On strong solutions and explicit formulas for solutions of stochastic integral equations

TL;DR: In this article, the authors consider the stochastic differential equation dx(t) = f(t, x(t))dt + b(T, x, t, t))dW(t), x(0) = x0 for t ≥ 0, where W is a standard d-dimensional Brownian motion, f is a bounded Borel function from [0, ∞) ×ℝ d to ℝ D, and b is an invertible matrix-valued function satisfying some regularity conditions.

TL;DR: In this paper , the authors considered multidimensional SDEs with distributional drift driven by symmetric, α-stable Lévy processes for α∈(1,2] by studying the associated (singular) martingale problem and by solving the Kolmogorov backward equation.

TL;DR: In this paper, the authors consider insurance derivatives depending on an external physical risk process, for example a temperature in a low dimensional climate model, and derive optimal strategies for exponential utility from terminal wealth, determine the indifference prices of the derivatives and interpret them in terms of diversification pressure.

TL;DR: In this paper, the authors considered a stochastic linear transport equation with a globally Holder continuous and bounded vector field and showed that the unique solution starting with a C 1 -initial condition remains of class C 1 in space.

TL;DR: In this paper, a quasi-isometric transformation of a phase space that allows passing from a diffusion process with nonzero drift coefficient to a process without drift is presented, and strong solutions of stochastic differential equations with a "bad" drift coefficient are constructed.

TL;DR: In this paper, the authors prove the existence of a strong solution of a stochastic integral equation of the form, using the theory of differential equations of parabolic type, and prove the proof of these criteria is based on finding formulas expressing via multiple Stochastic integrals, formulas which in the case give an expression for, if is a strong solutions of the stochastically equation.