| Title |
On backward Kolmogorov equation related to CIR process / |
| Authors |
Mackevičius, Vigirdas ; Mongirdaitė, Gabrielė |
| DOI |
10.15559/18-VMSTA98 |
| Full Text |
|
| Is Part of |
Modern stochastics: theory and applications.. Vilnius : VTeX. 2018, Vol. 5, no. 1, p. 113-127.. ISSN 2351-6054 |
| Keywords [eng] |
CIR process ; Kolmogorov equation ; Bessel process ; smooth solutions |
| Abstract [eng] |
We consider the existence of a classical smooth solution to the backward Kolmogorov equation related to the CIR process. Alfonsi showed that the equation has a smooth solution with partial derivatives of polynomial growth, provided that the initial function f is smooth with derivatives of polynomial growth. His proof was mainly based on the analytical formula for the transition density of the CIR process in the form of a rather complicated function series. In this paper, for a CIR process satisfying the condition σ2 ≤ 4θκ, we present a direct proof based on the representation of a CIR process in terms of a squared Bessel process and its additivity property. |
| Published |
Vilnius : VTeX |
| Type |
Journal article |
| Language |
English |
| Publication date |
2018 |
