Computation of Fredholm determinants for quadratic Ornstein-Uhlenbeck functionals. (English) Zbl 1357.60086
Summary: We derive closed form expressions for the Laplace transform of certain quadratic Brownian functionals based on the Ornstein-Uhlenbeck process, using both Fredholm determinants and PDE arguments. Classical and new bond pricing formulas in quadratic Brownian models are obtained as particular cases.
MSC:
| 60J60 | Diffusion processes |
| 44A10 | Laplace transform |
| 45B05 | Fredholm integral equations |
| 45D05 | Volterra integral equations |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
| 65F40 | Numerical computation of determinants |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91G60 | Numerical methods (including Monte Carlo methods) |
