Fuzzy fractional differential has the strength to capture the senses of memory and uncertainty simultaneously involved in dynamical systems. However, a solution for fuzzy fractional differential equations is not always found regularly. This paper discusses a numerical solution approach for the...

We introduce a novel stochastically correlated two-factor (i.e., bivariate) diffusion process under the square-root format, for which we analytically obtain the corresponding solutions for the conditional moment-generating functions and conditional characteristic functions. Such solutions...

We explore intertemporal preferences that are recursive and account for local intertemporal substitution. First, we establish a rigorous foundation for these preferences and analyze their properties. Next, we examine the associated optimal consumption problem, proving the existence and...

We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting...

The Heston model is one of the most used techniques for estimating the fair value and the risk measures associated with investment certificates. Typically, the pricing engine implements a significant number of projections of the underlying until maturity, it calculates the pay-off for all the...

The mining industry continues to play a significant role in developing the economy in developing countries. The need for minerals influences the magnitude of the mining industry, and safety concerns have taken on considerable importance in this sector. Equipment failure and breakdown will...

This study considers the classical Lotka-Volterra model for a prey-predator system with harvesting effort and catchability coefficients for both species incorporating a new prey-refuge parameter. Trapezoidal intuitionistic fuzzy numbers are considered to describe the initial values of the prey...

Neutrosophic sets are a generalization of fuzzy sets and intuitionistic fuzzy sets. They play an important role in addressing uncertainty, vagueness, and indeterminacy in problem-solving. Differential equations in a neutrosophic environment under Hukuhara differentiability are used to model the...

In this paper, we study the problem of dynamic convex risk measures via reflected backward stochastic differential equations with time delayed generators (RBSDEs with time delayed generators, in short). Under some assumptions on the generators of the equations, we prove that the RBSDEs with a...

This paper introduces the probabilistic formulation of continuous-time economic models: forward stochastic differential equations (SDE) govern the dynamics of backward-looking variables, and backward SDEs capture that of forward-looking variables. Deep learning streamlines the search for the...

This dissertation provides a contribution to the option pricing literature by means of some recent developments in probability theory, namely the Malliavin Calculus and the Wiener chaos theory. It sheds new light on some old and complicated problems by means of these new techniques. It...

In the light of present-day research, as we all know, the financial market owns the characteristics of self-similarity and long-range dependence and Fractional Brownian motion has these properties. From that point, The model with fractional stochastic volatility could be more businesslike than...

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...

Integral transforms plays important role in solving differential equations and integral equations. In this paper we discuss application of Aboodh transform and Mahgoub transform in solvingboundary value problem of system of ordinary differential equations and result shows that Aboodhtransform...

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...

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 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...

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...

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...

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 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...