Skip to main content

Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Table 2 A list of joint distributions

From: On the one-sided maximum of Brownian and random walk fragments and its applications to new exotic options called “meander option”

BM P ( · A , B θ dx )
P sup u θ B u A , B θ dx λ 2 e λ | x | λ 2 e λx e 2 λ max ( A , x ) dx
P sup u g θ B u A , B θ dx λ 2 e λ | x | 1 e 2 λA dx
P sup g θ u θ B u A , B θ dx λ 2 1 1 e 2 λA 1 x A e λ | x | e λx 2 λA dx
P sup u d θ B u A , B θ dx 1 x + A 1 x A λ 2 e λ | x | e λx 2 λA dx
P sup θ u d θ B u A , B θ dx 1 x + A 1 x A λ 2 e λ | x | dx
P sup g θ u d θ B u A , B θ dx 1 x + A 1 e 2 λA 1 x A λ 2 e λ | x | e λx 2 λA dx
  1. ()Note: We see on this line that sup u g θ B u and B θ are independent.