The main aim of this paper is to develop some basic theories of neutral stochastic functional differential equations (NSFDEs). Firstly, we establish a local existenceuniqueness theorem under the local ...
Stochastic dynamical systems arise in many scientific fields, such as asset prices in financial markets, neural activity in ...
Mathematics of Computation, Vol. 49, No. 180 (Oct., 1987), pp. 523-542 (20 pages) We present Runge-Kutta methods of high accuracy for stochastic differential ...
Kinetic theory provides a statistical framework for understanding how macroscopic behaviour emerges from the collective dynamics of microscopic constituents. This field has long been fundamental in ...
Brownian motion and Langevin's equation. Ito and Stratonovich Stochastic integrals. Stochastic calculus and Ito's formula. SDEs and PDEs of Kolmogorov. Fokker-Planck, and Dynkin. Boundary conditions, ...
This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...
In this paper we examine the capacity of arbitrage-free neural stochastic differential equation market models to produce realistic scenarios for the joint dynamics of multiple European options on a ...
This course is compulsory on the BSc in Actuarial Science. This course is available on the BSc in Business Mathematics and Statistics, BSc in Financial Mathematics and Statistics, BSc in Mathematics ...
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