Bayesian Estimation For Modulated Claim Hedging

The purpose of this paper is to establish a general super hedging formula under a pricing set Q . We will compute the price and the strategies for hedging an European claim and simulate that using different approaches including Dirichlet priors. We study Dirichlet processes centered around the distribution of continuous-time stochastic processes such as a continuous time Markov chain. We assume that the prior distribution of the unobserved Markov chain driving by the drift and volatility parameters of the geometric Brownian motion (GBM) is a Dirichlet process. We propose an estimation method based on Gibbs sampling. I. Introduction Models in which parameters move between a fixed number of regimes with switching controlled by an unobserved stochastic process, are very popular in a great variety of domains (Finance, Biology, Meteorology, Networks, etc.). This is notably due to the fact that this additional flexibility allows the model to account for random regime changes in the environment. In this paper we consider the estimation problem for a model described by a stochastic differential equation (SDE) with Markov