Japan Journal of Industrial and Applied Mathematics最新文献

Counterparty risk remains an issue in over-the-counter derivative transactions following the 2008 financial crisis. While the margin for a derivative transaction can only be transferred until just before the counterparty’s default, the exposure of the derivative transaction can vary stochastically during the margin period of risk, that is, the period from the counterparty’s default to the actual closing-out of the transaction. Thus, the anticipated positive exposure may not be recognized, resulting in counterparty risk. Considering it is difficult to calculate the initial margin (IM) according to the regulations, IM has been calculated in practice using a simplified method proposed by the International Swaps and Derivatives Association (ISDA), which is called the ISDA Standard Initial Margin Model (“ISDA SIMM”). In this study, we derive an approximate formula for some counterparty risk indicators for a stochastic volatility model and illustrate numerical analyses for a call option in the SABR model as an example to examine the effect of the discrepancy between regulations and practices in margin calculation. Our results imply that the IM calculated in practice may be insufficient for counterparty risk management, particularly when the market is volatile.

Multigrid reduction in time (MGRIT), one of the most popular parallel-in-time approaches, extracts temporal parallelism by constructing coarse grids in the time direction. The coarse-grid operator optimization method for MGRIT has achieved high convergence for one of the hyperbolic problems that had poor convergence performance: the one-dimensional linear advection problems with constant coefficients. This paper applies this optimization method to two-dimensional linear time-dependent Stokes and Oseen problems using the pressure projection and the staggered grid discretization methods. Although the time-stepping operator involves the projection operator, the commutativity in the periodic boundary conditions allows a similar adaptation of the coarse-grid operator optimization for scalar equations. This method can also be applied to Dirichlet boundary problems by modifying the operator obtained based on the assumption of periodic boundary conditions. We demonstrate that MGRIT can achieve reasonable convergence rates for these problems with a practical number of non-zero elements by using the optimization method. Numerical experiments show convergence estimates for periodic boundary problems, applications to Dirichlet boundary problems, and parallel results compared to the sequential time-stepping method.

A thermal convection in horizontal fluid layer under gravity is considered. The fluid is heated from above non-uniformly. An existence theorem of stationary solutions is proved and some flow patterns are shown by numerical computations.

This paper derives several mathematical properties of the generalized Cramér–Lundberg model proposed by Tomita et al. (J. Appl. Probab. 59(3):849-859, 2022). The model extends the Bayesian-estimator model of Dubey. (Versicherungsmathematiker. 2:130-141, 1977) to the case of multiple insurance policies. We study the instantaneous premium function and the dependence structure of the ruin probability on the intensity of the driving mixed Poisson process. In particular, we show that the conditional ruin probability is monotonic with respect to the intensity value under certain assumptions. Monte Carlo simulations suggest that, without these assumptions, the monotonicity does not generally hold. Our study contributes to the risk management of insurance companies in the sense that it reveals how the difference between the assumed and true distribution of the risk factor affects the ruin probability.

Numerical methods for computing the solutions of Markov backward stochastic differential equations (BSDEs) driven by continuous-time Markov chains (CTMCs) are explored. The main contributions of this paper are as follows: (1) we observe that Euler-Maruyama temporal discretization methods for solving Markov BSDEs driven by CTMCs are equivalent to exponential integrators for solving the associated systems of ordinary differential equations (ODEs); (2) we introduce multi-stage Euler–Maruyama methods for effectively solving “stiff” Markov BSDEs driven by CTMCs; these BSDEs typically arise from the spatial discretization of Markov BSDEs driven by Brownian motion; (3) we propose a multilevel spatial discretization method on sparse grids that efficiently approximates high-dimensional Markov BSDEs driven by Brownian motion with a combination of multiple Markov BSDEs driven by CTMCs on grids with different resolutions. We also illustrate the effectiveness of the presented methods with a number of numerical experiments in which we treat nonlinear BSDEs arising from option pricing problems in finance.

This study proposes a module designed for the automatic parameter control of peristaltic locomotion systems. The module comprises two populations of oscillators, each responsible for controlling the phase of periodic elongation–contraction motion and the friction force exerted by the ground, respectively. The parameter control algorithm operates independently in each module, with parameters updated through a selection algorithm applied to the elements in each module. Peristaltic locomotion systems, equipped with the proposed modules in the body segments, exhibit autonomous parameter controls, resulting in stable unidirectional locomotion. Consequently, the system can adapt to various environmental changes. Because the modules do not interact with each other, the system acts as a decentralized distributed system; thus, it is scalable to several body segments.

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the generalized orthogonal matching pursuit (gOMP) algorithm. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is presented based on restricted isometry property (RIP) and restricted orthogonality constant (ROC).

In this paper, we consider a bidimensional renewal risk model with dependent main claims and delayed claims. Concretely, suppose that an insurance company simultaneously operates two kinds of businesses which separately trigger two types of claims named main claims and delayed claims, respectively, the two lines of businesses share a common claim-arrival counting process, and the random pairs from the two main claims as well as the random pairs from the two delayed claims, independent of each other, follow bivariate Farlie–Gumbel–Morgenstern distributions with different parameters. Assuming that all the claims are subexponential, an asymptotic formula of finite-time ruin probability for such a model is derived as the initial surpluses tend to infinity, which extends some recent ones in the literature.

In magnetic resonance imaging, high angular resolution diffusion imaging (abbr. HARDI) is used to characterize non-Gaussian diffusion processes. One approach to analyzing HARDI data is to model the apparent diffusion coefficient with higher order diffusion tensors from a diffusivity function. An intrinsic property of the diffusivity function is positive semi-definite, which reflects the phenomenon of water molecular diffusion in complicated biological tissue environments. In this paper, we provide a workable criterion for judging the positive semi-definiteness of a diffusivity function and shows that it is effective via two numerical examples.

This paper investigates mathematical programming with equilibrium constraints including multiple interval-valued objective functions on Hadamard manifolds. In the first part, both necessary and sufficient optimality conditions for some types of efficient solutions are considered. After that, the Wolfe and Mond–Weir type dual problems are formulated and the duality relations under geodesic convexity assumptions are examined. Some examples are proposed to illustrate the results.