2,201 research outputs found
A two-stage stochastic mixed-integer program modelling and hybrid solution approach to portfolio selection problems
In this paper, we investigate a multi-period portfolio selection problem with a comprehensive set of real-world trading constraints as well as market random uncertainty in terms of asset prices. We formulate the problem into a two-stage stochastic mixed-integer program (SMIP) with recourse. The set of constraints is modelled as mixed-integer program, while a set of decision variables to rebalance the portfolio in multiple periods is explicitly introduced as the recourse variables in the second stage of stochastic program. Although the combination of stochastic program and mixed-integer program leads to computational challenges in finding solutions to the problem, the proposed SMIP model provides an insightful and flexible description of the problem. The model also enables the investors to make decisions subject to real-world trading constraints and market uncertainty.
To deal with the computational difficulty of the proposed model, a simplification and hybrid solution method is applied in the paper. The simplification method aims to eliminate the difficult constraints in the model, resulting into easier sub-problems compared to the original one. The hybrid method is developed to integrate local search with Branch-and-Bound (B&B) to solve the problem heuristically. We present computational results of the hybrid approach to analyse the performance of the proposed method. The results illustrate that the hybrid method can generate good solutions in a reasonable amount of computational time. We also compare the obtained portfolio values against an index value to illustrate the performance and strengths of the proposed SMIP model. Implications of the model and future work are also discussed
Dynamic changes and multi-dimensional evolution of portfolio optimization
Although there has been an increasing number of studies investigate portfolio optimization from different perspectives, few
attempts could be found that focus on the development trend
and hotspots of this research area. Therefore, it motivates us to
comprehensively investigate the development of portfolio optimization research and give some deep insights into this knowledge domain. In this paper, some bibliometric methods are
utilized to analyse the status quo and emerging trends of
portfolio optimization research on various aspects such as
authors, countries and journals. Besides, ‘theories’, ‘models’ and
‘algorithms’, especially heuristic algorithms are identified as the
hotspots in the given periods. Furthermore, the evolutionary analysis tends to presents the dynamic changes of the cutting-edge
concepts of this research area in the time dimension. It is found
that more portfolio optimization studies were at an exploration
stage from mean-variance analysis to consideration of multiple
constraints. However, heuristic algorithms have become the driving force of portfolio optimization research in recent years. Multidisciplinary analyses and applications are also the main trends of
portfolio optimization research. By analysing the dynamic changes
and multi-dimensional evolution in recent decades, we contribute
to presenting some deep insights of the portfolio optimization
research directly, which assists researchers especially beginners to
comprehensively learn this research field
Distributionally robust optimization with applications to risk management
Many decision problems can be formulated as mathematical optimization models. While deterministic
optimization problems include only known parameters, real-life decision problems
almost invariably involve parameters that are subject to uncertainty. Failure to take this
uncertainty under consideration may yield decisions which can lead to unexpected or even
catastrophic results if certain scenarios are realized.
While stochastic programming is a sound approach to decision making under uncertainty, it
assumes that the decision maker has complete knowledge about the probability distribution
that governs the uncertain parameters. This assumption is usually unjustified as, for most
realistic problems, the probability distribution must be estimated from historical data and
is therefore itself uncertain. Failure to take this distributional modeling risk into account
can result in unduly optimistic risk assessment and suboptimal decisions. Furthermore, for
most distributions, stochastic programs involving chance constraints cannot be solved using
polynomial-time algorithms.
In contrast to stochastic programming, distributionally robust optimization explicitly accounts
for distributional uncertainty. In this framework, it is assumed that the decision maker has
access to only partial distributional information, such as the first- and second-order moments
as well as the support. Subsequently, the problem is solved under the worst-case distribution
that complies with this partial information. This worst-case approach effectively immunizes
the problem against distributional modeling risk.
The objective of this thesis is to investigate how robust optimization techniques can be used
for quantitative risk management. In particular, we study how the risk of large-scale derivative
portfolios can be computed as well as minimized, while making minimal assumptions about
the probability distribution of the underlying asset returns. Our interest in derivative portfolios
stems from the fact that careless investment in derivatives can yield large losses or even
bankruptcy. We show that by employing robust optimization techniques we are able to capture
the substantial risks involved in derivative investments. Furthermore, we investigate how
distributionally robust chance constrained programs can be reformulated or approximated as
tractable optimization problems. Throughout the thesis, we aim to derive tractable models
that are scalable to industrial-size problems
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