12,827 research outputs found
A dynamic programming approach to constrained portfolios
This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of inter¬mediate wealth and/or consumption
Value-at-Risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston's model
We solve an expected utility-maximization problem with a Value-at-risk
constraint on the terminal portfolio value in an incomplete financial market
due to stochastic volatility. To derive the optimal investment strategy, we use
the dynamic programming approach. We demonstrate that the value function in the
constrained problem can be represented as the expected modified utility
function of a vega-neutral financial derivative on the optimal terminal wealth
in the unconstrained utility-maximization problem. Via the same financial
derivative, the optimal wealth and the optimal investment strategy in the
constrained problem are linked to the optimal wealth and the optimal investment
strategy in the unconstrained problem. In numerical studies, we substantiate
the impact of risk aversion levels and investment horizons on the optimal
investment strategy. We observe a 20% relative difference between the
constrained and unconstrained allocations for average parameters in a
low-risk-aversion short-horizon setting.Comment: 39 pages, 8 figure
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
Processing second-order stochastic dominance models using cutting-plane representations
This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian
National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)
Bayesian emulation for optimization in multi-step portfolio decisions
We discuss the Bayesian emulation approach to computational solution of
multi-step portfolio studies in financial time series. "Bayesian emulation for
decisions" involves mapping the technical structure of a decision analysis
problem to that of Bayesian inference in a purely synthetic "emulating"
statistical model. This provides access to standard posterior analytic,
simulation and optimization methods that yield indirect solutions of the
decision problem. We develop this in time series portfolio analysis using
classes of economically and psychologically relevant multi-step ahead portfolio
utility functions. Studies with multivariate currency, commodity and stock
index time series illustrate the approach and show some of the practical
utility and benefits of the Bayesian emulation methodology.Comment: 24 pages, 7 figures, 2 table
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Dynamic asset (and liability) management under market and credit risk
We introduce a modelling paradigm which integrates credit risk and market
risk in describing the random dynamical behaviour of the underlying fixed income assets.
We then consider an asset and liability management (ALM) problem and develop a mul-
tistage stochastic programming model which focuses on optimum risk decisions. These
models exploit the dynamical multiperiod structure of credit risk and provide insight
into the corrective recourse decisions whereby issues such as the timing risk of default is
appropriately taken into consideration. We also present a index tracking model in which
risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the
index. Both in- and out-of-sample (backtesting) experiments are undertaken to validate
our approach. In this way we are able to demonstrate the feasibility and flexibility of
the chosen framework
Towards using online portfolios in computing courses
The direct experience we had with teaching a summer pre-college computing course in which we adopted an online portfolio approach has led us to consider the use of online portfolios in our regular computer science undergraduate courses. The technical challenges we foresee include: the necessary support from the college\u27s IT department; the use of Microsoft-based web authoring technologies vs. the use of Open Source / freeware counterparts; the need for adequate technical knowledge on the part of our faculty; the need for server-side hardware and software resources
Tracking Error: a multistage portfolio model
We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.
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