We investigate the optimal consumption, portfolio, and life insurance decisions problem of a liquidity constrained household whose preference is given by the CES (constant elasticity of substitution) utility function. By applying the martingale and duality method, we obtain the closed-form solution for the household’s value function and optimal strategies. We provide a rigorous proof for the optimality

The reflection principle for Brownian motion gives a way to calculate the joint distribution of a hitting time and a one dimensional marginal. The Carr–Nadtochiy transform is a formulation that generalizes the reflection principle in this respect. The transform originated from a way to hedge so-called barrier options in the literature of financial mathematics. The existence of the transform has been

In this article, we consider a coefficient stability problem for one-dimensional stochastic differential equations driven by an \(\alpha\)-stable process with \(\alpha \in (1,2)\). More precisely, we find an upper bound for the \(L^{\alpha -1}(\varOmega ,{\mathbb {P}})\) distance between two solutions in terms of the \(L^{\alpha }\left( {\mathbb {R}},\mu^{\alpha }_{x_0}\right)\) distance of the coefficients

We propose a general theory of estimating interpolation error for smooth functions in two and three dimensions. In our theory, the error of interpolation is bound in terms of the diameter of a simplex and a geometric parameter. In the two-dimensional case, our geometric parameter is equivalent to the circumradius of a triangle. In the three-dimensional case, our geometric parameter also represents

Stationary waves of constant shape and constant propagation speed on rotational flows of two layers are computed numerically. Two layers are assumed to be of distinct constant vorticity distributions. Three different kinds of waves of finite depth are considered: pure capillary, capillary-gravity, and gravity waves. The problem is formulated as a bifurcation problem, which involves many parameters

The shortest bibranching problem is a common generalization of the minimum-weight edge cover problem in bipartite graphs and the minimum-weight arborescence problem in directed graphs. For the shortest bibranching problem, an efficient primal-dual algorithm is given by Keijsper and Pendavingh (J Comb Theory Ser B 73:130–145, 1998), and the tractability of the problem is ascribed to total dual integrality

In simulating physical systems, conservation of the total energy is often essential, especially when energy conversion between different forms of energy occurs frequently. Recently, a new fourth order energy-preserving integrator named MB4 was proposed based on the so-called continuous stage Runge–Kutta methods (Miyatake and Butcher in SIAM J Numer Anal 54(3):1993–2013, 2016). A salient feature of

NIST SP800-22 is one of the most widely used statistical testing tools for pseudorandom number generators (PRNGs). This tool consists of 15 tests (one-level tests) and two additional tests (two-level tests). Each one-level test provides one or more p-values. The two-level tests measure the uniformity of the obtained p-values for a fixed one-level test. One of the two-level tests categorizes the p-values

We present a numerical approach for determination of the spectral stability of solitary waves by computing eigenvalues and eigenfunctions of the corresponding eigenvalue problems, along with their continuation, for nonlinear wave equations in one space dimension. We illustrate the approach for the nonlinear Schrödinger (NLS) equation with a small potential, and numerically determine the spectral stability

Mathematical models for self-propelled motions are often utilized for understanding the mechanism of collective motions observed in biological systems. Indeed, several patterns of collective motions of camphor disks have been reported in experimental systems. In this paper, we show the existence of asymmetrically rotating solutions of a two-camphor model and give necessary conditions for their existence

The purpose of the paper is to establish higher-order Karush–Kuhn–Tucker higher-order necessary optimality conditions for set-valued optimization where the derivatives of objective and constraint functions are separated. We first introduce concepts of higher-order weak lower inner epiderivatives for set-valued maps and discuss some useful properties about new epiderivatives, for instance, convexity

In this paper, a new preconditioner for a class of \(2\times 2\) block linear systems is proposed. The proposed new preconditioner is a better approximation to the original coefficient matrix than the previous ones. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are discussed. Finally, two numerical examples are provided to show the

This paper presents a new projected Barzilai–Borwein method for the complementarity problem over symmetric cone by applying the Barzilai–Borwein-like steplengths to the projected method. A new descent direction is employed and a non-monotone line search is used in the method in order to guarantee the global convergence. The projected Barzilai–Borwein method is proved to be globally convergent under

For numerical simulation of elastic structures, data-driven computational approaches attempt to use a data set of material responses, without resorting to conventional modeling of the material constitutive equation. In a material data set in the stress–strain space, the data points are considered to lie on or near a low-dimensional manifold, rather distribute ubiquitously in the space. This paper presents

We propose a mathematical model to understand the transmission dynamics of HIV/AIDS in an environment. In addition to previous approaches, we incorporate two classes of isolated. By isolated we do not mean physical separation, but commitment to keep its status. We establish the well-posedness of our model and fully analyze the asymptotic behavior of the solutions which depends on the basic reproduction

The nonlinear matrix equation \(X^p=R+M^T(X^{-1}+B)^{-1}M\), where p is a positive integer, M is an arbitrary \(n\times n\) real matrix, R and B are symmetric positive semidefinite matrices, is considered. When \(p=1\), this matrix equation is the well-known discrete-time algebraic Riccati equation (DARE), we study the convergence rate of an iterative method which was proposed in Meng and Kim (J Comput

In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction–diffusion equations, and we will apply our nonlinear bounds to the Lotka–Volterra system of two and four competing species as examples. The idea used in a series of papers by the first author et al. for the establishment

This paper considers a bidimensional continuous-time renewal risk model, in which the two components of each pair of claim sizes are linked via the strongly asymptotic independence structure and the two claim-number processes from different lines of business are (almost) arbitrarily dependent. Precise asymptotic formulas for three kinds of finite-time ruin probabilities are established when the claim

