scholarly journals On monotone and primal-dual active set schemes for $$\ell ^p$$ ℓ p -type problems, $$p \in (0,1]$$ p ∈ ( 0 , 1 ]

2018 ◽  
Vol 72 (1) ◽  
pp. 45-85 ◽  
Author(s):  
Daria Ghilli ◽  
Karl Kunisch
Keyword(s):  
Active Set ◽  
Primal Dual ◽  
P Type

scholarly journals Nonlocal Allen-Cahn systems: analysis and a primal-dual active set method

2013 ◽  
Vol 33 (4) ◽  
pp. 1126-1155 ◽  
Author(s):  
L. Blank ◽  
H. Garcke ◽  
L. Sarbu ◽  
V. Styles
Keyword(s):  
Systems Analysis ◽  
Active Set ◽  
Active Set Method ◽  
Primal Dual

scholarly journals Primal-dual active-set method for solving the unilateral pricing problem of American better-of options on two assets

2021 ◽  
Vol 30 (1) ◽  
pp. 90-115
Author(s):  
Yiyuan Qian ◽  
◽  
Haiming Song ◽  
Xiaoshen Wang ◽  
Kai Zhang ◽  
...  
Keyword(s):  
Free Boundary ◽  
Variable Coefficients ◽  
Euler Method ◽  
The Finite Element Method ◽  
Variational Theory ◽  
Active Set ◽  
Bounded Linear ◽  
Active Set Method ◽  
Backward Euler ◽  
Primal Dual

<abstract><p>In this paper, an efficient numerical algorithm is proposed for the valuation of unilateral American better-of options with two underlying assets. The pricing model can be described as a backward parabolic variational inequality with variable coefficients on a two-dimensional unbounded domain. It can be transformed into a one-dimensional bounded free boundary problem by some conventional transformations and the far-field truncation technique. With appropriate boundary conditions on the free boundary, a bounded linear complementary problem corresponding to the option pricing is established. Furthermore, the full discretization scheme is obtained by applying the backward Euler method and the finite element method in temporal and spatial directions, respectively. Based on the symmetric positive definite property of the discretized matrix, the value of the option and the free boundary are obtained simultaneously by the primal-dual active-set method. The error estimation is established by the variational theory. Numerical experiments are carried out to verify the efficiency of our method at the end.</p></abstract>

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