Geometric Brownian Motion with Delay: Mean Square Characterisation

Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries

‎In this paper Lie symmetry analysis is applied to find new‎ solution for Fokker Plank equation of geometric Brownian motion‎. This analysis classifies the solution format of the Fokker Plank‎ ‎equation‎.

DC-dominant property of cone-preserving transfer functions

We consider a class of square MIMO transfer functions that map a proper cone in the space of L2 input signals to the same cone in the space of output signals. Transfer functions in this class have the “DC-dominant” property: the maximum radius of the operator spectrum is attained by a DC input signal and hence, the dynamic stability of the feedback interconnection of such transfer functions is ...

Mirror and Synchronous Couplings of Geometric Brownian Motions

The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and show that, unlike in the case of Brownian motion, the optimality fails in ge...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Lévy-sheffer Systems and the Longstaff-schwartz Algorithm for American Option Pricing

Glasserman and Yu (Ann. Appl. Probab. 14, 2004, p. 2090) have investigated the mean square error in the Longstaff-Schwartz algorithm for American option pricing, assuming that the underlying process is (geometric) Brownian motion. In this note we provide similar convergence results for the standard Poisson, Gamma, Pascal, and Meixner processes, pointing out the connection of the problem to the ...