Mathematical Finance Internal Seminar
|
Thu, 22/01/2009 13:00 |
Vicky Henderson |
Mathematical Finance Internal Seminar  |
DH 1st floor SR |
| We solve the problem of an agent with prospect theory preferences who seeks to liquidate a portfolio of (divisible) claims. Our methodology enables us to consider different formulations of prospect preferences in the literature (piecewise exponential or piecewise power) and various price processes. We find that these differences in specification matter - for instance, with piecewise power functions, the agent may liquidate at a loss relative to break-even, albeit the likelihood of liquidating at a gain is much higher than liquidating at a loss. This is consistent with the disposition effect documented in empirical and experimental studies. We find the agent does not choose to partially liquidate a position, but rather, if liquidation occurs, the entire position is sold. This is in contrast to partial liquidation when agents have standard concave utilities. | |||
|
Thu, 05/02/2009 13:00 |
Alex Kacelnik |
Mathematical Finance Internal Seminar |
DH 3rd floor SR |
| Virtually all decisions taken by living beings, from financial investments to life history, mate choice or anti-predator responses involve uncertainties and inter-temporal trade offs. Thus, hypothesis and formal models from these different fields often have heuristic value across disciplines. I will present theories and experiments about temporal discounting and risky choice originating in behavioural research on birds. Among other topics, I will address empirical observations showing risk aversion for gains and risk proneness for losses, exploring parallels and differences between Prospect Theory, Risk Sensitivity Theory and Scalar Utility Theory. | |||
|
Thu, 19/02/2009 13:00 |
Xuedong He |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| In this paper we employ the quantile formulation to solve the SP/A portfolio choice model in continuous time. We show that the original version of the SP/A model proposed by Lopes is ill-posed in the continuous-time setting. We then generalise the SP/A model to one where a utility function is included, while the probability weighting (distortion) function is still present. The feasibility and well-posedness of the model are addressed and an explicit solution is derived. Finally, we study how the aspiration level and the probability weighting function affect the optimal solution | |||
|
Thu, 05/03/2009 13:00 |
Robert Griffiths (Department of Statistics, Oxford) |
Mathematical Finance Internal Seminar |
DH 3rd floor SR |
| Diffusion process models for evolution of neutral genes have a particle dual coalescent process underlying them. Models are reversible with transition functions having a diagonal expansion in orthogonal polynomial eigenfunctions of dimension greater than one, extending classical one-dimensional diffusion models with Beta stationary distribution and Jacobi polynomial expansions to models with Dirichlet or Poisson Dirichlet stationary distributions. Another form of the transition functions is as a mixture depending on the mutant and non-mutant families represented in the leaves of an infinite-leaf coalescent tree. The one-dimensional Wright-Fisher diffusion process is important in a characterization of a wider class of continuous time reversible Markov processes with Beta stationary distributions originally studied by Bochner (1954) and Gasper (1972). These processes include the subordinated Wright-Fisher diffusion process. | |||
