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Portfolio optimization in a regime-switching market with derivatives

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第1期233卷 184-192页

作者： Fu, Jun Wei, Jiaqin Yang, Hailiang Univ Hong Kong Dept Stat & Actuarial Sci Hong Kong Hong Kong Peoples R China Macquarie Univ Dept Appl Finance & Actuarial Studies Fac Business & Econ Sydney NSW 2109 Australia

We consider the optimal asset allocation problem in a continuous-time regime-switching market. The problem is to maximize the expected utility of the terminal wealth of a portfolio that contains an option, an underlying stock and a risk-free bond. The difficulty that arises in our setting is finding a way to represent the return of the option by the returns of the stock and the risk-free bond in an incomplete regime-switching market. To overcome this difficulty, we introduce a functional operator to generate a sequence of value functions, and then show that the optimal value function is the limit of this sequence. The explicit form of each function in the sequence can be obtained by solving an auxiliary portfolio optimization problem in a single-regime market. And then the original optimal value function can be approximated by taking the limit. Additionally, we can also show that the optimal value function is a solution to a dynamic programming equation, which leads to the explicit forms for the optimal value function and the optimal portfolio process. Furthermore, we demonstrate that, as long as the current state of the Markov chain is given, it is still optimal for an investor in a multiple-regime market to simply allocate his/her wealth in the same way as in a single-regime market. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Functional operator Elasticity approach Portfolio optimization Regime switching dynamic programming principle

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The optimal control related to Riemannian manifolds and the viscosity solutions to Hamilton-Jacobi-Bellman equations

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SYSTEMS & CONTROL LETTERS 2014年第1期69卷 7-15页

作者： Zhu, Xuehong Nanjing Univ Aeronaut & Astronaut Sch Sci Nanjing 210016 Peoples R China

In this paper we study the optimal stochastic control problem for stochastic differential equations on Riemannian manifolds. The cost functional is specified by controlled backward stochastic differential equations in Euclidean space. Under some suitable assumptions, we conclude that the value function is the unique viscosity solution to the associated Hamilton-Jacobi-Bellman equation which is a fully nonlinear parabolic partial differential equation on Riemannian manifolds. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Riemannian manifold Hamilton-Jacobi-Bellman equation Backward stochastic differential equations dynamic programming principle Viscosity solution

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Analysis and control for transient responses of seismic-excited hysteretic structures

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SOIL dynamicS AND EARTHQUAKE ENGINEERING 2015年 73卷 58-65页

作者： Jin, X. L. Wang, Y. Huang, Z. L. Zhejiang Univ Dept Engn Mech State Key Lab Fluid Power Transmiss & Control Hangzhou 310027 Zhejiang Peoples R China

The semi-arialytical solution of transient responses and the bounded control strategy to minimize the transient responses for seismic-excited hysteretic structures are investigated in this manuscript, the hysteretic behavior is described by Duhem model while the seismic excitations by random processes with Kanai-Tajimi spectrum. The averaged Fokker-Planck-Kolmogorov equation with respect to the probability density of amplitude response is firstly derived by utilizing the stochastic averaging technique based on the generalized harmonic functions. The probability density is approximately expressed as a series expansion in terms of a set of specified basis functions with time-dependent coefficients which are determined through the Galerkin procedure. The quasi-optimal bounded control strategy to minimize the transient response is proposed based on the averaged system with respect to amplitude response and an appropriate performance index. The quasi-optimal control is derived from the minimum condition in the dynamic programming equation. The application and effectiveness of the proposed analytical procedure and control strategy are illustrated through one representative example. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Hysteretic structure Transient response Bounded control Seismic excitation Stochastic averaging Galerkin procedure dynamic programming principle

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OPTIMAL CONTRACTS AND ASSET PRICES IN A CONTINUOUS-TIME DELEGATED PORTFOLIO MANAGEMENT PROBLEM

