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Über dieses Buch

The scope of this volume is primarily to analyze from different methodological perspectives similar valuation and optimization problems arising in financial applications, aimed at facilitating a theoretical and computational integration between methods largely regarded as alternatives. Increasingly in recent years, financial management problems such as strategic asset allocation, asset-liability management, as well as asset pricing problems, have been presented in the literature adopting formulation and solution approaches rooted in stochastic programming, robust optimization, stochastic dynamic programming (including approximate SDP) methods, as well as policy rule optimization, heuristic approaches and others. The aim of the volume is to facilitate the comprehension of the modeling and methodological potentials of those methods, thus their common assumptions and peculiarities, relying on similar financial problems. The volume will address different valuation problems common in finance related to: asset pricing, optimal portfolio management, risk measurement, risk control and asset-liability management.

The volume features chapters of theoretical and practical relevance clarifying recent advances in the associated applied field from different standpoints, relying on similar valuation problems and, as mentioned, facilitating a mutual and beneficial methodological and theoretical knowledge transfer. The distinctive aspects of the volume can be summarized as follows:

Strong benchmarking philosophy, with contributors explicitly asked to underline current limits and desirable developments in their areas.

Theoretical contributions, aimed at advancing the state-of-the-art in the given domain with a clear potential for applications

The inclusion of an algorithmic-computational discussion of issues arising on similar valuation problems across different methods.

Variety of applications: rarely is it possible within a single volume to consider and analyze different, and possibly competing, alternative optimization techniques applied to well-identified financial valuation problems.

Clear definition of the current state-of-the-art in each methodological and applied area to facilitate future research directions.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Multi-Period Risk Measures and Optimal Investment Policies

This chapter provides an in-depth overview of an extended set of multi-period risk measures, their mathematical and economic properties, primarily from the perspective of dynamic risk control and portfolio optimization. The analysis is structured in four parts: the first part reviews characterizing properties of multi-period risk measures, it examines their financial foundations, and clarifies cross-relationships. The second part is devoted to three classes of multi-period risk measures, namely: terminal, additive and recursive. Their financial and mathematical properties are considered, leading to the proposal of a unifying representation. Key to the discussion is the treatment of dynamic risk measures taking their relationship with evolving information flows and time evolution into account: after convexity and coherence, time consistency emerges as a key property required by risk measures to effectively control risk exposure within dynamic programs. In the third part, we consider the application of multi-period measures to optimal investment policy selection, clarifying how portfolio selection models adapt to different risk measurement paradigms. In the fourth part we summarize and point out desirable developments and future research directions. Throughout the chapter, attention is paid to the state-of-the-art and methodological and modeling implications.
Zhiping Chen, Giorgio Consigli, Jia Liu, Gang Li, Tianwen Fu, Qianhui Hu

Chapter 2. Asset Price Dynamics: Shocks and Regimes

Security prices changes are known to have a non-normal distribution, with heavy tails. There are modifications to the standard geometric Brownian motion model which accomodate heavy tails, most notably (1) adding point processes to the Brownian motion or (2) classifying time into regimes. With regimes the prices follow Brownian motion dynamics within regime, but the parameters vary by regime. The unconditional distribution of returns is a mixture of normals, with the mixing coefficients being Markov transition probabilities. The contrasting approaches have a common link—risk factors. In the case of the point processes, the intensity of “shocks” depends on a set of factors, eg. bond-stock yield differential, credit spread, implied volatility, exchange rates. The factors drive shocks, which are a component of the returns. With regimes, the economic state is hidden (latent) and is determined by the period by period observations on factors. The characterization of regimes follows from description in terms of the set of risk factors. In this paper the link between the shocks and regimes is explored. The shocks times defined by risk factors are an alternative method of determining regimes and the classifications by shocks and by the Expectation-Maximization algorithm are examined. The connections factors → regimes → shocks further justifies a classifiaction of financial markets into homogeneous epochs. The regime structure leads to improved estimates for distribution parameters. The methods are applied to the prediction of returns on Sector Exchange Traded Funds (ETFs).The allocation of investment capital to funds based on predicted returns generates favorable wealth accumulation over a planning horizon.
Leonard MacLean, Yonggan Zhao

