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dynamic portfolio optimization with Looping Contagion Risk

SIAM JOURNAL ON FINANCIAL MATHEMATICS 2019年第1期10卷 1-36页

作者： Jia, Longjie Pistorius, Martijn Zheng, Harry Imperial Coll Dept Math London SW7 2AZ England

In this paper, we consider a utility maximization problem with defaultable stocks and looping contagion risk. We assume that the default intensity of one company depends on the stock prices of itself and other companies, and the default of the company induces immediate drops in the stock prices of the surviving companies. We prove that the value function is the unique viscosity solution of the Hamilton-Jacobi-Bellman equation. We also perform some numerical tests to compare and analyze the statistical distributions of the terminal wealth of log utility and power utility based on two strategies, one using the full information of intensity process and the other a proxy constant intensity process.

关键词： dynamic portfolio optimization looping contagion risk HJB equation viscosity solution robust tests statistical comparisons

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dynamic portfolio optimization for Utility-Based Models

Dynamic Portfolio Optimization for Utility-Based Models

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International Conference on Information and Financial Engineering

作者： Fulga, Cristinca INCREST Bucharest Dept Math R-79622 Bucharest Romania

ISBN: (纸本)9780769536064

portfolio management deals with the allocation of wealth among different investment opportunities, considering investor's preferences on risk. In this paper we consider a multiperiod model where the investor rebalances a portfolio at the beginning of each period facing uncertainty associated with the prices of the assets at future dates. Models of this decision problem tend to become very large because of the dynamic structure and uncertainty. We present a multiple period portfolio model over a finite horizon with transaction costs, a risk averse utility function and the uncertainty modeled using the scenario approach. We propose a new method for efficiently solving real problems;the procedure utilizes stochastic programming combined with decomposition and approximating techniques. Solving the resulting optimization problem relies on approximate dynamic programming techniques. The technique used for solving the portfolio problem provides a method whose effectiveness is proved by the experimental results.

关键词： dynamic portfolio optimization Progressive Hedging Algorithm Approximate dynamic Programming

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dynamic portfolio optimization via Augmented DDPG with Quantum Price Levels-Based Trading Strategy

Dynamic Portfolio Optimization via Augmented DDPG with Quant...

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International Joint Conference on Neural Networks (IJCNN)

作者： Lin, Runsheng Xing, Zihan Ma, Mingze Lee, Raymond S. T. BNU HKBU United Int Coll Dept Stat & Data Sci Zhuhai Peoples R China BNU HKBU United Int Coll Dept Comp Sci Zhuhai Peoples R China

ISBN: (纸本)9781665488679

With the development of deep learning, dynamic portfolio optimization (DPO) problem has received a lot of attention in recent years, not only in the field of finance but also in the field of deep learning. Some advanced research in recent years has proposed the application of Deep Reinforcement Learning (DRL) to the DPO problem, which demonstrated to be more advantageous than supervised learning in solving the DPO problem. However, there are still certain unsolved issues: 1) DRL algorithms usually have the problems of slow learning speed and high sample complexity, which is especially problematic when dealing with complex financial data. 2) researchers use DRL simply for the purpose of obtaining high returns, but pay little attention to the problem of risk control and trading strategy, which will affect the stability of model returns. In order to address these issues, in this study we revamped the intrinsic structure of the model based on the Deep Deterministic Policy Gradient (DDPG) and proposed the Augmented DDPG model. Besides, we also proposed an innovative risk control strategy based on Quantum Price Levels (QPLs) derived from Quantum Finance Theory (QFT). Our experimental results revealed that our model has better profitability as well as risk control ability with less sample complexity in the DPO problem compared to the baseline models.

关键词： dynamic portfolio optimization portfolio Management Deep Learning Reinforcement Learning Deep Reinforcement Learning Quantum Finance Theory Quantum Price Levels

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dynamic portfolio optimization Using Proximal Gradient Method 15

Dynamic Portfolio Optimization Using Proximal Gradient Metho...

