Robust consumption-investment problems with stochastic coefficients
FacultiesFakultät für Mathematik und Wirtschaftswissenschaften
LicenseStandard (Fassung vom 01.10.2008)
In this thesis we consider robust consumption-investment problems in a complete diffusion market with stochastic coefficients. We assume that the market price of risk process is unknown. The investor tries to maximize his expected utility under the worst-case parameter configuration. To solve robust consumption-investment problems, we derive a stochastic version of the Bellman-Isaac equations for differential games from the martingale optimality principle. A formal connection between a solution of these equations and the robust optimal value function is established by a verification theorem. We are able 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 a worst-case market price of risk process in terms of the solution of a backward stochastic differential equation (BSDE). The solution of this BSDE can be explicitly computed in case of deterministic coefficients. It is given by the unique solution of a partial differential equation for the popular model of coefficients driven by a factor process.
Subject HeadingsRückwärtsdifferentiationsmethode [GND]
Stochastische Differentialgleichung [GND]
Consumption: Economics. Mathematical models [LCSH]