@PhdThesis{diss_mods_00019558, author = {Feodoria, Mark-Roman}, title = {Optimal investment and utility indifference pricing in the presenceof small fixed transaction costs}, year = {2016}, publisher = {Christian-Albrechts-Universit{\"a}t zu Kiel}, address = {Kiel}, keywords = {Fixed transaction costs; Optimal investment and pricing; asymptotic expansions; Feste Transaktionskosten; Optimales Handeln und Bepreisen; Asymptotik}, abstract = {This thesis deals with utility maximization from terminal wealth under fixed transaction costs. We consider an investor with constant absolute risk aversion trading in a market consisting of one safe and one risky asset with general Ito dynamics. We assume that she has to pay a fixed transaction cost for each trade regardless of its size. Using a non-Markovian dynamic programming approach, we derive candidate strategy for optimality. This strategy lies in a random and time-dependent interval around the frictionless optimizer, changes to the latter once the boundaries of this interval are breached and liquidates all stock positions if the corresponding wealth falls below a given (stochastic) threshold. We verify the (almost) optimality of the candidate under suitable regularity assumptions. Furthermore, we give two examples of models fulfilling these assumptions and present an application to utility indifference pricing. After weakening the regularity assumptions, we derive a pricing formula for the European put option in the Black-Scholes model under fixed transaction costs. Our results verify the heuristics of (Korn, 1998, Section 5) in the absence of proportional costs, but for general Ito dynamics. Contrary to the related study of Altarovici et al. (2015a) in a different setup, our derivation and verification rely on martingale methods and tools from stochastic calculus like the change-of-variable formula from Peskir (2007) rather than homogenization and viscosity solutions.}, url = {https://macau.uni-kiel.de/receive/diss_mods_00019558}, file = {:https://macau.uni-kiel.de/servlets/MCRFileNodeServlet/dissertation_derivate_00006786/Feodoria_Dissertation_Druckversion.pdf:PDF}, language = {en} }