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15th International Conference on Computing Communication and Networking Technologies, ICCCNT 2024

作者： Hareni, M. Krishna, Surya Ayyappan, Swetha Jayan, Sarada Amrita Vishwa Vidyapeetham Amrita School of Computing Department of Computer Science and Engineering Bangalore India Amrita Vishwa Vidyapeetham Amrita School of Engineering Dept. of Mathematics Bangalore India

ISBN: (纸本)9798350370249

The focus of this project will be to develop a general optimization framework for optimal investment portfolios within the proximal gradient method, a suitable algorithm to solve non-smooth constrained optimization problems efficiently. Using historical ADM, Amazon, Apple, and Cisco stock price data, among others, we can derive the optimal allocation of assets that serves to minimize the overall portfolio volatility. While cautiously pre-treating the data on all the stocks through return calculation, our methodology proceeded to use the proximal gradient method in weighing investment optimally, subject to some constraint. In this respect, with our methodology having been applied, the computational advantage and reduction in time usage did become relatively significant. The proximal operator is known to be very effective in dealing with all forms of constraints, be it budgetary, maximum and minimum investment bounds on each asset, or risk constraints, in providing an optimized solution to the dynamic nature of financial markets. © 2024 IEEE.

关键词： dynamic portfolio optimization non-smooth constrained problems proximal gradient

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dynamic portfolio optimization with inverse covariance clustering

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EXPERT SYSTEMS WITH APPLICATIONS 2023年 213卷

作者： Wang, Yuanrong Aste, Tomaso UCL Dept Comp Sci Gower St London WC1E 6BT England UCL UCL Ctr Blockchain Technol Gower St London WC1E 6BT England London Sch Econ & Polit Sci Syst Risk Ctr London WC2A 2AE England

Market conditions change continuously. However, in portfolio investment strategies, it is hard to account for this intrinsic non-stationarity. In this paper, we propose to address this issue by using the Inverse Covariance Clustering (ICC) method to identify inherent market states and then integrate such states into a dynamic portfolio optimization process. Extensive experiments across three different markets, NASDAQ, FTSE and HS300, over a period of ten years, demonstrate the advantages of our proposed algorithm, termed Inverse Covariance Clustering-portfolio optimization (ICC-PO). The core of the ICC-PO methodology concerns the identification and clustering of market states from the analytics of past data and the forecasting of the future market state. It is therefore agnostic to the specific portfolio optimization method of choice. By applying the same portfolio optimization technique on a ICC temporal cluster, instead of the whole train period, we show that one can generate portfolios with substantially higher Sharpe Ratios, which are statistically more robust and resilient with great reductions in the maximum loss in extreme situations. This is shown to be consistent across markets, periods, optimization methods and selection of portfolio assets.

关键词： dynamic portfolio optimization portfolio management Financial market states Market regimes Temporal clustering Information filtering networks Covariance structure

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dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach

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QUANTITATIVE FINANCE 2019年第3期19卷 519-532页

作者： Zhang, Rongju Langrene, Nicolas Tian, Yu Zhu, Zili Klebaner, Fima Hamza, Kais CSIRO Data61 RiskLab Canberra ACT Australia Monash Univ Sch Math Sci Clayton Vic Australia

We present a simulation-and-regression method for solving dynamic portfolio optimization problems in the presence of general transaction costs, liquidity costs and market impact. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables, namely the portfolio value and the asset prices subject to permanent market impact. To handle endogenous state variables, we adapt a control randomization approach to portfolio optimization problems and further improve the numerical accuracy of this technique for the case of discrete controls. We validate our modified numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We identify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic optimization method protects the investor's capital under illiquid market conditions. Lastly, we analyze, under different liquidity conditions, the sensitivities of certainty equivalent returns and optimal allocations with respect to trading volume, stock price volatility, initial investment amount, risk aversion level and investment horizon.

