Zhang Li. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 67-69). / Abstracts in English and Chinese. / Chapter 1 --- Introduction and Literature Review --- p.1 / Chapter 2 --- The Tracking Portfolio Models --- p.7 / Chapter 2.1 --- Problem Formulation --- p.8 / Chapter 2.2 --- Reformulation of Tracking Models --- p.12 / Chapter 2.3 --- A Stochastic LQ Control Approach --- p.13 / Chapter 3 --- Efficient Tracking: Deterministic Market Parameters --- p.16 / Chapter 3.1 --- Solution to Model I --- p.17 / Chapter 3.2 --- A Special Case of Model I --- p.23 / Chapter 3.3 --- Solution to Model II --- p.24 / Chapter 3.4 --- A Special Case of Model II: Mean-Variance Portfolio Selection --- p.32 / Chapter 3.5 --- Solution to Model III --- p.36 / Chapter 4 --- Efficient Tracking: Markov-Modulated Market Parameters --- p.41 / Chapter 4.1 --- Problem Formulation --- p.42 / Chapter 4.2 --- Solution to Model I with Regime Switching --- p.47 / Chapter 4.3 --- Solution to Model II with Regime Switching --- p.52 / Chapter 4.4 --- Solution to Model III with Regime Switching --- p.59 / Chapter 5 --- Conclusion --- p.64 / Bibliography --- p.66

No description available.

Univ., Diss.--Bremen, 2002.

Thesis (M. S.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Reveliotis, Spyros; Committee Member: Ayhan, Hayriye; Committee Member: Goldsman, Dave; Committee Member: Shamma, Jeff; Committee Member: Zwart, Bert.

Thesis (Ph. D.)--Drexel University, 2006. / Includes abstract and vita. Includes bibliographical references (leaves 105-113).

摘要 本文於確定給付退休金計劃下，探討基金經理人於最差基金財務短絀情境發生前極大化管理目標之最適投資組合，基金比值過程定義為基金現值與負債指標之比例，管理人將於指定最差基金比值發生前極大化達成既定經營目標之機率，隨時間改變之基金投資集合包括無風險之現金、債券與股票。本研究建構隨機控制模型描述此最適化問題，並以動態規劃方法求解，由結果歸納，經理人之最適策略包含極小化基金比值變異之避險因素，風險偏好及跨期投資集合相關之避險因素與模型狀態變數相關之避險因素。本研究利用馬可夫練逼近法逼近隨機控制的數值解，結果顯示基金經理人須握有很大部位的債券，且不同的投資期間對於最適投資決策有很大的影響。 關鍵字: 短絀、確定給付、負債指標、隨機控制、動態規劃。 / Abstract This paper analyzes the portfolio problem that is a pension fund manager has to maximize the possibility of reaching his managerial goal before the worst scenario shortfall occurs in a defined benefit pension scheme. The fund ratio process defined as the ratio between the fund level and its accrued liability benchmark is attained to maximize the probability that the predetermined target is achieved before it falls below an intolerable boundary. The time-varying opportunity set in our study includes risk-free cash, bonds and stock index. The problems are formulated as a stochastic control framework and are solved through dynamics programming. In this study, the optimal portfolio are characterized by three components, the liability hedging component, the intertemporal hedging component against changes in the opportunity set, and the temporal hedging component minimizing the variation in fund ratio growth. The Markov chain approximation methods are employed to approximate the stochastic control solutions numerically. The result shows that fund managers should hold large proportions of bonds and time horizon plays a crucial role in constructing the optimal portfolio. Keywords: shortfall; defined benefit; liability benchmark; stochastic control; dynamic programming.

This dissertation is devoted to theories of processes we call ``Walsh semimartingales" and ``Walsh diffusions", as well as to related optimization problems of control and stopping. These processes move on the plane along rays emanating from the origin; and when at the origin, the processes choose the rays of their subsequent voyage according to a fixed probability measure---in a manner described by Walsh (1978) as a direct generalization of the skew Brownian motion. We first review in Chapter 1 some key results regarding the celebrated skew Brownian motions and Walsh Brownian motions. These results include the characterization of skew Brownian motions via stochastic equations in Harrison & Shepp (1981), the construction of Walsh Brownian motions in Barlow, Pitman & Yor (1989), and the important result of Tsirel'son (1997) regarding the nature of the filtration generated by the Walsh Brownian motion. Various generalizations of Walsh Brownian motions are described in detail in Chapter 2. We formally define there Walsh semimartingales as a subclass of planar processes we call ``semimartingales on rays". We derive for such processes Freidlin-Sheu-type change-of-variable formulas, as well as two-dimensional versions of the Harrison-Shepp equations. The actual construction of Walsh semimartingales is given next. Walsh diffusions are then defined as a subclass of Walsh semimartingales, described by stochastic equations which involve local drift and dispersion characteristics. The associated local submartingale problems, strong Markov properties, existence, uniqueness, asymptotic behavior, and tests for explosions in finite time, are studied in turn. Finally, with Walsh semimartingales as state-processes, we study in Chapter 3 succesively a pure optimal stopping problem, a stochastic control problem with discretionary stopping, and a stochastic game between a controller and a stopper. We derive for these problems optimal strategies in surprisingly explicit from. Crucial for the analysis underpinning these results, are the change-of-variable formulas derived in Chapter 2. Most of the results in Chapters 2 and 3 are based on two papers, [21] and [31], both cowritten by the author of this dissertation. Some results and proofs are rearranged and rewritten here.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--Worcester Polytechnic Institute. / Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration. Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration; energy balance method. Includes bibliographical references (p. 86-89).

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 117-130). Also available in electronic version. Access restricted to campus users.