Simple Markov models are fitted to a small sample of longitudinal categorical data of teachers' ratings of children's classroom behavior. Although the data consist only of observations at 5 occasions, it was possible, after dividing the data into two groups, to fit plausible models in continuous time. Measurement error and alternative longitudinal designs are discussed, and some possible educational implications are noted.
The objective of this thesis is to provide a simulations-free approximation to the price of multivariate derivatives and for the calculation of risk measures like Value at Risk (VaR). The first chapters are dedicated to the pricing of multivariate derivatives. In particular we focus on multivariate derivatives under switching regime Markov models. We consider the cases of two and three states of the switching regime Markov model, and derive analytic expressions for the first and second order moments of the occupation times of the continuous-time Markov process. Then we use these expressions to provide approximations for the derivative prices based on Taylor expansions. We compare our closed form approximations with Monte Carlo simulations. In the last chapter we also provide a simulations-free approximation for the VaR under a switching regime model with two states. We compare these VaR estimations with those obtained using Monte Carlo.
Rejoinder on: Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates