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The paper examines how reinsurance can be used to strike a balance between expected profit and VaR/CVaR risk. Conditions making truncated stop loss contracts optimal are derived, and it is argued that those are usually satisfied in practice. One of the prerequisites is that reinsurance is not too cheap, and an argument resembling arbitrage suggests that it is not.

Porting codes to GPU often requires major efforts. While several tools exist for automatically offload numerical libraries such as BLAS and LAPACK, they often prove impractical due to the high cost of mandatory data transfer. The new unified memory architecture in NVIDIA Grace-Hopper allows high bandwidth cache-coherent memory access of all memory from both CPU and GPU, potentially eliminating bottleneck faced in conventional architecture. This breakthrough opens up new avenues for application development and porting strategies. In this study, we introduce a new tool for automatic BLAS offload, the tool leverages the high speed cache coherent NVLink C2C interconnect in Grace-Hopper, and enables performant GPU offload for BLAS heavy applications with no code changes or recompilation. The tool was tested on two quantum chemistry or physics codes, great performance benefits were observed.

A burst buffer is a common method to bridge the performance gap between the I/O needs of modern supercomputing applications and the performance of the shared file system on large-scale supercomputers. However, existing I/O sharing methods require resource isolation, offline profiling, or repeated execution that significantly limit the utilization and applicability of these systems. Here we present ThemisIO, a policy-driven I/O sharing framework for a remote-shared burst buffer: a dedicated group of I/O nodes, each with a local storage device. ThemisIO preserves high utilization by implementing opportunity fairness so that it can reallocate unused I/O resources to other applications. ThemisIO accurately and efficiently allocates I/O cycles among applications, purely based on real-time I/O behavior without requiring user-supplied information or offline-profiled application characteristics. ThemisIO supports a variety of fair sharing policies, such as user-fair, size-fair, as well as composite policies, e.g., group-then-user-fair. All these features are enabled by its statistical token design. ThemisIO can alter the execution order of incoming I/O requests based on assigned tokens to precisely balance I/O cycles between applications via time slicing, thereby enforcing processing isolation. Experiments using I/O benchmarks show that ThemisIO sustains 13.5-13.7% higher I/O throughput and 19.5-40.4% lower performance variation than existing algorithms. For real applications, ThemisIO significantly reduces the slowdown by 59.1-99.8% caused by I/O interference.

The literature on optimal reinsurance does not deal with how much the effectiveness of such solutions is degraded by errors in parameters and models. The issue is investigated through both asymptotics and numerical studies. It is shown that the rate of degradation is often $O(1/n)$ as the sample size $n$ of historical observations becomes infinite. Criteria based on Value at Risk are exceptions that may achieve only $O(1/\sqrt{n})$. These theoretical results are supported by numerical studies. A Bayesian perspective on how to integrate risk caused by parameter error is offered as well.

Optimal reinsurance when Value at Risk and expected surplus is balanced through their ratio is studied, and it is demonstrated how results for risk-adjusted surplus can be utilized. Simplifications for large portfolios are derived, and this large-portfolio study suggests a new condition on the reinsurance pricing regime which is crucial for the results obtained. One or two-layer contracts now become optimal for both risk-adjusted surplus and the risk over expected surplus ratio, but there is no second layer when portfolios are large or when reinsurance prices are below some threshold. Simple approximations of the optimum portfolio are considered, and their degree of degradation compared to the optimum is studied which leads to theoretical degradation rates as the number of policies grows. The theory is supported by numerical experiments which suggest that the shape of the claim severity distributions may not be of primary importance when designing an optimal reinsurance program. It is argued that the approach can be applied to Conditional Value at Risk as well.

The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of insurance claim data. This paper discusses several composite models with commonly used bulk distributions, combined with a 2-parameter Pareto distribution above the threshold. We have explored how several threshold selection methods perform when estimating the reserve as well as the effect of the choice of bulk distribution, with varying sample size and tail properties. To investigate this, a simulation study has been performed. Our study shows that when data are sufficient, the square root rule has the overall best performance in terms of the quality of the reserve estimate. The second best is the exponentiality test, especially when the right tail of the data is extreme. As the sample size becomes small, the simultaneous estimation has the best performance. Further, the influence of the choice of bulk distribution seems to be rather large, especially when the distribution is heavy-tailed. Moreover, it shows that the empirical estimate of $p_{\leq b}$, the probability that a claim is below the threshold, is more robust than the theoretical one.