Innovations in Quantitative Risk Management

Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science

Data-Driven Models: An Alternative Discrete Hedging Strategy

Options hedging is a critical problem in financial risk management. The prevailing approach in financial derivative pricing and hedging has been to first assume a parametric model describing the underlying price dynamics. An option model function is then calibrated to current market option prices and various sensitivities are computed and used to hedge the option risk. It has been recognized that computing hedging position from the sensitivity of the calibrated model option value function is inadequate in minimizing the variance of the option hedging risk, as it fails to capture the model parameter dependence on the underlying price. We propose several data-driven approaches to directly learn a hedging function from the historical market option and underlying data by minimizing certain measures of the local hedging risk and total hedging risk. This thesis will focus on answering the following questions: 1) Can we efficiently build direct data-driven models for discrete hedging problems that outperform existing state-of-art parametric hedging models based on the market prices? 2) Can we incorporate feature selection and feature extraction into the data-driven models to further improve the performance of the discrete hedging? 3) Can we build efficient models for both the one-step local risk hedging problem and multi-step total risk hedging problem based on the state-of-art learning framework such as deep learning framework and kernel learning framework? Using the S&P 500 index daily options data for more than a decade ending in August 2015, we first propose a direct data-driven approach based on kernel learning framework and we demonstrate that the proposed method outperforms the parametric minimum variance hedging method, as well as minimum variance hedging corrective techniques based on stochastic volatility or local volatility models. Furthermore, we show that the proposed approach achieves significant gain over the implied Black-Sholes delta hedging for weekly and monthly hedging. Following the direct data-driven kernel learning approach, we propose a robust encoder-decoder Gated Recurrent Unit (GRU) model, for optimal discrete option hedging. The proposed model utilizes the Black-Scholes model as a pre-trained model and incorporates sequential information and feature selection. Using the S&P 500 index European option market data from January 2, 2004, to August 31, 2015, we demonstrate that the weekly and monthly hedging performance of the proposed model significantly surpasses that of the data-driven minimum variance (MV) method, the regularized kernel data-driven model, and the SABR-Bartlett method. In addition, the daily hedging performance of the proposed model also surpasses that of MV methods based on parametric models, the kernel method, and the SABR-Bartlett method. Lastly, we design multi-step data-driven models to hedge the option discretely until the expiry. We utilize the SABR model and Local Volatility Function (LVF) to augment existing market data and thus alleviate the problem of scarcity in market option prices. The augmented market data is used to train a sufficient total risk hedging model

Innovations in Quantitative Risk Management

Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science

Efficient pricing and estimation methods in finance

[Abstract not given by author

Hedging Contingent Claims in Markets with Jumps

Contrary to the Black-Scholes paradigm, an option-pricing model which incorporates the possibility of jumps more accurately reflects the evolution of stocks in the real world. However, hedging a contingent claim in such a model is a non-trivial issue: in many cases, an infinite number of hedging instruments are required to eliminate the risk of an option position. This thesis develops practical techniques for hedging contingent claims in markets with jumps. Both regime-switching and jump-diffusion models are considered

