8 research outputs found
Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty
We study robust stochastic optimization problems in the quasi-sure setting in
discrete-time. The strategies in the multi-period-case are restricted to those
taking values in a discrete set. The optimization problems under consideration
are not concave. We provide conditions under which a maximizer exists. The
class of problems covered by our robust optimization problem includes optimal
stopping and semi-static trading under Knightian uncertainty.Comment: arXiv admin note: text overlap with arXiv:1610.0923
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
Duality Theory for Robust Utility Maximisation
In this paper we present a duality theory for the robust utility maximisation
problem in continuous time for utility functions defined on the positive real
axis. Our results are inspired by -- and can be seen as the robust analogues of
-- the seminal work of Kramkov & Schachermayer [18]. Namely, we show that if
the set of attainable trading outcomes and the set of pricing measures satisfy
a bipolar relation, then the utility maximisation problem is in duality with a
conjugate problem. We further discuss the existence of optimal trading
strategies. In particular, our general results include the case of logarithmic
and power utility, and they apply to drift and volatility uncertainty
Review of stochastic differential equations in statistical arbitrage pairs trading
The use of stochastic differential equations offers great advantages for statistical arbitrage pairs trading. In particular, it allows the selection of pairs with desirable properties, e.g., strong mean-reversion, and it renders traditional rules of thumb for trading unnecessary. This study provides an exhaustive survey dedicated to this field by systematically classifying the large body of literature and revealing potential gaps in research. From a total of more than 80 relevant references, five main strands of stochastic spread models are identified, covering the ‘Ornstein–Uhlenbeck model’, ‘extended Ornstein–Uhlenbeck models’, ‘advanced mean-reverting diffusion models’, ‘diffusion models with a non-stationary component’, and ‘other models’. Along these five main categories of stochastic models, we shed light on the underlying mathematics, hereby revealing advantages and limitations for pairs trading. Based on this, the works of each category are further surveyed along the employed statistical arbitrage frameworks, i.e., analytic and dynamic programming approaches. Finally, the main findings are summarized and promising directions for future research are indicated