Explicit solution of an inverse first-passage time problem for L\'{e}vy processes and counterparty credit risk

For a given Markov process $X$ and survival function $\overline{H}$ on $\mathbb{R}^+$, the inverse first-passage time problem (IFPT) is to find a barrier function $b:\mathbb{R}^+\to[-\infty,+\infty]$ such that the survival function of the first-passage time $\tau_b=\inf \{t\ge0:X(t)<b(t)\}$ is given by $\overline{H}$. In this paper, we consider a version of the IFPT problem where the barrier is fixed at zero and the problem is to find an initial distribution $\mu$ and a time-change $I$ such that for the time-changed process $X\circ I$ the IFPT problem is solved by a constant barrier at the level zero. For any L\'{e}vy process $X$ satisfying an exponential moment condition, we derive the solution of this problem in terms of $\lambda$-invariant distributions of the process $X$ killed at the epoch of first entrance into the negative half-axis. We provide an explicit characterization of such distributions, which is a result of independent interest. For a given multi-variate survival function $\overline{H}$ of generalized frailty type, we construct subsequently an explicit solution to the corresponding IFPT with the barrier level fixed at zero. We apply these results to the valuation of financial contracts that are subject to counterparty credit risk.Comment: Published at http://dx.doi.org/10.1214/14-AAP1051 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

On perpetual American put valuation and first-passage in a regime-switching model with jumps

In this paper we consider the problem of pricing a perpetual American put option in an exponential regime-switching L\'{e}vy model. For the case of the (dense) class of phase-type jumps and finitely many regimes we derive an explicit expression for the value function. The solution of the corresponding first passage problem under a state-dependent level rests on a path transformation and a new matrix Wiener-Hopf factorization result for this class of processes.Comment: 22 pages, 3 figures. Tp appear in Finance and Stochastics

On Gerber-Shiu functions and optimal dividend distribution for a L\'{e}vy risk process in the presence of a penalty function

This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process (in the absence of dividend payments). The management of the company is assumed to control timing and size of dividend payments. The objective is to maximize the sum of the expected cumulative discounted dividend payments received until the moment of ruin and a penalty payment at the moment of ruin, which is an increasing function of the size of the shortfall at ruin; in addition, there may be a fixed cost for taking out dividends. A complete solution is presented to the corresponding stochastic control problem. It is established that the value-function is the unique stochastic solution and the pointwise smallest stochastic supersolution of the associated HJB equation. Furthermore, a necessary and sufficient condition is identified for optimality of a single dividend-band strategy, in terms of a particular Gerber-Shiu function. A number of concrete examples are analyzed.Comment: Published at http://dx.doi.org/10.1214/14-AAP1038 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The fetal profile line:a proposal for a sonographic reference line to classify forehead and mandible anomalies in the second and third trimester

Objectives To test the fetal profile (FP) line, defined as the line that passes through the anterior border of the mandible and the nasion, as a reference line for forehead and mandible anomalies. Methods Volumes of 248 normal and 24 pathological fetuses (1636 and 1937?weeks gestation, respectively) were analysed retrospectively. When the FP line passes anteriorly, across or posteriorly to the frontal bone, this was defined as negative, zero or positive, respectively. When the FP line was positive the distance (F distance) between the FP line and the frontal bone was measured. Results No cases with a negative FP line were found in the normal fetuses. Before 27?weeks gestation the FP line was always zero except in one case. After 27?weeks gestation the FP line was positive in up to 25% (F distance (mean, range): 2.8, 2.13.6?mm). The FP line correctly identified 13 cases with retrognathia, 5 cases with frontal bossing and 3 cases with a sloping forehead. Conclusion Although large prospective studies are needed, the FP line may be a useful tool to detect second trimester profile anomalies such as retrognathia, sloping forehead and frontal bossing with the possibility of quantifying the latter. (c) 2012 John Wiley & Sons, Ltd

Effectiveness of method improvements to reduce variability of brood termination rate in honey bee brood studies under semi-field conditions

Quantitative assessments of adverse effects of plant protection products on honey bee brood (Apis mellifera L.) may be carried out according to the methods given by the OECD Guidance Document No. 75 (2007). In recent years a number of studies displayed a strong variability in brood termination rates, a key endpoint. Due to these variances no definite conclusions regarding potential brood effects were possible, and the studies needed to be repeated. Due to this, attempts to improve the methodology were initiated by the Working Group ‘Honey bee brood' of the German AG Bienenschutz. In 2011, honey bee brood studies adapted to these identified possible improvements resulted in better results compared to historical data. Based on the analysed results, the working group recommends to improve the method by using bigger colonies with more brood, using 4 instead of 3 replicates for better interpretation of data, starting the study early in the season, avoiding major modifications of the colonies shortly before application and using larger tunnels with effective crop areas preferably &gt; 80 m². To carry out quicker brood cell assessments to reduce stress for the colonies, it is recommended to use digital brood assessment, which allows marking a higher number of cells (e.g. 200 to 400 cells)

From working collections to the World Germplasm Project: agricultural modernization and genetic conservation at the Rockefeller Foundation

This paper charts the history of the Rockefeller Foundation’s participation in the collection and long-term preservation of genetic diversity in crop plants from the 1940s through the 1970s. In the decades following the launch of its agricultural program in Mexico in 1943, the Rockefeller Foundation figured prominently in the creation of world collections of key economic crops. Through the efforts of its administrators and staff, the foundation subsequently parlayed this experience into a leadership role in international efforts to conserve so-called plant genetic resources. Previous accounts of the Rockefeller Foundation’s interventions in international agricultural development have focused on the outcomes prioritized by foundation staff and administrators as they launched assistance programs and especially their characterization of the peoples and ‘‘problems’’ they encountered abroad. This paper highlights instead how foundation administrators and staff responded to a newly emergent international agricultural concern—the loss of crop genetic diversity. Charting the foundation’s responses to this concern, which developed only after agricultural modernization had begun and was understood to be produced by the successes of the foundation’s own agricultural assistance programs, allows for greater interrogation of how the foundation understood and projected its central position in international agricultural research activities by the 1970s.Research for this article was supported in part by a grant-in-aid from the Rockefeller Archive Center

Haulout site selection by southern elephant seals at Marion Island

Using data from an ongoing mark-resight programme at Marion Island, we tested empirically whether southern elephant seals prefer certain terrestrial sites to others during the breeding, moulting and winter haulouts, and whether the pattern of site use is the same for different age and sex groups. Southern elephant seals preferred some sites, while discriminating against other sites, with different age and sex classes using different sites for certain haulout events. Wintering young animals did not show strong site selection. Some popular sites were used for all haulouts by all age and sex groups, and apparently have all the requirements of a good site for terrestrial haulout by southern elephant seals. Site selection becomes more apparent with age, suggesting the role of haulout experience in site selection