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921.
We investigate the total time of deducting fees for variable annuities with state-dependent fee. This fee charging method is studied recently by Bernard et al. (2014) and Delong (2014) in which the fees deducted from the policyholder’s account depend on the account value. However, both of them have not considered the problem of analyzing probabilistic properties of the total time of deducting fees. We approximate the maturity of a general variable annuity contract by combinations of exponential distributions which are (weakly) dense in the space that is composed of all probability distributions on the positive axis. Working under general jump diffusion process, we derive analytic formulas for the expectation of the time of deducting fees as well as its Laplace transform. 相似文献
922.
In this study, we propose a modelling framework for evaluating companies financed by random liabilities, such as insurance companies or commercial banks. In this approach, earnings and costs are driven by double exponential jump–diffusion processes and bankruptcy is declared when the income falls below a default threshold, which is proportional to the charges. A change of numeraire, under the Esscher risk neutral measure, is used to reduce the dimension. A closed form expression for the value of equity is obtained in terms of the expected present value operators, with and without disinvestment delay. In both cases, we determine the default threshold that maximizes the shareholder’s equity. Subsequently, the probabilities of default are obtained by inverting the Laplace transform of the bankruptcy time. In numerical applications of the proposed model, we apply a procedure for calibration based on market and accounting data to explain the behaviour of shares for two real-world examples of insurance companies. 相似文献
923.
Molecular dynamics simulations of charged and neutral solutes in dimethyl sulfoxide (DMSO)-chloroform mixtures reveal pronounced nonideality in the solute diffusion with changes of composition of the mixtures. The diffusion coefficient of the anionic solute first decreases, passes through a minimum at DMSO mole fraction of about 0.50, and then increases to reach its value for pure DMSO. The diffusion coefficients of the cationic and neutral solutes are found to decrease with increase in DMSO content of the solvent mixture. The extent of nonideality in the diffusion and orientational relaxation of solvent molecules is found to be somewhat stronger than that in diffusion of the anionic solute in these mixtures. We have also calculated the relaxation of hydrogen bonds formed between DMSO and chloroform molecules. The lifetimes of DMSO-chloroform hydrogen bonds are found to increase monotonically with increase in DMSO concentration. The average number of hydrogen bonds and their average energies are also computed. It is found that an increase in DMSO concentration causes a decrease in the number of DMSO-chloroform hydrogen bonds per DMSO or chloroform molecules but increases the strength of these hydrogen bonds. 相似文献
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927.
In this paper, we establish local Hölder estimate for non-negative solutions of the singular equation (M.P) below, for m in the range of exponents . Since we have trouble in finding the local energy inequality of v directly, we use the fact that the operator σ(−Δ) can be thought as the normal derivative of some extension v? of v to the upper half space (Caffarelli and Silvestre, 2007 [5]), i.e., v is regarded as boundary value of v? the solution of some local extension problem. Therefore, the local Hölder estimate of v can be obtained by the same regularity of v?. In addition, it enables us to describe the behavior of solution of non-local fast diffusion equation near their extinction time. 相似文献
928.
In this paper, we deal with the global existence and nonexistence of solutions to a nonlinear diffusion system coupled via nonlinear boundary flux. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions. The critical curve of Fujita type is conjectured with the aid of some new results, which extend the recent results of Wang et al. [Nonlinear Anal. 71 (2009) 2134-2140] and Li et al. [J. Math. Anal. Appl. 340 (2008) 876-883] to more general equations. 相似文献
929.
We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], α∈R, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some K∈R, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all α∈R. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,
930.
Kenichi Sakamoto Masahiro Yamamoto 《Journal of Mathematical Analysis and Applications》2011,382(1):426-447
We consider initial value/boundary value problems for fractional diffusion-wave equation: , where 0<α?2, where L is a symmetric uniformly elliptic operator with t-independent smooth coefficients. First we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to ∞ and the proofs are based on the eigenfunction expansions. Second for α∈(0,1), we apply the eigenfunction expansions and prove (i) stability in the backward problem in time, (ii) the uniqueness in determining an initial value and (iii) the uniqueness of solution by the decay rate as t→∞, (iv) stability in an inverse source problem of determining t-dependent factor in the source by observation at one point over (0,T). 相似文献