포트폴리오 관리를 위한 기계학습 기반 자산 배분 전략 및 디지털 자산 투자

학위논문(박사) -- 서울대학교대학원 : 공과대학 산업공학과, 2022. 8. 이재욱.자산 분산화와 위험 관리는 포트폴리오 관리의 핵심 요소이다. 자산 분산화란 자산간 상관관계를 추정하여 자산 배분을 기반으로 다중 자산 포트폴리오에 대한 분산 효과를 극대화하는 것을 의미한다. 위험 관리란 자산의 잠재적 위험과 변동성을 추정하여 자산 배분을 기반으로 주어진 포트폴리오에 대한 하방 위험을 최소화하는 것을 의미한다. 또한 포트폴리오 관리의 두 가지 중요한 절차는 다음과 같다. 첫째, 적절한 자산 배분 전략 시행을 위한 모형 개선 및 시행이다. 모형이 가진 내재적 한계로 인해 자산 배분 전략을 적절하게 수행하지 못하는 경우, 해당 포트폴리오 모형이 추구하는 목표를 달성하지 못하게 되어 바람직하지 않은 포트폴리오가 구축되는 문제가 발생할 수 있다. 이러한 목표는 여러 개의 자산을 포함하는 포트폴리오에 대한 분산 효과와 한가지 자산에 대한 포트폴리오 가치 방어를 통한 위험 관리를 포함한다. 둘째, 투자를 위한 자산군 선택이다. 기존의 자산군과 상관관계가 작은 새로운 자산군에 대한 선택이 효율적인 포트폴리오 구축에 있어 잠재적으로 큰 도움을 줄 수 있다. 본 논문은 포트폴리오 관리에 대한 이러한 두 가지 핵심과 절차에 초점을 맞추어 연구를 수행하였다. 자산 분산화와 위험 관리 각각의 관점에 대하여, 첫째, 기존 포트폴리오 모형의 구축 및 모수 추정에 대한 한계점을 개선하는 연구를 수행하였다. 둘째, 새로운 디지털 자산 시장에 대한 포트폴리오 분석을 수행하였다. 이에 따라, 본 논문의 구체적인 목표는 다음과 같이 두 가지로 정리될 수 있다. 첫째, 모형 구축 및 모수 추정에 대한 한계점을 갖는 기존 포트폴리오 관리 전략의 개선에 관한 연구를 수행하는 것이다. 구체적으로, 블랙-리터만 모형의 전망 구축과 합성 풋 옵션 전략의 모수 추정에 대한 문제를 다루었다. 둘째, 대체불가능 토큰과 암호화폐 시장을 포함하는 디지털 자산 시장에 관한 포트폴리오 분석 및 실증 결과를 살펴보는 것이다. 이때, 대체불가능 토큰에 대해서는 마코위츠의 평균-분산 모형을, 암호화폐에 대해서는 포트폴리오 보험 모형을 사용한다. 첫 번째 연구를 위해, 자산 수익률 이외의 외부적인 금융 데이터로부터 의미 있는 패턴을 추출할 수 있는 기계학습 모형을 사용하여 블랙-리터만 모형의 전망 구축을 수행하는 모형을 제안하였고, 이에 대한 실증 결과를 살펴 보았다. 또한, 합성 풋 옵션 전략에서 요구하는 변동성 모수 추정의 문제를 해결하기 위해 기계학습 기반 변동성 예측 모형을 사용하여 개선된 합성 풋 옵션 전략을 제안하고, 이에 대한 실증 연구를 수행하였다. 두 번째 연구를 위해서는, 기존 자산 기반 포트폴리오에 대해 대체불가능 토큰이 새로운 자산군으로써 분산 효과를 제공할 수 있는지를 살펴봄으로써 그 경제학적 가치를 검증해 보았고, 다양한 위험 측정 지표와 투자자 효용 측면에서 포트폴리오 보험 전략에 대한 암호화폐 시장에서의 실증 결과를 살펴보았다. 본 논문의 주요 실증 결과는 다음과 같다. 첫째, 기업 특성 변수를 결합하여 전망에 반영하였을 때, 블랙-리터만 모형에서 산출된 포트폴리오의 수익률 분포가 개선됨을 확인하였다. 또한, 기업 특성 변수를 반영할 때, 과거의 정보를 단순히 반영하는 것보다 기계학습 기법을 활용하여 미래에 대한 예측 방식으로 반영할 때 표본 외 성능 측면에서 훨씬 큰 개선이 나타났다. 해당 연구 결과는, 본 논문에서 제안된 기업 특성 변수 기반 전망 구축 방법론을 바탕으로 한 블랙-리터만 모형을 통해 더 잘 분산되고 더욱 효율적인 포트폴리오를 구축하는 것이 가능하다는 것을 보여준다는 점에서 의의가 있다. 둘째, 계량 경제 모형 및 포트폴리오 실증 분석 결과, 대체불가능 토큰은 기존 자산에 시장에 대해 헤지, 안전 피난처, 분산 효과를 갖는다는 증거를 발견하였다. 구체적으로, 대체불가능 토큰은 여러 국가의 주식 시장, 원유 시장, 채권 시장, 달러 지수에 대해 헤지 및 안전 피난처 효과를 보이며, 이러한 경향성은 자산 수익률 데이터의 해상도가 변함에 따라 그 정도가 달라진다. 특히 COVID-19 위기 동안, 채권 시장 및 달러 지수에 대해 더욱 강한 강도의 안전 피난처 효과를 보였다. 또한, 대체불가능 토큰 시장은 기존 자산 시장과 매우 구별되는 자산 시장으로써, 상관관계, 공행성, 변동성 스필오버 효과 및 마코위츠의 평균-분산 포트폴리오 모형을 통한 분석 결과, 대체불가능 토큰이 기존 자산군에 대한 강한 분산 효과를 가짐을 확인하였다. 이를 통해, 대체불가능 토큰의 편입이 균등 배분 포트폴리오 모형과 접점 포트폴리오 모형을 샤프 비율 측면에서 크게 개선 시킬 수 있음을 확인하였다. 셋째, 포트폴리오 가치 방어 오차 측면에서 합성 풋 옵션 전략에 변동성 모수 추정 오차에 의한 악영향이 존재함을 시뮬레이션 및 실제 금융 시장 데이터를 통해 확인하였다. 흥미롭게도, 포트폴리오 가치 방어 오차는 이러한 변동성 예측의 정확도와 직접적으로 연관되어 있다는 것을 통계적으로 확인하였다. 이는, 더욱 정확한 변동성 예측 모형을 통해 합성 풋 옵션의 모수 추정 오차 문제를 완화할 수 있다는 사실을 실증적으로 확인했다는 점에서 의의가 있다. 또 다른 결과로써, 전통적인 변동성 예측 방법론 및 기계학습 기반 변동성 예측 방법론 모두 단순 모형보다 성능이 좋다는 것을 확인하였다. 또한, 기계학습 모형이 가장 우수한 성능을 보였으며, 그중 익스트림 그라디언트 부스팅 (XGB) 모형이 포트폴리오 가치 방어 오차 및 변동성 예측 오차 측면에서 가장 좋은 성능을 보임을 확인하였다. 이러한 경향성은 기계학습 모형이 기존의 모형 보다 실현 변동성 (realized volatility)의 복잡한 파동 패턴을, 매우 변동성이 큰 시장 상황에서도 더욱 잘 잡아낸다는 사실을 지지하는 결과라 할 수 있다. 마지막으로, 하방 위험 측면에서, 포트폴리오 보험 전략들이 암호화폐 시장에서 벤치마크 방법론보다 더 좋은 성능을 보임을 실증적으로 확인하였다. 이러한 포트폴리오 보험 전략들은 매수 후 보유 전략보다 더 작은 위험을 보이는 것을 알 수 있었다. 또한, 흥미롭게도, 효용함수의 곡률 측면에서, 전망 이론 투자자의 포트폴리오 선택과 기대 효용 이론 투자자의 포트폴리오 선택의 경향성이 서로 반대로 나타남을 발견 하였다. 이러한 결과는, 전망 이론 투자자에 대하여 이익 대비 손실의 영향력이 더 클 수 있음을 나타낸다. 이와 더불어, 투자자의 손실 회피 경향이 포트폴리오 보험 전략에 대한 투자자의 선호를 더욱 강화시킬 수 있음을 확인하였다. 가장 놀라운 결과로써, 투자자가 어떤 효용 함수를 따르는지에 관계없이, 암호화폐 시장에서 포트폴리오 보험 전략이 매수 후 보유 전략 보다 높은 효용을 주는 영역이 기존 자산 시장에서보다 더 넓음을 확인하였다. 이는 포트폴리오 보험 전략이 더 많은 수의 암호화폐 투자자에 대해 위험 관리 측면에서 더 큰 경제학적 가치를 제공해 줄 수 있음을 실증하는 결과라는 점에서 의의가 있다. 본 논문은 블랙-리터만 모형의 다중 자산 포트폴리오와 합성 풋 옵션 전략의 개별 자산 포트폴리오에 대한 포트폴리오 관리 모형을 자산 분산화와 위험 관리 측면에서 개선하는 연구를 수행하였다. 또한, 마코위츠의 평균-분산 모형과 포트폴리오 보험 모형을 사용하여 대체불가능 토큰과 암호화폐 시장을 포함한 새로운 디지털 자산 시장에서의 포트폴리오 분석을 수행하였다. 