian noise. Another is that fourth‐order statistics contain phase information, whereas second‐order statistics do not. In the continuing development of the mathematical properties of fourth‐order statistics, several researchers have derived existence conditions and definitions for the unaliased and aliased principal domains of the discrete trispectrum, which is significantly more complex than the power or energy spectrum. The consistencies and inconsistencies of these results are presented and resolved in this paper. The most flexible definitions give four individual principal domains for the discrete trispectrum: two unaliased and two aliased. The most useful combinations are those that combine the two unaliased domains together and the two aliased domains together, which can be done easily from the four individual domains. The relationship between the individual trispectral domains and signal bandwidth is important when using the fourth‐order statistic for applications because they have particular properties that can be detrimental to some deconvolution algorithms. The reasons for this, as well as the validity of proposed solutions to this problem, are explained by the trispectral structure and its origins.

Second-Order Statistics of MRC Reception With a Transparent Amplify-and-Forward Relay

2020 ◽  
Vol 12 (1) ◽  
pp. 1-14
Author(s):  
Jia-Chin Lin ◽  
Chun-Lin Lin
Keyword(s):  
Order Statistics ◽  
Spatial Diversity ◽  
Second Order ◽  
Maximal Ratio Combining ◽  
Relay Network ◽  
Upper And Lower Bounds ◽  
Amplify And Forward ◽  
Second Order Statistics ◽  
Af Relay ◽  
The Impact

Achievable spatial diversity supported by a single transparent amplify-and-forward (AF) relay relies on disintegrated channel state information (CSI) that can be acquired at the destination. This paper studies the impact of the quantization of the source-relay (SR) CSI in terms of the first- and second-order statistics of maximal-ratio combining (MRC) reception with the incomplete SR CSI at the destination. Probability density functions (PDFs) of the upper and lower bounds of the signal-to-noise ratio (SNR) achieved at the destination are derived. Corresponding level-crossing rate (LCR) and average fade-duration (AFD), which are undoubtedly required to choose parameters of forward error correcting (FEC) mechanisms across the transparent AF relay network, are evaluated via Monte Carlo simulations. The simulations show that the SNR PDF, LCR and AFD highly depends not only on the accuracy of SR CSI at the destination but also on the location of the AF relay.

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