The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected...The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.展开更多
Salinity is one of the major abiotic factors affecting the growth and productivity of crops in Hetao Irrigation District, China. In this study, the salinity tolerances of three local crops, wheat （Triticum aestinum L...Salinity is one of the major abiotic factors affecting the growth and productivity of crops in Hetao Irrigation District, China. In this study, the salinity tolerances of three local crops, wheat （Triticum aestinum L.）, maize （Zea mays L.） and sunflower （Helianthus annuus L.）, growing in 76 farm fields are evaluated with modified discount function. Salinity ecological zones appropriate for these local crops are characterized and a case study is presented for crop salinity ecological zoning. The results show that the yield reductions of wheat, maize and sunflower when grown in saline soils are attributed primarily to a reduction in spikelet number, 1 000-grain weight and seed number per head, respectively. Sunflower is the most tolerant crop among the three which had a salinity tolerance index （ST-index） of 12.24, followed by spring maize and spring wheat with ST-Indices of 9.00 and 7.43, respectively. According to the crop salinity tolerance results, the arable land in the Heping Village of this district was subdivided into four salinity ecological zones： the most suitable, suitable, sub-suitable and unsuitable zones. The area proportion of the most suitable zone for wheat, maize and sunflower within the Heping Village was 27.5, 46.5 and 77.5%, respectively. Most of the most suitable zone occurred in the western part of the village. The results of this study provide the scientific basis for optimizing the local major crop distribution and improving cultural practices management in Hetao Irrigation District.展开更多
In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a ...In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.展开更多
We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iterati...We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iteration mothed can be used to compute the values of expected discounted dividends until ruin and the new penalty function. Applying the new function and the recursion method proposed in Section 5, we obtain the arbitrary moments of discounted dividend payments until ruin.展开更多
基金supported by the National Natural science Foundation of china(70271069)
文摘The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.
基金supported by the Special Fund for Agro-Scientific Research in the Public Interest, China (2009030012-3)
文摘Salinity is one of the major abiotic factors affecting the growth and productivity of crops in Hetao Irrigation District, China. In this study, the salinity tolerances of three local crops, wheat （Triticum aestinum L.）, maize （Zea mays L.） and sunflower （Helianthus annuus L.）, growing in 76 farm fields are evaluated with modified discount function. Salinity ecological zones appropriate for these local crops are characterized and a case study is presented for crop salinity ecological zoning. The results show that the yield reductions of wheat, maize and sunflower when grown in saline soils are attributed primarily to a reduction in spikelet number, 1 000-grain weight and seed number per head, respectively. Sunflower is the most tolerant crop among the three which had a salinity tolerance index （ST-index） of 12.24, followed by spring maize and spring wheat with ST-Indices of 9.00 and 7.43, respectively. According to the crop salinity tolerance results, the arable land in the Heping Village of this district was subdivided into four salinity ecological zones： the most suitable, suitable, sub-suitable and unsuitable zones. The area proportion of the most suitable zone for wheat, maize and sunflower within the Heping Village was 27.5, 46.5 and 77.5%, respectively. Most of the most suitable zone occurred in the western part of the village. The results of this study provide the scientific basis for optimizing the local major crop distribution and improving cultural practices management in Hetao Irrigation District.
文摘In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type （2） distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.
文摘We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iteration mothed can be used to compute the values of expected discounted dividends until ruin and the new penalty function. Applying the new function and the recursion method proposed in Section 5, we obtain the arbitrary moments of discounted dividend payments until ruin.