본 논문의 결과를 바탕으로, 투자자들은 자산 분산화와 위험 관리 관점에서 더욱 개선된 포트폴리오 전략을 달성할 수 있으며, 이를 통해 개선된 포트폴리오 관리를 위한 더욱더 효율적이고 바람직한 투자 포트폴리오를 구축할 수 있게 될 것으로 기대된다.The core of portfolio management is asset diversification and risk management. Asset diversification is to maximize the diversification effect for a multi-asset portfolio based on asset allocation by estimating the correlation between assets. Risk management is to minimize the downside risk for a given portfolio based on asset allocation by estimating the potential risk and volatility of an asset. The essential portfolio management procedure is twofold; (i) model improvement and implementation for appropriate model specifications and portfolio construction and (ii) asset class selection for investment. The first part is necessary to implement the strategy adequately to achieve the aim of that model, such as robust multi-asset portfolio management via asset diversification and single asset risk management via robust protection level maintenance. The second part is vital because a new asset class uncorrelated to the traditional asset class has potential opportunities for efficient portfolio construction. Accordingly, this dissertation focuses on research from two perspectives dealing with the above two essential procedures. Regarding the perspective of asset diversification and risk management, the first is a study on addressing and improving the existing portfolio strategy models' limitations in model construction and estimation of input parameters for appropriate model specification. The second is a portfolio analysis of new emerging asset markets. The first aim of this dissertation is to improve the existing portfolio management strategy in model construction for the Black–Litterman framework and input parameter estimation for the synthetic put strategy for the appropriate model specification. The second aim is to investigate the empirical results using portfolio analysis in the emerging digital asset markets, including Non-Fungible Tokens (NFTs) and the cryptocurrency market, based on the mean-variance framework or portfolio insurance framework. For the first aim, we propose to use machine learning-based models to extract the meaningful pattern of external financial data for the Black–Litterman model using firm characteristics. Furthermore, we propose to use machine learning-based forecasting models to estimate the input parameters required for portfolio insurance strategy to mitigate the difficulty of addressing complex financial data. For the second aim, we examine the economic value of NFT in terms of diversification effect on traditional asset-based portfolios and portfolio insurance strategy results regarding various risk measures and investor's utility in the cryptocurrency market. The main findings in this dissertation are summarized as follows. First, our empirical results show that combining characteristics into view improves the distribution of portfolio returns in the Black–Litterman approach. Furthermore, prediction via machine learning affects improvement in the out-of-sample performance compared to using past information. Our study suggests that using the proposed model can result in a more efficient and diversified portfolio of the Black–Litterman framework. Second, our empirical results of portfolio analysis in the NFT market show evidence of the hedge, safe haven, and diversification properties of NFTs, confirming two main findings: (i) NFTs act as a hedge and safe haven for several country's stock markets and oil, bond, and USD indices and these effects in stock markets fade as frequency changes, especially showing stronger safe haven benefits for bond and USD indices during the COVID-19 periods, and (ii) NFTs are distinct from traditional assets, potentially resulting in portfolio diversification which is confirmed by preliminary analysis including correlation, co-movement, and volatility spillover and portfolio analysis based on Markowitz's mean–variance framework, improving the performance of equally weighted and tangency portfolio strategies in terms of Sharpe ratio. Third, our findings indicate that the adverse effect of volatility misestimation exists in terms of protection level error in the synthetic put strategy. We surprisingly find the protection error of insured portfolios directly linked to the precision of volatility forecasting, implying that this misestimation issue can be mitigated by employing more accurate volatility forecasting models. Another finding is that all methodologies, including traditional and machine learning-type, are better than the naive approach. Moreover, machine learning-type models, especially