Robust consumption-investment problems with stochastic coefficients [Elektronische Ressource] / vorgelegt von Christoph Wopperer

Universitat UlmFakultat fur Mathematik undWirtschaftswissenschaftenRobust consumption-investment problemswith stochastic coe cientsDissertationzur Erlangung des Doktorgrades Dr. rer. nat.der Fakult at fur Mathematik und Wirtschaftswissenschaftender Universit at Ulmvorgelegt vonChristoph Woppereraus ErlangenUlm, November 2010Amtierender Dekan: Prof. Dr. Werner Kratz1. Gutachter: Prof. Dr. Ulrich Rieder2.hter: Prof. Dr. Rudiger KieselTag der Promotion: 14.02.2011AbstractIn this thesis we consider robust consumption-investment problems in a complete di u-sion market with stochastic coe cients. We assume that the market price of risk processis unknown. The investor tries to maximize his expected utility under the worst-caseparameter con guration. To solve robust consumption-investment problems, we derivea stochastic version of the Bellman-Isaac equations for di erential games from the mar-tingale optimality principle. A formal connection between a solution of these equationsand the robust optimal value function is established by a veri cation theorem. We areable to solve the Bellman-Isaac equations for power, exponential and logarithmic utility.In this way we can characterize a robust optimal consumption-investment strategy and aworst-case market price of risk process in terms of the solution of a backward stochasticdi erential equation ( Bsde). The solution of this Bsde can be explicitly computed incase of deterministic coe cients.