In a peer-to-peer complex environment, information is permanently diffused. Such an environment can be modeled as a graph, where there are flows of information. The interest of such modeling is that (1) one can describe the exchanges through time from an initial state of the network, (2) the...

We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By...

In this paper, we present a stochastic optimal control model to optimize an insurance firm problem in the case where its cash-balance process is assumed to be described by a stochastic differential equation driven by Teugels martingales. Noticing that the insurance firm is able to control its...

We study graphon mean-field backward stochastic differential equations (BSDEs) with jumps and associated dynamic risk measures. We establish the existence, uniqueness and measurability of solutions under some regularity assumptions. For an interacting mean-field particle system with...

Stochastic Hamiltonian partial differential equations, which possess the multi-symplectic conservation law, are an important and fairly large class of systems. The multi-symplectic methods inheriting the geometric features of stochastic Hamiltonian partial differential equations provide...

We define a class of not necessarily linear C0-semigroups (Pt)t≥0 on Cb(E) (more generally, on Cκ(E):=1κCb(E), for some growth bounding continuous function κ) equipped with the mixed topology τM1 for a large class of topological state spaces E. In the linear case we prove that such...

Asset allocation and option pricing models are often formulated by means of linear stochastic differential equations. We show that this class of models is not identifiable from information contained in discrete-time data when the expected return process is unobservable. The indeterminacy arises...

Solving non-linear parabolic partial differential equations (PDEs) in high dimension becomes an interest for its curse of dimensionality problem. Recently, a deep learning method associated with a backward stochastic differential equation (deep-BSDE) to solve the PDEs draws intensive discussions...

The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs) was originally formulated using Euler time discretizations and a uniform space grid. In this paper, we utilize a tree-like spatial discretization that approximates the BSDE on the...

We derive a Hattendorff differential equation and a recursion governing the evolution of continuous and discrete time evolution respectively of the variance of the loss at time t random variable given that the state at time t is j, for a multistate Markov insurance model (denoted by 2σt(j)). We...

This paper considers a mean-variance portfolio selection problem when the stock price has a 3/2 stochastic volatility in a complete market. Specifically, we assume that the stock price and the volatility are perfectly negative correlated. By applying a backward stochastic differential equation...

We study a small open economy displaying Pareto-distributed wealth resulting from random death. The government runs a distribution scheme on inheritance. We present the mathematical background that allows to study the dynamics of means. We end up with ordinary differential equations for the mean...

Theoretical and experimental studies of noncooperative games increasingly recognize Nash equilibrium as a limiting outcome of players' repeated interaction. This note, while sharing that view, illustrates and advocates combined use of convex optimization and differential equations, the purpose...

In this paper, we established and carried-out the computational solution of some first order delay differential equations (DDEs) using hybrid extended backward differentiation formulae method in block forms without the application of interpolation techniques in determining the delay term. The...

discrete schemes was worked-out in block forms to solve some stochastic time-dependent first order delay differential equations. It was observed that the scheme for step number k = 4 performed better and faster in terms of accuracy than the schemes for step number k = 3 and 2 respectively after...

In this paper, the discrete schemes of extrapolated block Adams Moulton methods were obtained through the continuous formulation of the linear multistep collocation method by matrix inversion approach for the numerical solutions of first-order delay differential equations (DDEs) without the use...

Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the...

This paper revisits the debate about the appropriate differential equation that governs the evolution of knowledge in models of endogenous growth. We argue that the assessment of the appropriateness of an equation of motion should not only be based on its implications for the future, but that it...

A family of Exponentially Fitted Block Backward Differentiation Formulas (EFBBDFs) whose coefficients depend on a parameter and step-size is developed and implemented on the Black-Scholes partial differential equation (PDE) for the valuation of options on a non-dividend-paying stock. Specific...

In this paper, enlightened by the asymptotic expansion methodology developed by Li (2013b) and Li and Chen (2016), we propose a Taylor-type approximation for the transition densities of the stochastic differential equations (SDEs) driven by the gamma processes, a special type of Levy processes....

We propose a new forward-backward stochastic differential equation solver for highdimensional derivative pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our...

While many eminent economists have expressed disdain about the abstract nature of contemporary economic theory and how it is removed from reality, few offer a cogent solution to this problem. Jay Forrester, a control engineer turned economist proposed replacing the abstract economic model with a...

This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem's solution to more general cases is investigated, based on which a discussion is further conducted on the existence of solutions for a few...

We propose a novel Monte Carlo simulation method for two-dimensional stochastic differential equation (SDE) systems based on approximation through continuous-time Markov chains (CTMCs). Specifically, we propose an efficient simulation framework for asset prices under general stochastic local...

The econometric data to which autoregressive moving-average models are commonly applied are liable to contain elements from a limited range of frequencies. If the data do not cover the full Nyquist frequency range of [0,π] radians, then severe biases can occur in estimating their parameters....

In option pricing models with correlated stochastic processes, an option premium is commonly a solution to a partial differential equation (PDE) with mixed derivatives in more than two space dimensions. Alternating direction implicit (ADI) finite difference methods are popular for solving a PDE...

This paper studies the effect of variance swap in hedging volatility risk under the mean-variance criterion. We consider two mean-variance portfolio selection problems under Heston's stochastic volatility model. In the first problem, the financial market is complete and contains three primitive...

We study numerical algorithms for reflected anticipated backward stochastic differential equations (RABSDEs) driven by a Brownian motion and a mutually independent martingale in a defaultable setting. The generator of a RABSDE includes the present and future values of the solution. We introduce...

The paper contends that neoclassical ideology stems, to a great extent, from mathematical analysis. It is suggested that mainstream economic thought can be comprehensively revisited if both histories of mathematical and economic thought are to be taken collaboratively into account. Ideology is...

Adomain decomposition method is a powerful technique to solve nonlinear differential equations and nonlinear Integro - differential equations. This paper presents a novel way of computing Adomian polynomials for nonlinear terms occur in nonlinear differential equations through partial Bell...

We provide solution formulas for (linear and non-linear) jump-diffusion backward stochastic differential equations (BSDEs) under diverse enlarged filtration approaches. We also derive a comparison theorem for BSDEs in an enlarged filtration framework and present several applications of our...

In insurance mathematics, optimal control problems over an infinite time horizon arise when computing risk measures. An example of such a risk measure is the expected discounted future dividend payments. In models which take multiple economic factors into account, this problem is...

We characterise the entire set of symmetric stationary Markov-perfect Nash equilibria (MPE) in a differential game of public good investment, using the canonical problem of climate change as an example. We provide a sufficient and necessary condition for MPE and show how the entire set of MPE is...

Das Buch gibt einen Überblick über alle wichtigen Begriffe rund um den Einkommensteuertarif, wie Grenzsteuersatz oder kalte Progression, um nur zwei zu nennen. Die Begriffe werden nicht nur erklärt, sondern auch mit genauen Berechnungen und Beispielen dargelegt. Das Buch eignet sich für...

This paper examines demand systems where the demand for a good depends on other prices only through a common price aggregator (a scalar function of all prices). We refer to this property as ``generalized separability'' and provide the functional forms of demand that this property implies when...