XGB, are the best in terms of protection and forecasting error in implementing the synthetic put strategy. This tendency supports the evidence that machine learning is better than traditional models in capturing the complex fluctuation pattern of realized volatility in highly volatile market conditions. Finally, our findings demonstrate the outperformance of portfolio insurance strategies in terms of skewness and downside risks in the cryptocurrency market. It reveals the lower-risk feature of these strategies compared to buy-and-hold. Moreover, we surprisingly find that, in terms of curvature, the portfolio choice of prospect theory investors is opposite to the expected utility theory investors. It implies the greater impact of losses than gains on the prospect theory investors. The larger loss-aversion propensity reinforces investors' preference for portfolio insurance strategies. As the most shocking result, we find portfolio insurance, when compared to the buy-and-hold strategy, provides a better opportunity to offer a higher utility in the cryptocurrency market than the traditional stock market, regardless of the investor's utility. It implies that portfolio insurance strategies can provide greater economic value in terms of risk management for a larger number of cryptocurrency investors. By improving the portfolio management models in terms of asset diversification of the multi-asset portfolio of the Black–Litterman model and risk management of a given portfolio or a single asset of synthetic put strategy, and by examining the portfolio analysis in new digital asset markets such as NFT and cryptocurrency market based on mean-variance and portfolio insurance framework, this dissertation's overall findings can help investors achieve an improved portfolio strategy and obtain a more efficient and well-diversified portfolio for the improved portfolio management.Chapter 1 Introduction 1 1.1 Background and motivation 1 1.2 Aims of the Dissertation 11 1.3 Organization of the Dissertation 13 Chapter 2 Black–Litterman model considering firm characteristic variables 15 2.1 Chapter overview 15 2.2 Data and Methodology 17 2.2.1 Data 17 2.2.2 Methodology 18 2.3 Empirical results 25 Chapter 3 Portfolio analysis for Non-Fungible Token market 28 3.1 Chapter overview 28 3.2 Data 31 3.2.1 Data for a hedge and safe haven effect 32 3.2.2 Data for a diversification effect 33 3.3 Methodology 36 3.3.1 Methods for a hedge and safe haven effect 36 3.3.2 Methods for a diversification effect 38 3.4 Empirical results 41 3.4.1 Results of a hedge and safe haven effect 41 3.4.2 Results of a diversification effect 49 Chapter 4 Volatility forecasting for portfolio insurance strategy 57 4.1 Chapter overview 57 4.2 Data 63 4.2.1 The Monte Carlo simulation data 63 4.2.2 The real-world data 66 4.3 Portfolio insurance strategy 69 4.3.1 Synthetic put strategy 69 4.3.2 Protection level error 73 4.4 Volatility forecasting models 76 4.4.1 Naive model 76 4.4.2 GARCH-type models 77 4.4.3 HAR-RV-type models 79 4.4.4 Machine learning-type models 81 4.4.5 Forecasting performance measure and statistical test 89 4.5 Experimental design and procedure 90 4.5.1 The Monte Carlo simulation 91 4.5.2 The real-world data simulation 92 4.6 Empirical results 94 4.6.1 The Monte Carlo simulation results 94 4.6.2 The real-world data simulation results 99 Chapter 5 Portfolio insurance strategy in the cryptocurrency market 108 5.1 Chapter overview 108 5.2 Portfolio insurance strategies 123 5.2.1 SL strategy 123 5.2.2 CPPI strategy 124 5.2.3 TIPP strategy 126 5.2.4 VBPI strategy 127 5.3 Downside risks 130 5.3.1 MDD and AvDD 130 5.3.2 VaR 132 5.3.3 ES 133 5.3.4 Semideviation 133 5.3.5 Omega ratio 134 5.4 Investor’s utility 136 5.4.1 Expected utility theory 136 5.4.2 Prospect theory 138 5.5 Data and experimental design 140 5.5.1 Data 140 5.5.2 Experimental design 143 5.6 Empirical results 147 5.6.1 Downside risk results 147 5.6.2 Investor’s utility results 159 Chapter 6 Conclusion 167 6.1 Summary and contributions 167 6.2 Future work 178 Bibliography 180 Appendices 218 A Appendix to Chapter 3 218 B Appendix to Chapter 4 220 C Appendix to Chapter 5 220 국문초록 228박

