scholarly journals On optimal periodic dividend and capital injection strategies for spectrally negative Lévy models

2018 ◽  
Vol 55 (4) ◽  
pp. 1272-1286 ◽  
Author(s):  
Kei Noba ◽  
José-Luis Pérez ◽  
Kazutoshi Yamazaki ◽  
Kouji Yano
Keyword(s):  
Arrival Time ◽  
Arrival Times ◽  
Classical Sense ◽  
Capital Injection ◽  
Dividend Payments ◽  
Poisson Arrival ◽  
Optimal Dividend ◽  
Injection Strategies

Abstract De Finetti’s optimal dividend problem has recently been extended to the case when dividend payments can be made only at Poisson arrival times. In this paper we consider the version with bail-outs where the surplus must be nonnegative uniformly in time. For a general spectrally negative Lévy model, we show the optimality of a Parisian-classical reflection strategy that pays the excess above a given barrier at each Poisson arrival time and also reflects from below at 0 in the classical sense.

scholarly journals On Periodic Dividends for the Classical Risk Model with Debit Interest

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Hua Dong ◽  
Xianghua Zhao
Keyword(s):  
Differential Equations ◽  
Risk Model ◽  
Classical Risk Model ◽  
Arrival Times ◽  
Numerical Examples ◽  
Dividend Payments ◽  
Poisson Arrival ◽  
Optimal Dividend ◽  
Debit Interest ◽  
The Classical Risk Model

A periodic dividend problem is studied in this paper. We assume that dividend payments are made at a sequence of Poisson arrival times, and ruin is continuously monitored. First of all, three integro-differential equations for the expected discounted dividends are obtained. Then, we investigate the explicit expressions for the expected discounted dividends, and the optimal dividend barrier is given for exponential claims. A similar study on a generalized Gerber–Shiu function involving the absolute time is also performed. To demonstrate the existing results, we give some numerical examples.

scholarly journals Optimal Dividend and Capital Injection Strategies for a Risk Model under Force of Interest

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Ying Fang ◽  
Zhongfeng Qu
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Insurance Company ◽  
Threshold Strategy ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
Optimal Injection ◽  
Force Of Interest ◽  
Capital Injections ◽  
Injection Strategies

As a generalization of the classical Cramér-Lundberg risk model, we consider a risk model including a constant force of interest in the present paper. Most optimal dividend strategies which only consider the processes modeling the surplus of a risk business are absorbed at 0. However, in many cases, negative surplus does not necessarily mean that the business has to stop. Therefore, we assume that negative surplus is not allowed and the beneficiary of the dividends is required to inject capital into the insurance company to ensure that its risk process stays nonnegative. For this risk model, we show that the optimal dividend strategy which maximizes the discounted dividend payments minus the penalized discounted capital injections is a threshold strategy for the case of the dividend payout rate which is bounded by some positive constant and the optimal injection strategy is to inject capitals immediately to make the company's assets back to zero when the surplus of the company becomes negative.

scholarly journals Optimal Dividend and Capital Injection Strategies in the Cramér-Lundberg Risk Model

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Yan Li ◽  
Guoxin Liu
Keyword(s):  
Value Function ◽  
Risk Model ◽  
Capital Injection ◽  
Time Of Ruin ◽  
Optimal Dividend ◽  
The Time Of Ruin ◽  
Hamilton Jacobi Bellman ◽  
Injection Barrier ◽  
The Value Function ◽  
Injection Strategies

We discuss the optimal dividend and capital injection strategies in the Cramér-Lundberg risk model. The value functionV(x)is defined by maximizing the discounted value of the dividend payment minus the penalized discounted capital injection until the time of ruin. It is shown thatV(x)can be characterized by the Hamilton-Jacobi-Bellman equation. We find the optimal dividend barrierb, the optimal upper capital injection barrier 0, and the optimal lower capital injection barrier-z*. In the case of exponential claim size especially, we give an explicit procedure to obtainb,-z*, and the value functionV(x).

scholarly journals Optimal Dividend and Capital Injection Problem with Transaction Cost and Salvage Value: The Case of Excess-of-Loss Reinsurance Based on the Symmetry of Risk Information

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 276 ◽  
Author(s):  
Qingyou Yan ◽  
Le Yang ◽  
Tomas Baležentis ◽  
Dalia Streimikiene ◽  
Chao Qin
Keyword(s):  
Transaction Cost ◽  
Risk Information ◽  
Insurance Company ◽  
Optimal Control Strategy ◽  
Ruin Time ◽  
Discounted Cost ◽  
Capital Injection ◽  
Surplus Process ◽  
Optimal Dividend ◽  
A Company

This paper considers the optimal dividend and capital injection problem for an insurance company, which controls the risk exposure by both the excess-of-loss reinsurance and capital injection based on the symmetry of risk information. Besides the proportional transaction cost, we also incorporate the fixed transaction cost incurred by capital injection and the salvage value of a company at the ruin time in order to make the surplus process more realistic. The main goal is to maximize the expected sum of the discounted salvage value and the discounted cumulative dividends except for the discounted cost of capital injection until the ruin time. By considering whether there is capital injection in the surplus process, we construct two instances of suboptimal models and then solve for the corresponding solution in each model. Lastly, we consider the optimal control strategy for the general model without any restriction on the capital injection or the surplus process.

