Matti Koivu

Epi-convergent discretizations of stochastic programs via integration quadratures

Summary.The simplest and the best-known method for numerical approximation of high-dimensional integrals is the Monte Carlo method (MC), i.e. random sampling. MC has also become the most popular method for constructing numerically solvable approximations of stochastic programs. However, certain modern integration quadratures are often superior to crude MC in high-dimensional integration, so it seems natural to try to use them also in discretization of stochastic programs. This paper derives conditions that guarantee the epi-convergence of the resulting objectives to the original one. Our epi-convergence result is closely related to some of the existing ones but it is easier to apply to discretizations and it allows the feasible set to depend on the probability measure. As examples, we prove epi-convergence of quadrature-based discretizations of three different models of portfolio management and we study their behavior numerically. Besides MC, our discretizations are the only existing ones with guaranteed epi-convergence for these problem classes. In our tests, modern quadratures seem to result in faster convergence of optimal values than MC.

Technical and cost efficiency of oral health care provision in Finnish health centres

In this study we measured the productive efficiency of public dental health provision across Finland. The analysis was based on data envelopment analysis (DEA) using linear programming. In addition, we investigated various factors explaining the technical and cost efficiency of public dental care using a parametric Tobit model. These analyses revealed substantial variation in productive efficiency between health centres in different municipalities. The level of cost inefficiency was generally between 20% and 30%. Good dental health of the population, high rates of unemployment and high per capita expenditure on primary care in the municipality were associated with technical and cost inefficiency. According to the results, cost efficiency would not be improved by shifting input allocation towards more auxiliary manpower in health centres. Individual efficiency scores were clearly sensitive to the choice of output specification. Changing the unit of output measurement from visit- to patient-based measures affected markedly the ranking of dental health centres. However, the set of exogenous correlates associated to inefficiency was strikingly similar for both types of output specification. More resources are needed if the coverage of public dental care is extended to all age groups. The health centre specific efficiency scores obtained in this study can be used locally to evaluate, design and implement structural changes in the production processes.

A stochastic programming model for asset liability management of a Finnish pension company

This paper describes a stochastic programming model that was developed for asset liability management of a Finnish pension insurance company. In many respects the model resembles those presented in the literature, but it has some unique features stemming from the statutory restrictions for Finnish pension insurance companies. Particular attention is paid to modeling the stochastic factors, numerical solution of the resulting optimization problem and evaluation of the solution. Out-of-sample tests clearly favor the strategies suggested by our model over static fixed-mix and dynamic portfolio insurance strategies.

Variance reduction in sample approximations of stochastic programs

Abstract.This paper studies the use of randomized Quasi-Monte Carlo methods (RQMC) in sample approximations of stochastic programs. In numerical integration, RQMC methods often substantially reduce the variance of sample approximations compared to Monte Carlo (MC). It seems thus natural to use RQMC methods in sample approximations of stochastic programs. It is shown, that RQMC methods produce epi-convergent approximations of the original problem. RQMC and MC methods are compared numerically in five different portfolio management models. In the tests, RQMC methods outperform MC sampling substantially reducing the sample variance and bias of optimal values in all the considered problems.

CALIBRATED OPTION BOUNDS

This paper proposes a numerical approach for computing bounds for the arbitrage-free prices of an option when some options are available for trading. Convex duality reveals a close relationship with recently proposed calibration techniques and implied trees. Our approach is intimately related to the uncertain volatility model of Avellaneda, Levy and Paras, but it is more general in that it is not based on any particular form of the asset price process and does not require the sellers price of an option to be a differentiable function of the cash-flows of the option. Numerical tests on S&P500 options demonstrate the accuracy and robustness of the proposed method.

Dealing with Interval Scale Data in Data Envelopment Analysis

This papaer considers the problem of interval scale data in the most widely used models of Data Envelopment Analysis (DEA), the CCR, and the BCC models. Radial models require inputs and outputs measured on the ratio scale. Our focus is on how to deal with interval scale variables especially when the interval scale variable is a difference of two ratio scale variables like profit or the decrease/increase in bank accounts. Using these ratio scale variables as variables in the DEA model we suggest radial models. An approach to how to deal with interval scale variables when we relax the radiality assumption is also discussed.

Modeling assets and liabilities of a Finnish pension insurance company: a VEqC approach

This paper develops a stochastic model for assets and liabilities of a Finnish pension insurance company. The assets and liabilities are expressed in terms of seven economic factors from Finland and the EU-area. The development of these factors is modeled with a Vector Equilibrium Correction model, that incorporates statistical information with expert views in the form of user specified growth rates and long term equilibria. The forecast performance of the resulting model is tested and the model is used in long-term solvency and asset liability simulations.

Galerkin methods in dynamic stochastic programming

The Galerkin method is a classical technique for approximating infinite-dimensional optimization problems with finite-dimensional ones. When applied to convex multistage stochastic programmes, it yields computationally attractive alternatives to scenario tree-based discretizations. We describe its implementations for dynamic portfolio optimization problems and report some encouraging numerical results.

An Adaptive Importance Sampling Technique

This paper proposes a new adaptive importance sampling (AIS) technique for approximate evaluation of multidimensional integrals. Whereas known AIS algorithms try to find a sampling density that is approximately proportional to the integrand, our algorithm aims directly at the minimization of the variance of the sample average estimate. Our algorithm uses piecewise constant sampling densities, which makes it also reminiscent of stratified sampling. The algorithm was implemented in C-programming language and compared with VEGAS and MISER.

Risk Management for Central Banks and Other Public Investors: Strategic asset allocation for fixed-income investors

Introduction The goal of strategic asset allocation (SAA) is to find an optimal allocation of funds across different asset classes subject to a relatively long investment horizon. The optimal allocation of funds should always reflect the risk–return preferences of an institution and the machinery underlying the strategic asset allocation decisions should be based on a transparent and accountable process with which such allocations can be determined and reviewed at regular intervals. Often ‘modern portfolio theory’ is presented following Markowitz (1959) and Sharpe (1964) in the context of the Capital Asset Pricing Model (CAPM) and mean-variance portfolio analysis as the basic theory for how equity markets behave in equilibrium and how investors should position themselves on the efficient frontier, depending on their risk aversion. This theory is central to the understanding of modern finance and thus important for students and market practitioners alike. However, when it comes to actual portfolio allocation decisions and the practical implementation of portfolio allocation decisions in public and private investment organizations the CAPM leaves, quite understandably, many questions unanswered. It is some of these missing answers that the present chapter aims at addressing. In doing so, the viewpoint of a strategic investor is taken; however, elements relevant for tactical asset allocation and portfolio managers are also touched upon. In particular, the focal point of the exposition is that of a central banks reserves management. This perspective naturally narrows the investment universe considerably.