Several Mathematical Problems in Investment Management

This thesis studies four mathematical problems in investment management. All four problems arise from practical challenges and are data-driven. Chapter 2 investigates the Kelly portfolio strategy. The full Kelly strategy's deficiency in the face of estimation errors in practice can be mitigated by fractional or shrinkage Kelly strategies. This chapter provides an alternative, the RL Kelly strategy, based on a reinforcement learning (RL) framework. RL algorithms are developed for the practical implementation of the RL Kelly strategy. Extensive simulation studies are conducted, and the results confirm the superior performance of the RL Kelly strategies. In Chapter 3, we study the discrete-time mean-variance problem under an RL framework. The continuous-time problem was theoretically studied by the existing literature but was subject to a discretization error in implementations. We compare our discrete-time model with the continuous-time model in terms of theoretical results and numerical performance. In a daily trading market setting, we find both discrete-time and continuous-time models achieve comparable performance. However, the discrete-time model outperforms better than the continuous-time model when the trading is less frequent. Our discrete-time model is not subject to the discretization error. Chapter 4 explores the valuation problem of large variable annuity (VA) portfolios. A computationally appealing methodology for the valuation of large VA portfolios is a metamodelling framework that evaluates a small set of representative contracts, fits a predictive model based on these computed values, and then extrapolates the model to estimate the values of the remaining contracts. This chapter proposes a new two-phase procedure for selecting representative contracts. The representatives from the first phase are determined using contract attributes as in existing metamodelling approaches, but those in the second phase are chosen by utilizing the information contained in the values of the representatives from the first phase. Two numerical studies confirm that our two-phase selection procedure improves upon conventional approaches from the existing literature. Chapter 5 focuses on the capture ratio which is a widely-used investment performance measure. We study the statistical problem of estimating the capture ratio based on a finite number of observations of a fund's returns. We derive the asymptotic distribution of the estimator, and use it for testing whether one fund has a capture ratio that is statistically significantly higher than another. We also perform hypothesis tests with real-world hedge fund data. Our analysis raises concerns regarding the models and sample sizes used for estimating capture ratios in practice

