Likelihood inference for non-linear jump diffusions with state-dependent intensity

Dr Etienne Pienaar will present this seminar.

Jump diffusion processes can be seen as a generalisation of standard diffusion processes whereby the trajectory of the underlying diffusion process is allowed to be perturbed by a jump process.

Unfortunately, the analysis of diffusion models in general is extremely difficult, due in most part to the intractability of the probabilistic dynamics of such processes, with only a few simple models having analytically tractable transitional densities.

For these purposes, we develop a method for approximating the transitional densities of a class of time-inhomogeneous jump diffusions with state-dependent and/or stochastic intensity. By deriving a system of equations that govern the evolution of the moments of the process, Pienaar will show that we are able to approximate the transitional density through a density factorisation that contrasts the dynamics of the jump diffusion with that of its jump free counterpart.

In this talk, Pienaar will also briefly discuss some of his experiences with industry and share some thoughts on how to change/develop the interface between industry and the untapped brain power residing within statistics (and other) departments. He will argue that the current climate in academia may present a unique opportunity to change/improve business models in scientific academia.

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