Heuristic Optimisation in Financial Modelling

There is a large number of optimisation problems in theoretical and applied finance that are difficult to solve as they exhibit multiple local optima or are not ‘well- behaved’ in other ways (eg, discontinuities in the objective function). One way to deal with such problems is to adjust and to simplify them, for instance by dropping constraints, until they can be solved with standard numerical methods. This paper argues that an alternative approach is the application of optimisation heuristics like Simulated Annealing or Genetic Algorithms. These methods have been shown to be capable to handle non-convex optimisation problems with all kinds of constraints. To motivate the use of such techniques in finance, the paper presents several actual problems where classical methods fail. Next, several well-known heuristic techniques that may be deployed in such cases are described. Since such presentations are quite general, the paper describes in some detail how a particular problem, portfolio selection, can be tackled by a particular heuristic method, Threshold Accepting. Finally, the stochastics of the solutions obtained from heuristics are discussed. It is shown, again for the example from portfolio selection, how this random character of the solutions can be exploited to inform the distribution of computations.Optimisation heuristics, Financial Optimisation, Portfolio Optimisation

The role of learning on industrial simulation design and analysis

The capability of modeling real-world system operations has turned simulation into an indispensable problemsolving methodology for business system design and analysis. Today, simulation supports decisions ranging from sourcing to operations to finance, starting at the strategic level and proceeding towards tactical and operational levels of decision-making. In such a dynamic setting, the practice of simulation goes beyond being a static problem-solving exercise and requires integration with learning. This article discusses the role of learning in simulation design and analysis motivated by the needs of industrial problems and describes how selected tools of statistical learning can be utilized for this purpose

Asset Pricing Theories, Models, and Tests

An important but still partially unanswered question in the investment field is why different assets earn substantially different returns on average. Financial economists have typically addressed this question in the context of theoretically or empirically motivated asset pricing models. Since many of the proposed “risk” theories are plausible, a common practice in the literature is to take the models to the data and perform “horse races” among competing asset pricing specifications. A “good” asset pricing model should produce small pricing (expected return) errors on a set of test assets and should deliver reasonable estimates of the underlying market and economic risk premia. This chapter provides an up-to-date review of the statistical methods that are typically used to estimate, evaluate, and compare competing asset pricing models. The analysis also highlights several pitfalls in the current econometric practice and offers suggestions for improving empirical tests

Whole Farm Income Insurance in a Canadian Context

This paper employs mean-variance and mean-skewness optimization to investigate farmers’ crop choices under Gross Revenue Insurance (GRIP), Whole Farm Income Insurance, the Canadian Agricultural Income Stabilization program, and its modified 2008 program AgrInvest. To our knowledge this paper is the first to fully consider the endogenous optimization of whole farm insurance in a farm optimization model. The results indicate that farmers will alter farm plans significantly in response to the type of insurance offered and the level of subsidy. Farmers will take on production risks that they would not otherwise take and this risk taking behavior is exacerbated by subsidy.Agricultural Insurance, Skewness Maximization, Mean-Variance, Farm Income Insurance, GRIP, CAIS, AgrInvest, Agricultural Finance,

Randomized Solutions to Convex Programs with Multiple Chance Constraints

The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled outcomes of the uncertainty (`scenarios'). A key merit of this approach is that it neither assumes knowledge of the uncertainty set, as it is common in robust optimization, nor of its probability distribution, as it is usually required in stochastic optimization. Moreover, the scenario approach is computationally efficient as its solution is based on a deterministic optimization program that is canonically convex, even when the original chance-constrained problem is not. Recently, researchers have obtained theoretical foundations for the scenario approach, providing a direct link between the number of scenarios and bounds on the constraint violation probability. These bounds are tight in the general case of an uncertain optimization problem with a single chance constraint. However, this paper shows that these bounds can be improved in situations where the constraints have a limited `support rank', a new concept that is introduced for the first time. This property is typically found in a large number of practical applications---most importantly, if the problem originally contains multiple chance constraints (e.g. multi-stage uncertain decision problems), or if a chance constraint belongs to a special class of constraints (e.g. linear or quadratic constraints). In these cases the quality of the scenario solution is improved while the same bound on the constraint violation probability is maintained, and also the computational complexity is reduced.Comment: This manuscript is the preprint of a paper submitted to the SIAM Journal on Optimization and it is subject to SIAM copyright. SIAM maintains the sole rights of distribution or publication of the work in all forms and media. If accepted, the copy of record will be available at http://www.siam.or

Time Varying Sensitivities on a GRID architecture

We estimate time varying risk sensitivities on a wide range of stocks' portfolios of the US market. We empirically test, on a 1926-2004 Monthly CRSP database, a classic one factor model augmented with a time varying specification of betas. Using a Kalman filter based on a genetic algorithm, we show that the model is able to explain a large part of the variability of stock returns. Furthermore we run a Risk Management application on a GRID computing architecture. By estimating a parametric Value at Risk, we show how GRID computing offers an opportunity to enhance the solution of computational demanding problems with decentralized data retrieval.