Chapter 3. Scenario Optimization Methods in Portfolio Analysis and Design

This chapter discusses techniques for analysis and optimization of portfolio statistics, based on direct use of samples of random data. For a given and fixed portfolio of financial assets, a classical approach for evaluating, say, the value-at-risk (V@R) of the portfolio is a model-based one, whereby one first assumes some stochastic model for the component returns (e.g., Normal), then estimates the parameters of this model from data, and finally computes the portfolio V@R. Such a process hinges upon critical assumptions (e.g., the elicited return distribution), and leaves unclear the effects of model estimation errors on the computed quantity of interest. Here, we propose an alternative direct route that bypasses the assumption and estimation of a model for the returns, and provides the estimated quantity of interest (together with its out-of-sample reliability tag) directly from data generated by a scenario generation oracle. This idea is then extended to the situation where one simultaneously optimizes over the portfolio composition, in order to achieve an optimal portfolio with a guaranteed level of expected shortfall probability. Such a scenario-based portfolio design approach is here developed for both single-period and multi-period allocation problems. The methodology underpinning the proposed computational method is that of random convex programming (RCP). Besides the described data-driven problems, we show in this chapter that the RCP paradigm can also be employed alongside more standard mean-variance portfolio optimization settings, in the presence of ambiguity in the statistical model of the returns, providing a viable technique to address robust portfolio optimization problems.
Giuseppe Carlo Calafiore

Chapter 4. Robust Approaches to Pension Fund Asset Liability Management Under Uncertainty

This entry considers the problem of a typical pension fund that collects premiums from sponsors or employees and is liable for fixed payments to its customers after retirement. The fund manager’s goal is to determine an investment strategy so that the fund can cover its liabilities while minimizing contributions from its sponsors and maximizing the value of its assets. We develop robust optimization and scenario-based stochastic programming approaches for optimal asset-liability management, taking into consideration the uncertainty in asset returns and future liabilities. Our focus is on computational tractability and ease of implementation under conditions typically encountered in practice, such as asymmetries in the distributions of asset returns. Computational results from tests with real and generated data are presented to illustrate the performance of these models.
Dessislava Pachamanova, Nalan Gülpınar, Ethem Çanakoğlu

Chapter 5. Liability-Driven Investment in Longevity Risk Management

This paper studies optimal investment from the point of view of an investor with longevity-linked liabilities. The relevant optimization problems rarely are analytically tractable, but we are able to show numerically that liability driven investment can significantly outperform common strategies that do not take the liabilities into account. In problems without liabilities the advantage disappears, which suggests that the superiority of the proposed strategies is indeed based on connections between liabilities and asset returns.
Helena Aro, Teemu Pennanen

Chapter 6. Pricing Multiple Exercise American Options by Linear Programming

We consider the problem of computing the lower hedging price of American options of the call and put type written on a non-dividend paying stock in a non-recombinant tree model with multiple exercise rights. We prove using a simple argument that an optimal exercise policy for an option with h exercise rights is to delay exercise until the last h periods. The result implies that the mixed-integer programming model for computing the lower hedging price and the optimal exercise and hedging policy has a linear programming relaxation that is exact, i.e., the relaxation admits an optimal solution where all variables required to be integral have integer values.
Monia Giandomenico, Mustafa Ç. Pınar

Chapter 7. Optimizing a Portfolio of Liquid and Illiquid Assets

Current market conditions pose new challenges for institutional investors. Traditional asset and liability models are struggling to meet investors’ needs due to poor performance of equity and bond markets. The move of portfolio allocation to alternative assets is evident. As a result, illiquidity issues and rebalancing difficulty arise. We propose some new tactics of commodity futures to enhance the performance of portfolio return as well as solving illiquidity issues. Hidden Markov Model and multistage stochastic optimization are used to systematically optimize portfolio over a set of assets.
John M. Mulvey, Woo Chang Kim, Changle Lin