Inner product functional encryption (IPFE) is one class of functional encryption supporting only inner product functionality. All previous IPFE schemes are bounded schemes, meaning that the vector length that can be handled in the scheme is fixed in the setup phase. In this paper, we propose the first unbounded IPFE schemes, in which we do not have to fix the lengths of vectors in the setup phase and

In this paper, a new iterative refinement for ill-conditioned linear systems is derived based on discrete gradient methods for gradient systems. It is proved that the new method is convergent for any initial values irrespective of the choice of the stepsize h. Some properties of the new iterative refinement are presented. It is shown that the condition number of the coefficient matrix in the linear

For continuous functions, midpoint convexity characterizes convex functions. By considering discrete versions of midpoint convexity, several types of discrete convexities of functions, including integral convexity, L\(^\natural\)-convexity and global/local discrete midpoint convexity, have been studied. We propose a new type of discrete midpoint convexity that lies between L\(^\natural\)-convexity

The original article has been corrected.

In this paper we focus on qualitative properties of solutions to a nonlocal nonlinear partial integro-differential equation (PIDE). Using the theory of abstract semilinear parabolic equations we prove existence and uniqueness of a solution in the scale of Bessel potential spaces. Our aim is to generalize known existence results for a wide class of Lévy measures including with a strong singular kernel

In this paper, we deduce the asymptotic error distribution of the Euler method for the nonlinear filtering problem with continuous-time observations. As studied in previous works by several authors, the error structure of the method is characterized by conditional expectations of some functionals of multiple stochastic integrals. Our main result is to prove the stable convergence of a sequence of such

The existence of a solution to an important singular coagulation equation with a multiple fragmentation kernel has been recently proved in Jpn J Ind Appl Math 35(3):1283–1302, 2018. This paper proves the uniqueness of the solution to the same problem in the function space \(\varOmega _{.,r_2} (T) = \bigcup _{\lambda >0 }\varOmega _{\lambda , r_2} (T)\), where \(\varOmega _{\lambda , r_2} (T)\) is the

In this paper, we address the weighted linear matroid intersection problem from computation of the degree of the determinant of a symbolic matrix. We show that a generic algorithm computing the degree of noncommutative determinants, proposed by the second author, becomes an \(O(mn^3 \log n)\) time algorithm for the weighted linear matroid intersection problem, where two matroids are given by column

We propose some conjectures on the asymptotic distribution of the probabilistic Burgers cellular automaton (PBCA), which is defined by a simple rule of particle motion with a probabilistic parameter. Asymptotic distribution of configurations converges to a unique steady state for PBCA. We propose a new and widely-applicable approach to analyze probabilistic particle systems and apply it concretely

Many applications arising from machine learning, statistics and image processing can be formulated as a convex minimization model with separable structures both in objective function and constraints. The Peaceman–Rachford splitting method is very efficient for solving these problems, but it is not convergent in the absence of some restrictive assumptions. In this paper, we propose a linearized Peaceman–Rachford

This paper considers a dependent risk model with stochastic return and Brownian perturbation, where there exists a dependence structure between the claim sizes and the inter-arrival times and the price process of the investment portfolio is a geometric Lévy process. When the claim sizes have heavy-tailed distributions, the asymptotic lower and upper bounds of the finite-time ruin probability have been

Let \((B_t)_{t\in [0,\infty )}\) be a real Brownian motion on a probability space \((\varOmega ,{\mathcal {F}},P)\). Our concern is whether and how a noncausal type stochastic differential \(dX_t=a(t,\omega )\,dB_t+b(t,\omega )\,dt\) is determined from its stochastic Fourier coefficients (SFCs for short) \((e_n,dX):\)\(=\int _{0}^L\overline{e_n(t)}\,dX_t\) with respect to a CONS \((e_n)_{n\in {\mathbb

To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method that typically includes other conventional particle methods, such as smoothed particle hydrodynamics or moving particle semi-implicit methods. A new regularity of discrete

In this paper, for the implicit complementarity problem, it is shown that the solution’s sign patterns can be calculated via solving a linear system under some assumptions. Next, Newton iteration is applied to a equivalent nonlinear equation with quadratic convergence and the non-singularity of the Jacobian is discussed. Moreover, a superlinearly convergent hybrid method is established by combining

Quadratic integer programming problems with cardinality constraint have many applications in real life. Portfolio selection is an important application in financial optimization. In this paper we develop an exact and efficient algorithm for quadratic integer programming problems with cardinality constraint. This iterative algorithm is actually a branch and bound method, which adopts a domain cut and

Empty houses, Akiya, are of substantial concern to the ageing society of Japan; the ratio of Akiya is projected to worsen to 30.5% in 2033. Such a high ratio of Akiya will influence the social system and the Japanese economy overall in the near future. Nonetheless, Akiya continues to increase unabated because there are no specific government measures to address the problem. In this study, we develop

We consider numerical methods for computing eigenvalues located in the interior part of the spectrum of a large symmetric matrix. For such difficult eigenvalue problems, an effective solution is to use the Harmonic Ritz pairs in projection methods because the error bounds on the Harmonic Ritz pairs are well studied. In this paper, we prove global convergence of the iterative projection methods with

We present Laguerre Voronoi based subdivision algorithms for the quadrilateral and hexahedral meshing of particle systems within a bounded region in two and three dimensions, respectively. Particles are smooth functions over circular or spherical domains. The algorithm first breaks the bounded region containing the particles into Voronoi cells that are then subsequently decomposed into an initial quadrilateral