# Browsing by Subject "Portfolio optimization"

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Item Applications of forward performance processes in dynamic optimal portfolio management(2017-12) Han, Xiao, Ph. D.; Zariphopoulou, Thaleia, 1962-; Carvalho, Carlos; Muthuraman, Kumar; Tompaidis, Stathis; Sirbu, MihaiShow more The classical optimal investment models are cast in a finite or infinite horizon setting, assuming an a priori choice of a market model (or a family of models) as well as a priori choice of a utility function of terminal wealth and/or intermediate consumption. Once these choices are made, namely, the horizon, the model and the risk preferences, stochastic optimization technique yield the maximal expected utility (value function) and the optimal policies wither through the Hamilton-Jacobi-Bellman equation in Makovian models or, more generally, via duality in semi-martingale models. A fundamental property of the solution is time-consistency, which follows from the Dynamic Programming Principle (DPP). This principle provides the intuitively pleasing interpretation of the value function as the intermediate (indirect) utility. It also states that the value function is a martingale along the optimal wealth trajectory and a super-martingale along every admissible one. These properties provide a time-consistent framework of the solutions, which ``pastes" naturally one investment period to the next. Despite its mathematical sophistication, the classical expected utility framework cannot accommodate model revision, nor horizon flexibility nor adaptation of risk preferences, if one desires to retain time-consistency. Indeed, the classical formulation is by nature ``backwards" in time and, thus, it does not allow any ``forward in time" changes. For example, on-line learning, which typically occurs in a non-anticipated way, cannot be implemented in the classical setting, simply because the latter evolves backwards while the former progresses forward in time. To alleviate some of these limitations while, at the same time, preserving the time-consistency property, Musiela and Zariphopoulou proposed an alternative criterion, the so-called forward performance process. This process satisfies the DPP forward in time, and generalizes the classical expected utility. For a large family of cases, forward performance processes have been explicitly constructed for general Ito-diffusion markets. While there has already been substantial mathematical work on this criterion, concrete applications to applied portfolio management are lacking. In this thesis, the aim is to focus on applied aspects of the forward performance approach and build meaningful connections with practical portfolio management. The following topics are being studied. Chapter 2 starts with providing an intuitive characterization of the underlying performance measure and the associated risk tolerance process, which are the most fundamental ingredients of the forward approach. It also provides a novel decomposition of the initial condition and, in turn, its inter-temporal preservation as the market evolves. The main steps involve a system of stochastic differential equations modeling various stochastic sensitivities and risk metrics. Chapter 3 focuses on the applications of the above results to lifecycle portfolio management. Investors are firstly classified by their individual risk preference generating measures and, in turn, mapped to different groups that are consistent with the popular practice of age-based de-leveraging. The inverse problem is also studied, namely, how to infer the individual investor-type measure from observed investment behavior. Chapter 4 provides applications of the forward performance to the classical problem of mean-variance analysis. It examines how sequential investment periods can be ``pasted together" in a time-consistent manner from one evaluation period to the next. This is done by mapping the mean-variance to a family of forward quadratic performances with appropriate stochastic and path-dependent coefficients. Quantitative comparisons with the classical approach are provided for a class of market settings, which demonstrate the superiority and flexibility of the forward approach.Show more Item Essays on data-driven optimization(2019-06-20) Zhao, Long, Ph. D.; Muthuraman, Kumar; Chakrabarti, Deepayan; Tompaidis, Efstathios; Caramanis, ConstantineShow more The estimation of a data matrix contains two parts: the well estimated and the poorly estimated. The latter is usually throwing away because the estimations are off. As argued in this paper, ignoring is the wrong thing to do as the poorly estimated part is orthogonal to the well estimated. I will show how to use such orthogonality information via robust optimization and provide application in portfolio optimization, least-square regression, and dimension reduction. Across a large number of experiments, utilizing the orthogonality information consistently improves the performance.Show more Item Optimal portfolio choice : beyond the traditional expected utility maximization paradigm(2020-05-13) Lalkov, Vasko; Zariphopoulou, Thaleia, 1962-; Hasenbein, John J.Show more This thesis focuses on two major portfolio selection approaches: the traditional mean-variance approach and the heuristic approach based on risk budgeting. The main results from mean-variance are reviewed, as well as some novel results, followed by new contributions in the area of calculating expected functionals of the optimal wealth in a log-normal market. The available theory behind the risk budgeting approach is revisited, with the main arguments for and against the approach explained. The equally weighted portfolio, referred to as the risk parity portfolio, is compared against other heuristically derived portfolios and the more traditional mean-variance portfolio.Show more Item Optimization of production allocation under price uncertainty : relating price model assumptions to decisions(2011-08) Bukhari, Abdulwahab Abdullatif; Jablonowski, Christopher J.; Lasdon, Leon S.; Dyer, James S.Show more Allocating production volumes across a portfolio of producing assets is a complex optimization problem. Each producing asset possesses different technical attributes (e.g. crude type), facility constraints, and costs. In addition, there are corporate objectives and constraints (e.g. contract delivery requirements). While complex, such a problem can be specified and solved using conventional deterministic optimization methods. However, there is often uncertainty in many of the inputs, and in these cases the appropriate approach is neither obvious nor straightforward. One of the major uncertainties in the oil and gas industry is the commodity price assumption(s). This paper investigates this problem in three major sections: (1) We specify an integrated stochastic optimization model that solves for the optimal production allocation for a portfolio of producing assets when there is uncertainty in commodity prices, (2) We then compare the solutions that result when different price models are used, and (3) We perform a value of information analysis to estimate the value of more accurate price models. The results show that the optimum production allocation is a function of the price model assumptions. However, the differences between models are minor, and thus the value of choosing the “correct” price model, or similarly of estimating a more accurate model, is small. This work falls in the emerging research area of decision-oriented assessments of information value.Show more Item Portfolio optimization using stochastic programming with market trend forecast(2014-08) Yang, Yutian, active 21st century; Bard, Jonathan F.; Lasdon, Leon S., 1939-Show more This report discusses a multi-stage stochastic programming model that maximizes expected ending time profit assuming investors can forecast a bull or bear market trend. If an investor can always predict the market trend correctly and pick the optimal stochastic strategy that matches the real market trend, intuitively his return will beat the market performance. For investors with different levels of prediction accuracy, our analytical results support their decision of selecting the highest return strategy. Real stock prices of 154 stocks on 73 trading days are collected. The computational results verify that accurate prediction helps to exceed market return while portfolio profit drops if investors partially predict or forecast incorrectly part of the time. A sensitivity analysis shows how risk control requirements affect the investor's decision on selecting stochastic strategies under the same prediction accuracy.Show more