Chapter 8. Stabilizing Implementable Decisions in Dynamic Stochastic Programming

We present a novel approach to address sampling error when discretely approximating a dynamic stochastic programme with a limited finite number of scenarios to represent the underlying path probability distribution. This represents a tentative solution to the problems first identified in our companion paper (Dempster et al., A comparative study of sampling methods for stochastic programming, forthcoming). Conventional approaches to such problems have been to find the best discretization of the statistical properties of the simulated processes in terms of the objective of the problem based on probability metrics. Here we consider the stability of the implementable decisions of a stochastic programme, which is key to financial investment and asset liability management (ALM) problems, while simultaneously reducing the discretization bias resulting from small-sample scenario discretization. We tackle discretization error by reducing the degrees of freedom of the decision space in a financially meaningful way by constraining the decisions to lie within a carefully chosen subspace. This avoids overfitting the optimized decisions to the simulated in-sample scenarios which often do not generalize to unseen scenarios drawn from the same probability distribution of paths. We illustrate the application of versions of the proposed technique using a practical four-stage ALM problem previously studied in Dempster et al. (J Portf Manag 32(2):51–61, 2006. Empirical results show their effectiveness in reducing the discretization bias and improving the stability of the implementable decisions without adding much to the computational complexity of the original problem.
Michael A. H. Dempster, Elena A. Medova, Yee Sook Yong

Chapter 9. The Growth Optimal Investment Strategy Is Secure, Too

This paper is a revisit of discrete time, multi period and sequential investment strategies for financial markets showing that the log-optimal strategies are secure, too. Using exponential inequality of large deviation type, the rate of convergence of the average growth rate is bounded both for memoryless and for Markov market processes. A kind of security indicator of an investment strategy can be the market time achieving a target wealth. It is shown that the log-optimal principle is optimal in this respect.
László Györfi, György Ottucsák, Harro Walk

Chapter 10. Heuristics for Portfolio Selection

Portfolio selection is about combining assets such that investors’ financial goals and needs are best satisfied. When operators and academics translate this actual problem into optimisation models, they face two restrictions: the models need to be empirically meaningful, and the models need to be soluble. This chapter will focus on the second restriction. Many optimisation models are difficult to solve because they have multiple local optima or are ‘badly-behaved’ in other ways. But on modern computers such models can still be handled, through so-called heuristics. To motivate the use of heuristic techniques in finance, we present examples from portfolio selection in which standard optimisation methods fail. We then outline the principles by which heuristics work. To make that discussion more concrete, we describe a simple but effective optimisation technique called Threshold Accepting and how it can be used for constructing portfolios. We also summarise the results of an empirical study on hedge-fund replication.
Manfred Gilli, Enrico Schumann

Chapter 11. Optimal Financial Decision Making Under Uncertainty

We use a fairly general framework to analyze a rich variety of financial optimization models presented in the literature, with emphasis on contributions included in this volume and a related special issue of OR Spectrum. We do not aim at providing readers with an exhaustive survey, rather we focus on a limited but significant set of modeling and methodological issues. The framework is based on a benchmark discrete-time stochastic control optimization framework, and a benchmark financial problem, asset-liability management, whose generality is considered in this chapter. A wide set of financial problems, ranging from asset allocation to financial engineering problems, is outlined, in terms of objectives, risk models, solution methods, and model users. We pay special attention to the interplay between alternative uncertainty representations and solution methods, which have an impact on the kind of solution which is obtained. Finally, we outline relevant directions for further research and optimization paradigms integration.
Giorgio Consigli, Daniel Kuhn, Paolo Brandimarte

Backmatter

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