A Brownian population model.
A diffusion approximation in the ruin problem for a controlled Markov chain
A maximum principle approach to risk indifference pricing with partial information.
A model discrimination method for processes with different memory structure.
A model for liver homeostasis using modified mean-reverting Ornstein-Uhlenbeck process.
A stochastic two species competition model: nonequilibrium fluctuation and stability.
Adaptive dynamics in logistic branching populations
The biological theory of adaptive dynamics proposes a description of the long-time evolution of an asexual population, based on the assumptions of large population, rare mutations and small mutation steps. Under these assumptions, the evolution of a quantitative dominant trait in an isolated population is described by a deterministic differential equation called 'canonical equation of adaptive dynamics'. In this work, in order to include the effect of genetic drift in this model, we consider instead...
Alpha-stable branching and beta-coalescents.
Analytical approximation of the transition density in a local volatility model
We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps.
Appendix on return-time sequences