Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results

Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem considered is that of the corresponding two-dimensional risk process first leaving the positive quadrant; another is that of entering the negative quadrant. When the claims arrive according to a Poisson process, we obtain a closed form expression for the ultimate ruin probability. In the general case, we analyze the asymptotics of the ruin probability when the initial reserves of both companies tend to infinity under a Cram\'{e}r light-tail assumption on the claim size distribution.Comment: Published in at http://dx.doi.org/10.1214/08-AAP529 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Learning from farmer-led access and benefit sharing. Conclusions.

This special issue of Farming Matters magazine has explored the ways in which access and benefit sharing of plant genetic resources can work for family farmers. On one hand it presents cases that demonstrate the limited extent to which family farmers have been able to benefit from the ‘formal’ ABS process: the rather complex arrangements between international agreements and national authorities, institutions and communities. On the other hand, this publication uncovers some of the effective principles and mechanisms for access and benefit sharing that are part and parcel of farmers’ everyday practices, even when formal ABS regulations have not yet been designed or implemented

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

Assemblies of aziridinemethanols

Contains fulltext : 14060.pdf (publisher's version ) (Open Access

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

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