Utility maximisation and utility indifference pricing for exponential semimartingale models.

Summary In this thesis we consider the utility maximization and indifference price formation problem for exponential semimartingale models depending on a random factor ξ. The challenge is to solve the indifference price problem using space magnification and filtration. We reduce the maximization problem in the magnified filtration to the conditional problem, knowing {ξ = v}, which we solve using a dual approach. For HARA-utility we introduce information such as relative entropies and Hellinger-type integrals, as well as the corresponding information processes, enfin to express, via these processes, the maximal utility. In particular, we study exponential Lévy models, where the information processes are deterministic which considerably simplifies the calculations of indifference prices. Infin, we apply the results to the geometric Brownian motion model and the diffusion-jump model that includes Brownian motion and Poisson processes. In the logarithmic, power, and exponential utility cases, we provide the explicit formulas for the information, and then, using numerical methods, we solve the equations to obtain the indifference prices in the case of selling a European option.