Joint distributions for stochastic functional differential equations. Issue 5 (3rd July 2016)

• Record Type: Journal Article
• Authors: Takeuchi, Atsushi
• Is Part Of: Stochastics. Volume 88:Issue 5(2016)
• Page Start: 711
• Page End: 736
• Publication Date: 2016-07-03
• Subjects: Stochastic functional differential equations -- Malliavin calculus -- density function -- option pricing formula -- computations of the Greeks; 34K50 -- 60H07 -- 62G07 -- 91G20 -- 91G80; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2015.1137575
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : Consider stochastic functional differential equations, whose coefficients depend on past histories. The solution determines a non-Markov process. In the present paper, we shall obtain the existence of smooth densities for joint distributions of solutions, under the uniformly elliptic condition on the diffusion coefficients, via the Malliavin calculus. As an application, we shall study the computations of the Greeks on options associated with the asset price dynamics models with delayed effects.