关键词： dynamic portfolio optimization Multi-period asset allocation Transaction cost Liquidity cost Permanent market impact Least squares Monte Carlo

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dynamic portfolio optimization WITH A DEFAULTABLE SECURITY AND REGIME-SWITCHING

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MATHEMATICAL FINANCE 2014年第2期24卷 207-249页

作者： Capponi, Agostino Figueroa-Lopez, Jose E. Purdue Univ Sch Ind Engn W Lafayette IN 47907 USA Purdue Univ Dept Stat W Lafayette IN 47907 USA

We consider a portfolio optimization problem in a defaultable market with finitely-many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market coefficients are assumed to depend on the market regime in place, which is modeled by a finite state continuous time Markov process. By separating the utility maximization problem into a predefault and postdefault component, we deduce two coupled Hamilton-Jacobi-Bellman equations for the post- and predefault optimal value functions, and show a novel verification theorem for their solutions. We obtain explicit constructions of value functions and investment strategies for investors with logarithmic and Constant Relative Risk Aversion utilities, and provide a precise characterization of the directionality of the bond investment strategies in terms of corporate returns, forward rates, and expected recovery at default. We illustrate the dependence of the optimal strategies on time, losses given default, and risk aversion level of the investor through a detailed economic and numerical analysis.

关键词： utility maximization dynamic portfolio optimization credit risk Hamilton-Jacobi-Bellman equations regime-switching models

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dynamic mean-LPM portfolio optimization under the mean-reverting market 28

Dynamic mean-LPM portfolio optimization under the mean-rever...

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28th Chinese Control and Decision Conference

作者： Niu, Yiwei Gao, Jianjun Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Shanghai Univ Finance & Econ Sch Informat Management & Engn Shanghai 200433 Peoples R China

ISBN: (纸本)9781467397148

This paper studies the dynamic mean-LPM portfolio optimization problem with mean-reverting market. Rich empirical evidence shows that the stock return exhibits certain degree of mean-reverting property. However, the study of dynamic mean-risk model with mean-reverting market is rare in the literature. Due to the complicated constraints in this kind of dynamic optimization model, it is hard to use the stochastic control approach directly. Instead, under our market setting, we are able solve this problem semi-analyticall by using the martingale approach. Once the optimal terminal wealth is identified, we use some numerical approach and the Monte Carlo method to find the optimal wealth process and portfolio process for given state. Our method provide investor a simple tool to deal with the sophisticated model for guiding the portfolio management.

关键词： dynamic portfolio optimization Lower Partial Moment Martingale Method

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dynamic mean-LPM portfolio optimization under the mean-reverting market

Dynamic mean-LPM portfolio optimization under the mean-rever...

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第28届中国控制与决策会议

作者： Yiwei Niu Jianjun Gao Department of Automation Shanghai Jiao Tong University School of Information Management & Engineering Shanghai University of Finance and Economics

ISBN: (纸本)9781467397155

This paper studies the dynamic mean-LPM portfolio optimization problem with mean-reverting *** empirical evidence shows that the stock return exhibits certain degree of mean-reverting ***,the study of dynamic mean-risk model with mean-reverting market is rare in the *** to the complicated constraints in this kind of dynamic optimization model,it is hard to use the stochastic control approach ***,under our market setting,we are able solve this problem semi-analyticall by using the martingale *** the optimal terminal wealth is identified,we use some numerical approach and the Monte Carlo method to find the optimal wealth process and portfolio process for given *** method provide investor a simple tool to deal with the sophisticated model for guiding the portfolio management.

关键词： dynamic portfolio optimization Lower Partial Moment Martingale Method

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dynamic programming with Hermite approximation

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2015年第3期81卷 245-267页

作者： Cai, Yongyang Judd, Kenneth L. Stanford Univ Hoover Inst Stanford CA 94305 USA Univ Chicago Chicago IL 60637 USA NBER Cambridge MA 02138 USA

Numerical dynamic programming algorithms typically use Lagrange data to approximate value functions over continuous states. Hermite data can be easily obtained from solving the Bellman equation and used to approximate the value functions. We illustrate the use of Hermite data with one-, three-, and six-dimensional examples. We find that Hermite approximation improves the accuracy in value function iteration (VFI) by one to three digits using little extra computing time. Moreover, VFI with Hermite approximation is significantly faster than VFI with Lagrange approximation for the same accuracy, and this advantage increases with the dimension of the continuous states.

关键词： dynamic programming Value function iteration Hermite approximation dynamic portfolio optimization Multi-country optimal growth model

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