scholarly journals Detection of specific areas and densities for ultrasound tomography

2019 ◽  
pp. 121-127
Author(s):  
Victoria Erofeeva ◽  
Vasilisa Galyamina ◽  
Kseniya Gonta ◽  
Anna Leonova ◽  
Oleg Granichin ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Ultrasound Imaging ◽  
Arrival Time ◽  
Detection Accuracy ◽  
Problem Solution ◽  
Ultrasound Tomography ◽  
Arrival Times ◽  
Whole Process ◽  
Imaging Reconstruction ◽  
Tomography Data

In this paper we consider the problem of ultrasound tomography. Recently, an increased interest in ultrasound tomography has been caused by non-invasiveness of the method and increased detection accuracy (as compared to radiation tomography), and also ultrasound tomography does not put at risk human health. We study possibilities of detection of specific areas and determining their density using ultrasound tomography data. The process of image reconstruction based on ultrasound data is computationally complex and time consuming. It contains the following parts: calculation of the time-of-flight (TOF) of a signal, detection of specific areas, calculation of density of specific areas. The calculation of the arrival time of a signal is a very important part, because the errors in the calculation of quantities strongly influence the total problem solution. We offer ultrasound imaging reconstruction technology that can be easily parallelized. The whole process is described: from extracting the arrival times of signals raw data feeding from physical receivers to obtaining the desired results.

scholarly journals REFRACTION–REFLECTION STRATEGIES IN THE DUAL MODEL

2016 ◽  
Vol 47 (1) ◽  
pp. 199-238 ◽  
Author(s):  
José-Luis Pérez ◽  
Kazutoshi Yamazaki
Keyword(s):  
Additional Condition ◽  
Numerical Results ◽  
Dual Model ◽  
Maximal Rate ◽  
Absolutely Continuous ◽  
Capital Injection ◽  
Surplus Process ◽  
Optimal Dividend

AbstractWe study the dual model with capital injection under the additional condition that the dividend strategy is absolutely continuous. We consider a refraction–reflection strategy that pays dividends at the maximal rate whenever the surplus is above a certain threshold, while capital is injected so that it stays non-negative. The resulting controlled surplus process becomes the spectrally positive version of the refracted–reflected process recently studied by Pérez and Yamazaki (2015). We study various fluctuation identities of this process and prove the optimality of the refraction–reflection strategy. Numerical results on the optimal dividend problem are also given.

Joint microseismic event location and anisotropic velocity inversion with the cross double-difference method using downhole microseismic data

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. KS63-KS73
Author(s):  
Yangyang Ma ◽  
Congcong Yuan ◽  
Jie Zhang
Keyword(s):  
Arrival Time ◽  
Velocity Model ◽  
P Wave ◽  
Double Difference ◽  
S Wave ◽  
Arrival Times ◽  
Monitoring Well ◽  
The Cross ◽  
Microseismic Event ◽  
Wave Arrival

We have applied the cross double-difference (CDD) method to simultaneously determine the microseismic event locations and five Thomsen parameters in vertically layered transversely isotropic media using data from a single vertical monitoring well. Different from the double-difference (DD) method, the CDD method uses the cross-traveltime difference between the S-wave arrival time of one event and the P-wave arrival time of another event. The CDD method can improve the accuracy of the absolute locations and maintain the accuracy of the relative locations because it contains more absolute information than the DD method. We calculate the arrival times of the qP, qSV, and SH waves with a horizontal slowness shooting algorithm. The sensitivities of the arrival times with respect to the five Thomsen parameters are derived using the slowness components. The derivations are analytical, without any weak anisotropic approximation. The input data include the cross-differential traveltimes and absolute arrival times, providing better constraints on the anisotropic parameters and event locations. The synthetic example indicates that the method can produce better event locations and anisotropic velocity model. We apply this method to the field data set acquired from a single vertical monitoring well during a hydraulic fracturing process. We further validate the anisotropic velocity model and microseismic event locations by comparing the modeled and observed waveforms. The observed S-wave splitting also supports the inverted anisotropic results.

scholarly journals The Astrometric Possibilities of Very-Long-Baseline Interferometry

1986 ◽  
Vol 109 ◽  
pp. 143-155
Author(s):  
D. S. Robertson
Keyword(s):  
Plane Wave ◽  
Arrival Time ◽  
Very Long Baseline Interferometry ◽  
Radio Sources ◽  
Arrival Times ◽  
Long Baseline ◽  
The Difference ◽  
Different Sources

In the application of Very-Long-Baseline Interferometry (VLBI) to astrometric problems the fundamental observable is the difference in the arrival times of a wavefront at two widely separated receiving stations. Since the radio sources being observed are sufficiently distant that the arriving wavefront can be considered to be a plane wave, the differential arrival time is a measure of the component of the baseline in the direction of the source. Equivalently, if the baseline is known, the differential arrival time is sufficient to determine a circle on the sky containing the source. It is easy to show that a minimum of ten observations distributed among three different sources is sufficient to determine all of the source coordinates and the baseline coordinates simultaneously (Robertson, 1975).

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