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第5期19卷 3186-3216页

作者： Dou, Zheng Lai, Shaoyong Xihua Univ Sch Econ Chengdu 611139 Peoples R China Southwestern Univ Finance & Econ Sch Econ Math Chengdu 611130 Peoples R China

We study optimal contracts and asset prices in a financial market in which an investor delegates a portfolio manager to manage her wealth. The agency frictions are caused by the manager's "shirking" action and hidden effort. The shirking action converts part of the return of the managed portfolio into the manager's income without reducing his utility. The manager's effort improves the return of the portfolio but reduces the manager's utility. We illustrate this dynamic principal-agent problem under hidden effort and observable effort, respectively. When the effort is hidden, to alleviate the impact of moral hazard, the investor pays more for the manager's performance and always keeps the optimal contract related to the returns of the manager's portfolio and market portfolio, and their quadratic (co)variations. When the manager's effort is observable, the optimal contract is related to the return of the market portfolio if the agency friction caused by the shirking action is serious, but is only related to the return of the manager's portfolio if shirking is not serious. Analysing the expected utility of the manager, we find that he has a disposition to hide information about effort to pursue a higher expected utility.

关键词： Optimal contracts asset-management dynamic programming principle principal-agent problem moral hazard

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Portfolio selection problem with Value-at-Risk constraints under non-extensive statistical mechanics

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2016年 298卷 64-71页

作者： Zhao, Pan Xiao, Qingxian Univ Shanghai Sci & Technol Sch Business Shanghai Peoples R China West Anhui Univ Coll Finance & Math Luan Anhui Peoples R China West Anhui Univ Financial Risk Intelligent Control & Prevent Inst Luan Anhui Peoples R China

The optimal portfolio selection problem is a major issue in the financial field in which the process of asset prices is usually modeled by a Wiener process. That is, the return distribution of the asset is normal. However, several empirical results have shown that the return distribution of the asset has the characteristics of fat tails and aiguilles and is not normal. In this work, we propose an optimal portfolio selection model with a Value-at-Risk (VaR) constraint in which the process of asset prices is modeled by the non-extensive statistical mechanics instead of the classical Wiener process. The model can describe the characteristics of fat tails and aiguilles of returns. Using the dynamic programming principle, we derive a Hamilton-Jacobi-Bellman (HJB) equation. Then, employing the Lagrange multiplier method, we obtain closed-form solutions for the case of logarithmic utility. Moreover, the empirical results show that the price process can more accurately fit the empirical distribution of returns than the familiar Wiener process. In addition, as the time increases, the constraint becomes binding. That is, to control the risk the agent reduces the proportion of the wealth invested in the risky asset. Furthermore, at the same confidence level, the agent reduces the proportion of the wealth invested in the risky asset more quickly under our model than under the model based on the Wiener process. This can give investors a good decision-making reference. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Non-extensive statistics Portfolio selection Value-at-Risk Utility dynamic programming principle

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Robust stochastic control modeling of dam discharge to suppress overgrowth of downstream harmful algae

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APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY 2018年第3期34卷 338-354页

作者： Yoshioka, Hidekazu Yaegashi, Yuta Shimane Univ Fac Life & Environm Sci Matsue Shimane 6908504 Japan Kyoto Univ Grad Sch Agr Kyoto Japan Japan Soc Promot Sci Kyoto Japan

The mathematical concept of multiplier robust control is applied to a dam operation problem, which is an urgent issue on river water environment, as a new industrial application of stochastic optimal control. The goal of the problem is to find a fit-for-purpose and environmentally sound operation policy of the flow discharge from a dam so that overgrowth of the harmful algae Cladophora glomerataKutzing in its downstream river is effectively suppressed. A minimal stochastic differential equation for the algae growth dynamics with uncertain growth rate is first presented. The performance index to be maximized by the operator of the dam while minimized by nature is formulated within the framework of differential games. The dynamic programming principle leads to a Hamilton-Jacobi-Bellman-Isaacs equation whose solution determines the worst-case optimal operation policy of the dam, ie, the policy that the operator wants to find. Application of the model to overgrowth suppression of Cladophora glomerataKutzing just downstream of a dam in a Japanese river is then carried out. Values of the model parameters are identified with which the model successfully reproduces the observed population dynamics. A series of numerical experiments are performed to find the most effective operation policy of the dam based on a relaxation of the current policy.