Optimal portfolio allocation of commodity related assets using a controlled forward-backward algorithm

In the first part of this thesis we develop an investment consumption model with convex transaction costs and optional stochastic returns for a finite time horizon. The model is a simplified approach for the investment in a portfolio of commodity related assets like real options or production facilities. In contrast to common models like [Awerbuch, Burger 2003] our model is a multi time step approach that optimizes the investment strategy rather then calculating a static imaginary optimal portfolio. On one hand, our numerical results are consistent with the well-known investment-consumption theory in the literature. On the other hand, this is the first in-depth numerical study of a case with convex transaction costs and optional returns. Our focus in the analyses is the form of the investment strategy and its behavior with respect to model parameters. In the second part, an algorithm for solving continuous-time stochastic optimalcontrol problems is presented. The numerical scheme is based on the Stochastic Maximum Principle (SMP) as an alternative to the widely studied dynamic programming principle (DPP). By using the SMP, [Peng 1990] obtained a system of coupled forward-backward stochastic differential equations (FBSDE) with an external optimality condition. We extend the numerical scheme of [Delarue, Menozzi 2005] by a Newton-Raphson method to solve the FBSDE system and the optimality condition simultaneously. This is the first fully implemented algorithm for the solution of stochastic optimal control problems through the solution of the corresponding extended FBSDE system. We show that the key to its success and numerical advantage is the fact that it tracks the gradient of the value function and an adjusted Hessian backwards in time. The additional information is then exploited for the optimization

Essays in Robust and Data-Driven Risk Management

Risk defined as the chance that the outcome of an uncertain event is different than expected. In practice, the risk reveals itself in different ways in various applications such as unexpected stock movements in the area of portfolio management and unforeseen demand in the field of new product development. In this dissertation, we present four essays on data-driven risk management to address the uncertainty in portfolio management and capacity expansion problems via stochastic and robust optimization techniques.The third chapter of the dissertation (Portfolio Management with Quantile Constraints) introduces an iterative, data-driven approximation to a problem where the investor seeks to maximize the expected return of his/her portfolio subject to a quantile constraint, given historical realizations of the stock returns. Our approach involves solving a series of linear programming problems (thus) quickly solves the large scale problems. We compare its performance to that of methods commonly used in finance literature, such as fitting a Gaussian distribution to the returns. We also analyze the resulting efficient frontier and extend our approach to the case where portfolio risk is measured by the inter-quartile range of its return. Furthermore, we extend our modeling framework so that the solution calculates the corresponding conditional value at risk CVaR) value for the given quantile level.The fourth chapter (Portfolio Management with Moment Matching Approach) focuses on the problem where a manager, given a set of stocks to invest in, aims to minimize the probability of his/her portfolio return falling below a threshold while keeping the expected portfolio returnno worse than a target, when the stock returns are assumed to be Log-Normally distributed. This assumption, common in finance literature, creates computational difficulties. Because the portfolio return itself is difficult to estimate precisely. We thus approximate the portfolio re-turn distribution with a single Log-Normal random variable by the Fenton-Wilkinson method and investigate an iterative, data-driven approximation to the problem. We propose a two-stage solution approach, where the first stage requires solving a classic mean-variance optimization model, and the second step involves solving an unconstrained nonlinear problem with a smooth objective function. We test the performance of this approximation method and suggest an iterative calibration method to improve its accuracy. In addition, we compare the performance of the proposed method to that obtained by approximating the tail empirical distribution function to a Generalized Pareto Distribution, and extend our results to the design of basket options.The fifth chapter (New Product Launching Decisions with Robust Optimization) addresses the uncertainty that an innovative firm faces when a set of innovative products are planned to be launched a national market by help of a partner company for each innovative product. Theinnovative company investigates the optimal period to launch each product in the presence of the demand and partner offer response function uncertainties. The demand for the new product is modeled with the Bass Diffusion Model and the partner companies\u27 offer response functions are modeled with the logit choice model. The uncertainty on the parameters of the Bass Diffusion Model and the logic choice model are handled by robust optimization. We provide a tractable robust optimization framework to the problem which includes integer variables. In addition, weprovide an extension of the proposed approach where the innovative company has an option to reduce the size of the contract signed by the innovative firm and the partner firm for each product.In the sixth chapter (Log-Robust Portfolio Management with Factor Model), we investigate robust optimization models that address uncertainty for asset pricing and portfolio management. We use factor model to predict asset returns and treat randomness by a budget of uncertainty. We obtain a tractable robust model to maximize the wealth and gain theoretical insights into the optimal investment strategies

