- Series
- Mathematical Finance/Financial Engineering Seminar
- Time
- Friday, April 19, 2013 - 2:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Ruoting Gong – Rutgers University
- Organizer
- Christian HoudrÃ©

**Please Note:** Hosts: Christian Houdre and Liang Peng

We prove stochastic representation formulae for solutions to elliptic boundary value and
obstacle problems associated with a degenerate Markov diffusion process on the
half-plane. The degeneracy in the diffusion coefficient is proportional to the \alpha-power
of the distance to the boundary of the half-plane, where 0 < \alpha < 1 . This generalizes the
well-known Heston stochastic volatility process, which is widely used as an asset price
model in mathematical finance and a paradigm for a degenerate diffusion process. The
generator of this degenerate diffusion process with killing, is a second-order,
degenerate-elliptic partial differential operator where the degeneracy in the operator
symbol is proportional to the 2\alpha-power of the distance to the boundary of the
half-plane. Our stochastic representation formulae provides the unique solution to the
degenerate partial differential equation with partial Dirichlet condition, when we seek
solutions which are suitably smooth up to the boundary portion \Gamma_0 contained in the
boundary of the half-plane. In the case when the full Dirichlet condition is given, our
stochastic representation formulae provides the solutions which are not guaranteed to be
any more than continuous up to the boundary portion \Gamma_0 .