关键词： Cladophora glomerata Kutzing dynamic programming principle flow discharge Hamilton-Jacobi-Bellman-Isaacs equation model misspecification multiplier robust control

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Fuzzy optimal control with application to discounted profit advertising problem

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2012年第5期23卷 187-192页

作者： Baten, Md. Azizul Kamil, Anton Abdulbasah Univ Utara Malaysia Sch Quantitat Sci Dept Decis Sci Kedah 06010 Malaysia Univ Sains Malaysia Sch Distance Educ Math Program George Town Malaysia

A fuzzy optimal control model was formulated maximizing the expected discounted objective function subject to fuzzy differential equation for fuzzy control system. We proved that the value function of fuzzy optimal control problem satisfied the dynamic programming principle. The optimality equation in fuzzy optimal control was derived and an example was carried out to obtain the optimality conditions by using the optimality equation. As an application, we used the Bellman's principle of optimality to solve the fuzzy advertising model.

关键词： Fuzzy optimal control dynamic programming principle optimality equation profit advertising model

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Zero-sum differential games involving hybrid controls

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2006年第1期128卷 75-102页

作者： Dharmatti, S Ramaswamy, M Indian Inst Sci Dept Math Bangalore 560012 Karnataka India Tata Inst Fundamental Res IISc TIFR Math Program Bangalore Karnataka India

We study a zero-sum differential game with hybrid controls in which both players are allowed to use continuous as well as discrete controls. Discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, an autonomous jump set A or a controlled jump set C, where one controller can choose to jump or not. At each jump, the trajectory can move to a different Euclidean space. One player uses all the three types of controls, namely, continuous controls, autonomous jumps, and controlled jumps;the other player uses continuous controls and autonomous jumps. We prove the continuity of the associated lower and upper value functions V- and V+. Using the dynamic programming principle satisfied by V- and V+, we derive lower and upper quasivariational inequalities satisfied in the viscosity sense. We characterize the lower and upper value functions as the unique viscosity solutions of the corresponding quasivariational inequalities. Lastly, we state an Isaacs like condition for the game to have a value.

关键词： dynamic programming principle viscosity solutions quasivariational inequalities hybrid control differential games

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Formula for a solution of u_t+H(u,Du)=g

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PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES 2000年第4期110卷 393-414页

作者： Adimurthi Gowda, GDV TIFR Ctr Bangalore 560012 Karnataka India

We study the continuous as well as the discontinuous solutions of Hamilton-Jacobi equation u(t) + H(u, Du) = g in R-n x R+ with u(x, 0) = u(0)(x). The Hamiltonian H(s,p) is assumed to be convex and positively homogeneous of degree one inp for each s in R. If H is non increasing in s, in general, this problem need not admit a continuous viscosity solution. Even in this case we obtain a formula for discontinuous viscosity solutions.

关键词： Hamilton-Jacobi equation dynamic programming principle viscosity sub and super solutions

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DETERMINISTIC IMPULSE CONTROL-PROBLEMS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1985年第3期23卷 419-432页

作者： BARLES, G Ecole Normale Superieure St. Cloud et Ceremade Bandol Fr Ecole Normale Superieure St. Cloud et Ceremade Bandol Fr

We prove that the optimal cost function of a deterministic impulse control problem is the unique viscosity solution of a first-order Hamilton–Jacobi quasi-variational inequality in $\mathbb{R}^N $.

关键词： deterministic impulse control dynamic programming principle viscosity solution first-order Hamilton–Jacobi equations quasi-variational inequality

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