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Inspired by the double-debt problem in Japan where the mortgagor has to pay the remaining loan even if their house was destroyed by a catastrophic event, we model the lender's cash flow, by an exponential functional of a renewal-reward process. We propose an insurance add-on to the loan repayments and analyse the asymptotic behavior of the distribution of the first hitting time, which represents the probability of full repayment. We show that the finite-time probability of full loan repayment converges exponentially fast to the infinite-time one. In a few concrete scenarios, we calculate the exact form of the infinite-time probability and the corresponding premiums. [ABSTRACT FROM AUTHOR]

This study proposes a Kolmogorov-Smirnov-type test to assess the spherical symmetry of the first-order intensity function of a spatial point process (SPP). Spherical symmetry, which is an important assumption in the well known epidemictype aftershock sequence (ETAS) model, means that the intensity function of an SPP is invariant under a spherical transformation in a Euclidean space. An important property of first-order spherical symmetry is that the expected number of points within a sector region is proportional to the angle measure of the region. This provides a way to construct our test statistic. The asymptotic distribution of the test statistic is obtained under the framework of increasing domain asymptotics, with weak dependence. We show that the resulting test statistic converges weakly to the absolute maximum of a zero mean Gaussian process under the null hypothesis, and that it is also consistent under the alternative hypothesis. A simulation study shows that the type-I error probability of the test is close to the significance level, and the power increases to one as the magnitude of nonspherical symmetry increases. An application of the ETAS model to earthquakes in Japan shows that the first-order spherical symmetry assumption can be approximately accepted. [ABSTRACT FROM AUTHOR]

The paper considers a high-dimensional likelihood ratio (LR) test on the block compound symmetric (BCS) covariance structure of a multivariate Gaussian population. When the dimension of each block p, the number of blocks u and the sample size n satisfy that p = p (n) → ∞ and pu

In depth assessment of seismicity distribution for a particular region like Fukushima, prefecture is key towards reliable seismic hazard analysis for the area. Assessment of seismicity becomes more challenging for those areas lying close to mega subduction zone like in this study. Development of accurate input data like seismicity and faults data can reduce bias in the results and can improve quality of analysis. To assess the influence of seismicity on hazard analysis, two approaches known as Gutenberg-Richter law and the Gumbel’s extreme asymptotic distributions are employed. It is found that b value calculated through Gutenberg-Richter law has shown better b value of 1.0 according to tectonics of the Fukushima area. However, Gumbel’s approach which uses maximum earthquake of each years have shown b value of 0.6 and used for calculating future earthquake potential. Comparison of earthquake distribution in both cases has shown that in areas where we have rich seismicity data Gutenberg-Richter law is found much applicable as compared to Gumbel’s approach. Fault kinematics is done through software called FaultKin6 developed by (Rick Allmendinger) which resulted that Idosawa fault is a normal fault based on the fact that P axis is greater than 45° showing extension in N-S direction for Idosawa fault. Resultantly, it is tried to highlight the need to take normal faults in seismic hazard analysis probabilistically in design when they exist within stress field of big subduction zone. Peak ground acceleration is calculated by using PEER NGA West-2 models for Idosawa fault, and 0.22 g is found as PGA value. [ABSTRACT FROM AUTHOR]

This paper explores likelihood-based tests for parameter constancy in I (2) cointegrated vector autoregressive (CVAR) models. A new class of test statistics for parameter stability is introduced in the I (2) CVAR framework. This study proves that their asymptotic distributions take non-standard forms involving the integrals of Brownian motions, but they are free of any nuisance parameters. It is thus feasible to approximate the non-standard distributions by simulation. Selected quantiles of the approximate distributions are presented as statistical tables for applied use. Monte Carlo experiments are also conducted to investigate finite-sample properties of the test statistics. Finally, an empirical study of Japan's fixed-term deposit data is performed to demonstrate the practicality of the proposed tests in applied research. [ABSTRACT FROM AUTHOR]