We consider generalized linear transient convection-diffusion problems for differential forms on bounded domains in . These involve Lie derivatives with respect to a prescribed smooth vector field. We construct both new Eulerian and semi-Lagrangian approaches to the discretization of the Lie derivatives…
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6 results for “semi-Lagrangian”
Develops a new method for pricing GMWBs with jumps and stochastic interest rates.
problem Pricing guaranteed minimum withdrawal benefits (GMWBs) with jumps and stochastic interest rates.
method Combines semi-Lagrangian method with Fourier pricing and Green's function.
result Mathematically demonstrates convergence to the viscosity solution of the HJB-QVI.
This work is motivated by numerical solutions to Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) associated with combined stochastic and impulse control problems. In particular, we consider (i) direct control, (ii) penalized, and (iii) semi-Lagrangian discretization schemes applied to the HJBQVI proble…
Numerical valuation of European options under two-asset infinite-activity exponential Lévy modelsmath.NA
Method extends option valuation for 2D Lévy models.
problem Valuation of European options under 2-asset infinite-activity Lévy models.
method Developed numerical method extending Wang et al. (2007) for 1D to 2D, using Fourier transform for integral term and semi-Lagrangian theta-method for temporal discretization.
result Favourable second-order convergence for Normal Tempered Stable dynamics.
In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic properties: partial Cartan structure, prolongation of vector fields, etc. A constituti…
PDE models for the valuation of a non callable defaultable coupon bond under an extended JDCEV modelq-fin.CP
We consider a two-factor model for the valuation of a non callable defaultable bond which pays coupons at certain given dates. The model under consideration is the Jump to Default Constant Elasticity of Variance (JDCEV) model. The JDCEV model is an improvement of the reduced form approach, which unifies credit and equi…