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On reinsurance and investment for large insurance portfolios 总被引:1,自引:0,他引:1
We consider a problem of optimal reinsurance and investment for an insurance company whose surplus is governed by a linear diffusion. The company’s risk (and simultaneously its potential profit) is reduced through reinsurance, while in addition the company invests its surplus in a financial market. Our main goal is to find an optimal reinsurance-investment policy which minimizes the probability of ruin. More specifically, in this paper we consider the case of proportional reinsurance, and investment in a Black-Scholes market with one risk-free asset (bond, or bank account) and one risky asset (stock). We apply stochastic control theory to solve this problem. It transpires that the qualitative nature of the solution depends significantly on the interplay between the exogenous parameters and the constraints that we impose on the investment, such as the presence or absence of shortselling and/or borrowing. In each case we solve the corresponding Hamilton-Jacobi-Bellman equation and find a closed-form expression for the minimal ruin probability as well as the optimal reinsurance-investment policy. 相似文献
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In this paper we discuss the approximate basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated diffusion processes with idiosyncratic and systematic jumps. We suggest a new approximate pricing formula which is the weighted sum of Roger and Shi’s lower bound and the conditional second moment adjustments. We show that the approximate value is always within the lower and upper bounds of the option and is very sharp in our numerical tests. 相似文献
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We derive a new crossing criterion of hazard rates to identify a stochastic order relation between two random variables. We apply this crossing criterion in the context of life tables to derive stochastic ordering results among three families of fractional age assumptions: the family of linear force of mortality functions, the family of quadratic survival functions and the power family. Further, this criterion is used to derive tight bounds for functionals of future lifetimes that exhibit an increasing force of mortality with given one-year survival probabilities. Numerical examples illustrate our findings. 相似文献
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We consider a discrete time risk model where dividends are paid to insureds and the claim size has a discrete phase-type distribution, but the claim sizes vary according to an underlying Markov process called an environment process. In addition, the probability of paying the next dividend is affected by the current state of the underlying Markov process. We provide explicit expressions for the ruin probability and the deficit distribution at ruin by extracting a QBD (quasi-birth-and-death) structure in the model and then analyzing the QBD process. Numerical examples are also given. 相似文献
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Christian Hess 《Insurance: Mathematics and Economics》2009,44(3):497-504
We present mathematical results allowing one to evaluate the moments of order 1 and 2 of the cedent’s share in the framework of reinsurance treaties based on ordered claim sizes. These results consist of closed analytical formulas that do not involve any approximation procedure. This is illustrated by numerical examples when the claim number has the Poisson or the negative binomial distribution, and the claim cost has the exponential or the Pareto distribution. 相似文献
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The fluorescence behavior of pyrene in oil droplets of a surfactant-free oil-in-water emulsion was studied for benzene, fluorobenzene,
n-hexane and cyclohexane droplets in water. The excimer–monomer fluorescence ratio immediately after sonication, I
E/I
M(0), of the benzene/water emulsion was 8–10 times larger than for the benzene solution. The ratio I
E/I
M(t) increased in the first 10–20 min before it decreased to zero. Similar behavior was observed for the fluorobenzene/water
emulsion, while I
E/I
M(0) for emulsions with n-hexane and cyclohexane was smaller than for benzene and fluorobenzene/water emulsions. I
E/I
M(t) hardly changed with time for the n-hexane and cyclohexane/water emulsions. This different behavior was attributed to the increased solubility of nanometer-size
droplets with benzene and fluorobenzene.
Received: 20 June 2001 Accepted: 19 April 2001 相似文献
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Karl-Theodor Eisele 《Insurance: Mathematics and Economics》2008,42(1):65-72
We show how to generalize the result given in [Eisele, K.-Th., 2006. Recursions for compound phase distributions. Insurance: Math. Econom. 38, 149-156] to the multivariate case, i.e. we find a Panjer-like recursion principle for the distribution of a multivariate compound phase variable. Recursion formulas and procedures for the bivariate case are given in detail. We give a possible application for agricultural risks and calculate concrete examples via a VB-program. 相似文献
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具有四个有穷的IM公共小函数的整函数 总被引:6,自引:0,他引:6
本文证明了两个非常数整函数若具有四个有穷的IM公共小函数,则它们必恒等.从而在整函数的情形下,Nevanlinna五值定理中的五个IM公共值能否更换为五个IM公共小函数(含∞)的问题的回答是肯定的. 相似文献