Viability theory
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
European option pricing with transaction costs
SIAM Journal on Control and Optimization
Numerical analysis of American option pricing in a jump-diffusion model
Mathematics of Operations Research
A Posteriori Finite Element Error Estimation for Diffusion Problems
SIAM Journal on Scientific Computing
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
On the Approximation of Optimal Stopping Problems with Application to Financial Mathematics
SIAM Journal on Scientific Computing
On the Valuation of Asian Options by Variational Methods
SIAM Journal on Scientific Computing
An adaptive extrapolation discontinuous Galerkin method for the valuation of Asian options
Journal of Computational and Applied Mathematics
Asset liquidity and the valuation of derivative securities
Journal of Computational and Applied Mathematics
| Hi-index | 7.30 |
We consider theoretical and approximation aspects of the stochastic optimal control of ultradiffusion processes in the context of a prototype model for the selling price of a European call option. Within a continuous-time framework, the dynamic management of a portfolio of assets is effected through continuous or point control, activation costs, and phase delay. The performance index is derived from the unique weak variational solution to the ultraparabolic Hamilton-Jacobi equation; the value function is the optimal realization of the performance index relative to all feasible portfolios. An approximation procedure based upon a temporal box scheme/finite element method is analyzed; numerical examples are presented in order to demonstrate the viability of the approach.