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)

Option pricing with transaction costs using a Markov chain approximation

An efficient algorithm is developed to price European options in the presence of proportional transaction costs, using the optimal portfolio framework of Davis (in: Dempster, M.A.H., Pliska, S.R. (Eds.), Mathematics of Derivative Securities. Cambridge University Press, Cambridge, UK). A fair option price is determined by requiring that an infinitesimal diversion of funds into the purchase or sale of options has a neutral effect on achievable utility. This results in a general option pricing formula, in which option prices are computed from the solution of the investor's basic portfolio selection problem, without the need to solve a more complex optimisation problem involving the insertion of the option payoff into the terminal value function. Option prices are computed numerically using a Markov chain approximation to the continuous time singular stochastic optimal control problem, for the case of exponential utility. Comparisons with approximately replicating strategies are made. The method results in a uniquely specified option price for every initial holding of stock, and the price lies within bounds which are tight even as transaction costs become large. A general definition of an option hedging strategy for a utility maximising investor is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed

Applying a global optimisation algorithm to Fund of Hedge Funds portfolio optimisation

Portfolio optimisation for a Fund of Hedge Funds (“FoHF”) has to address the asymmetric, non-Gaussian nature of the underlying returns distributions. Furthermore, the objective functions and constraints are not necessarily convex or even smooth. Therefore traditional portfolio optimisation methods such as mean-variance optimisation are not appropriate for such problems and global search optimisation algorithms could serve better to address such problems. Also, in implementing such an approach the goal is to incorporate information as to the future expected outcomes to determine the optimised portfolio rather than optimise a portfolio on historic performance. In this paper, we consider the suitability of global search optimisation algorithms applied to FoHF portfolios, and using one of these algorithms to construct an optimal portfolio of investable hedge fund indices given forecast views of the future and our confidence in such views.portfolio optimisation; optimization; fund of hedge funds; global search optimisation; direct search; pgsl; hedge fund portfolio

A novel risk assessment and optimisation model for a multi-objective network security countermeasure selection problem

Budget cuts and the high demand in strengthening the security of computer systems and services constitute a challenge. Poor system knowledge and inappropriate selection of security measures may lead to unexpected financial and data losses. This paper proposes a novel Risk Assessment and Optimisation Model (RAOM) to solve a security countermeasure selection problem, where variables such as financial cost and risk may affect a final decision. A Multi-Objective Tabu Search (MOTS) algorithm has been developed to construct an efficient frontier of non-dominated solutions, which can satisfy organisational security needs in a cost-effective manner

A Study of Scalarisation Techniques for Multi-Objective QUBO Solving

In recent years, there has been significant research interest in solving Quadratic Unconstrained Binary Optimisation (QUBO) problems. Physics-inspired optimisation algorithms have been proposed for deriving optimal or sub-optimal solutions to QUBOs. These methods are particularly attractive within the context of using specialised hardware, such as quantum computers, application specific CMOS and other high performance computing resources for solving optimisation problems. These solvers are then applied to QUBO formulations of combinatorial optimisation problems. Quantum and quantum-inspired optimisation algorithms have shown promising performance when applied to academic benchmarks as well as real-world problems. However, QUBO solvers are single objective solvers. To make them more efficient at solving problems with multiple objectives, a decision on how to convert such multi-objective problems to single-objective problems need to be made. In this study, we compare methods of deriving scalarisation weights when combining two objectives of the cardinality constrained mean-variance portfolio optimisation problem into one. We show significant performance improvement (measured in terms of hypervolume) when using a method that iteratively fills the largest space in the Pareto front compared to a n\"aive approach using uniformly generated weights

The application of water cycle algorithm to portfolio selection

Portfolio selection is one of the most vital financial problems in literature. The studied problem is a nonlinear multi-objective problem which has been solved by a variety of heuristic and metaheuristic techniques. In this article, a metaheuristic optimiser, the multiobjective water cycle algorithm (MOWCA), is represented to find efficient frontiers associated with the standard mean-variance (MV) portfolio optimisation model. The inspired concept of WCA is based on the simulation of water cycle process in the nature. Computational results are obtained for analyses of daily data for the period January 2012 to December 2014, including S&P100 in the US, Hang Seng in Hong Kong, FTSE100 in the UK, and DAX100 in Germany. The performance of the MOWCA for solving portfolio optimisation problems has been evaluated in comparison with other multi-objective optimisers including the NSGA-II and multiobjective particle swarm optimisation (MOPSO). Four well-known performance metrics are used to compare the reported optimisers. Statistical optimisation results indicate that the applied MOWCA is an efficient and practical optimiser compared with the other methods for handling portfolio optimisation problems

Deep combinatorial optimisation for optimal stopping time problems : application to swing options pricing

A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the derivation of a dynamic programming principle nor a backward stochastic differential equation. Unlike continuous optimization where automatic differentiation is used directly, we propose a likelihood ratio method for gradient computation. Numerical tests are done on the pricing of American and swing options. The proposed algorithm succeeds in pricing high dimensional American and swing options in a reasonable computation time, which is not possible with classical algorithms

Model-independent pricing with insider information: a Skorokhod embedding approach

In this paper, we consider the pricing and hedging of a financial derivative for an insider trader, in a model-independent setting. In particular, we suppose that the insider wants to act in a way which is independent of any modelling assumptions, but that she observes market information in the form of the prices of vanilla call options on the asset. We also assume that both the insider's information, which takes the form of a set of impossible paths, and the payoff of the derivative are time-invariant. This setup allows us to adapt recent work of Beiglboeck, Cox and Huesmann (2016) to prove duality results and a monotonicity principle, which enables us to determine geometric properties of the optimal models. Moreover, we show that this setup is powerful, in that we are able to find analytic and numerical solutions to certain pricing and hedging problems