Robust Utility Maximization in a Stochastic Factor Model

We give an explicit PDE characterization for the solution of a robust utility maximization problem in an incomplete market model, whose volatility, interest rate process, and long-term trend are driven by an external stochastic factor process. The robust utility functional is defined in terms of a HARA utility function with negative risk aversion and a dynamically consistent coherent risk measure, which allows for model uncertainty in the distributions of both the asset price dynamics and the factor process. Our method combines two recent advances in the theory of optimal investments: the general duality theory for robust utility maximization and the stochastic control approach to the dual problem of determining optimal martingale measures.optimal investment, model uncertainty, incomplete markets, stochastic volatility, coherent risk measures, optimal control, convex duality

A Characterization of the optimal risk-Sensitive average cost in finite controlled Markov chains

This work concerns controlled Markov chains with finite state and action spaces. The transition law satisfies the simultaneous Doeblin condition, and the performance of a control policy is measured by the (long-run) risk-sensitive average cost criterion associated to a positive, but otherwise arbitrary, risk sensitivity coefficient. Within this context, the optimal risk-sensitive average cost is characterized via a minimization problem in a finite-dimensional Euclidean space.Comment: Published at http://dx.doi.org/10.1214/105051604000000585 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Control Approach to Robust Utility Maximization with Logarithmic Utility and Time-Consistent Penalties

We propose a stochastic control approach to the dynamic maximization of robust utility functionals that are defined in terms of logarithmic utility and a dynamically consistent convex risk measure. The underlying market is modeled by a diffusion process whose coefficients are driven by an external stochastic factor process. In particular, the market model is incomplete. Our main results give conditions on the minimal penalty function of the robust utility functional under which the value function of our problem can be identified with the unique classical solution of a quasilinear PDE within a class of functions satisfying certain growth conditions. The fact that we obtain classical solutions rather than viscosity solutions is important for the use of numerical algorithms, whose applicability is demonstrated in examples.Optimal investment, model uncertainty, incomplete markets, stochastic volatility, coherent risk measure, convex risk measure, optimal control, convex duality

Critical currents at the Bragg glass to vortex glass transition

We present simulations of the transport properties of superconductors at the transition from the Bragg glass (BG) to the vortex glass (VG) phase. We study the frustrated anisotropic 3D XY model with point disorder, which has been shown to have a first order transition as a function of the intensity of disorder. We add an external current to the model and we obtain current-voltage curves as a function of disorder at a low temperature. We find that the in-plane critical current has a steep increase at the BG-VG transition, while the c-axis critical current has a discontinous jump down, this later result in agreement with the first-order character of the transition.Comment: 4 pages, 5 figures. Introduction changed. Accepted for publication in Physical Review Letter