Sequential Machine learning Approaches for Portfolio Management

Cette thèse envisage un ensemble de méthodes permettant aux algorithmes d'apprentissage statistique de mieux traiter la nature séquentielle des problèmes de gestion de portefeuilles financiers. Nous débutons par une considération du problème général de la composition d'algorithmes d'apprentissage devant gérer des tâches séquentielles, en particulier celui de la mise-à-jour efficace des ensembles d'apprentissage dans un cadre de validation séquentielle. Nous énumérons les desiderata que des primitives de composition doivent satisfaire, et faisons ressortir la difficulté de les atteindre de façon rigoureuse et efficace. Nous poursuivons en présentant un ensemble d'algorithmes qui atteignent ces objectifs et présentons une étude de cas d'un système complexe de prise de décision financière utilisant ces techniques. Nous décrivons ensuite une méthode générale permettant de transformer un problème de décision séquentielle non-Markovien en un problème d'apprentissage supervisé en employant un algorithme de recherche basé sur les K meilleurs chemins. Nous traitons d'une application en gestion de portefeuille où nous entraînons un algorithme d'apprentissage à optimiser directement un ratio de Sharpe (ou autre critère non-additif incorporant une aversion au risque). Nous illustrons l'approche par une étude expérimentale approfondie, proposant une architecture de réseaux de neurones spécialisée à la gestion de portefeuille et la comparant à plusieurs alternatives. Finalement, nous introduisons une représentation fonctionnelle de séries chronologiques permettant à des prévisions d'être effectuées sur un horizon variable, tout en utilisant un ensemble informationnel révélé de manière progressive. L'approche est basée sur l'utilisation des processus Gaussiens, lesquels fournissent une matrice de covariance complète entre tous les points pour lesquels une prévision est demandée. Cette information est utilisée à bon escient par un algorithme qui transige activement des écarts de cours (price spreads) entre des contrats à terme sur commodités. L'approche proposée produit, hors échantillon, un rendement ajusté pour le risque significatif, après frais de transactions, sur un portefeuille de 30 actifs.This thesis considers a number of approaches to make machine learning algorithms better suited to the sequential nature of financial portfolio management tasks. We start by considering the problem of the general composition of learning algorithms that must handle temporal learning tasks, in particular that of creating and efficiently updating the training sets in a sequential simulation framework. We enumerate the desiderata that composition primitives should satisfy, and underscore the difficulty of rigorously and efficiently reaching them. We follow by introducing a set of algorithms that accomplish the desired objectives, presenting a case-study of a real-world complex learning system for financial decision-making that uses those techniques. We then describe a general method to transform a non-Markovian sequential decision problem into a supervised learning problem using a K-best paths search algorithm. We consider an application in financial portfolio management where we train a learning algorithm to directly optimize a Sharpe Ratio (or other risk-averse non-additive) utility function. We illustrate the approach by demonstrating extensive experimental results using a neural network architecture specialized for portfolio management and compare against well-known alternatives. Finally, we introduce a functional representation of time series which allows forecasts to be performed over an unspecified horizon with progressively-revealed information sets. By virtue of using Gaussian processes, a complete covariance matrix between forecasts at several time-steps is available. This information is put to use in an application to actively trade price spreads between commodity futures contracts. The approach delivers impressive out-of-sample risk-adjusted returns after transaction costs on a portfolio of 30 spreads