Two seminar lectures by Mohamed MNIF and Yaozhong HU
Monday 19 August 2019 Mohamed MNIF from the Ecole Polytechnique de Tunisie and Yaozhong HU from the University of Alberta will give two seminar lectures at the section of Stochastic analysis, Finance and risks. Titles and Abstracts below.
10.15 -11.00: Mohamed MNIF, Ecole Polytechnique de Tunisie (LEGI)
Optimal stopping contract for Public Private Partnerships under moral hazard and risk-sharing
We study a principal agent problem with optimal stopping. We assume that the principal which is the public in our case ("she") pays a rent to the agent which is the consortium ("he"), while the latter gives a best response characterized by his effort until a terminal date decided by the public when she stops the contract and gives compensation to the consortium.
We solve the first-best and the second-best problems associated with this framework. In the second best, the value function is characterized as the solution of the corresponding Hamilton Jacobi Bellman Variational Inequality. We characterize the optimal strategy by the solution of the variational inequality which we solve numerically by using the Howard algorithm and we show that the optimal rent is not a linear function of the effort.
11.15 -12.00: Yaozhong HU, University of Alberta
Generalized moment estimators for alpha-stable Ornstein–Uhlenbeck motions from discrete observations
We study the parameter estimation problem for discretely observed Ornstein–Uhlenbeck processes driven by α-stable Lévy motions. A method of moments via ergodic theory and via sample characteristic functions is proposed to estimate all the parameters involved in the Ornstein–Uhlenbeck processes. We obtain the strong consistency and asymptotic normality of the proposed joint estimators when the sample size n → ∞ while the sampling time step h remains arbitrarily fixed. We also design a procedure to select the grid points in the characteristic functions in certain optimal way for the proposed estimators. This is a joint work with Yiying Cheng and Hongwei Long.