On reinsurance and investment for large insurance portfolios

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.     

Approximate basket options valuation for a jump-diffusion model

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.     

Comparison and bounds for functionals of future lifetimes consistent with life tables

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.     

灰色预测模型在汇率分析中的应用

首先建立IM（1,1）预测模型,在此基础上再使用马尔科夫预测方法,构造出一种全新的预测方法,应用于汇率的预测与控制中。     

A risk model with paying dividends and random environment

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.     

A Hybrid PAPR Reduction Scheme in OFDM-IM Using Phase Rotation Factors and Dither Signals on Partial Sub-Carriers

As a multi-carrier modulation technique, a high peak-to-average power ratio (PAPR) is a common issue suffered by orthogonal frequency division multiplexing with index modulation (OFDM-IM) due to its system structure. High PAPR may cause signal distortion, which affects correct symbol transmission. This paper tries to inject dither signals to the inactive (idle) sub-carriers, which is a unique transmission structure of OFDM-IM, to reduce PAPR. Unlike the previous works, which utilize all idle sub-carriers, the proposed PAPR reduction scheme utilizes selected partial sub-carriers. This method performs well in terms of bit error rate (BER) performance and energy efficiency, which are obvious drawbacks of the previous PAPR reduction works due to the introduction of dither signals. In addition, in this paper, phase rotation factors are combined with the dither signals to compensate for the PAPR reduction performance degradation due to the insufficient use of partial idle sub-carriers. Moreover, an energy detection scheme is designed and proposed in this paper in order to distinguish the index of phase rotation factor used for transmission. It is shown by extensive simulation results that the proposed hybrid PAPR reduction scheme is able to implement an impressive PAPR reduction performance among existing dither signa-based schemes as well as classical distortion-less PAPR reduction schemes. In addition, the proposed method obtains better error performance and energy efficiency than that of the previous works. At the error probability 10−4, the proposed method can achieve around 5 dB gain compared to the conventional dither signal-based schemes     

Computing the mean and the variance of the cedent’s share for largest claims reinsurance covers

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.     

Pyrene fluorescence measurements of metastable oil droplets in surfactant-free oil-in-water emulsions

 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     

Recursions for multivariate compound phase variables

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.