107,902 research outputs found
Robust Optimal Control for a Consumption-investment Problem
We give an explicit PDE characterization for the solution of the problem of maximizing the utility of both terminal wealth and intertemporal consumption under model uncertainty. The underlying market model consists of a risky asset, whose volatility 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 risk aversion parameter 0Optimal Consumption, Robust Control, Model Uncertainty, Incomplete Markets, Stochastic Volatility, Coherent Risk Measures, Convex Duality
Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs
This paper studies the properties of the optimal portfolio-consumption
strategies in a {finite horizon} robust utility maximization framework with
different borrowing and lending rates. In particular, we allow for constraints
on both investment and consumption strategies, and model uncertainty on both
drift and volatility. With the help of explicit solutions, we quantify the
impacts of uncertain market parameters, portfolio-consumption constraints and
borrowing costs on the optimal strategies and their time monotone properties.Comment: 35 pages, 8 tables, 1 figur
Horizon-unbiased Investment with Ambiguity
In the presence of ambiguity on the driving force of market randomness, we
consider the dynamic portfolio choice without any predetermined investment
horizon. The investment criteria is formulated as a robust forward performance
process, reflecting an investor's dynamic preference. We show that the market
risk premium and the utility risk premium jointly determine the investors'
trading direction and the worst-case scenarios of the risky asset's mean return
and volatility. The closed-form formulas for the optimal investment strategies
are given in the special settings of the CRRA preference
Robust Maximization of Consumption with Logarithmic Utility
We analyze the stochastic control approach to the dynamic maximization of the robust utility of consumption and investment. The robust utility functionals 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. 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.Robust utility maximization, optimal consumption, stochastic factor model, stochastic control, convex risk measure, dynamic consistency, Hamilton-Jacobi-Bellman equation
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