Portfolio optimization and model predictive control: A kinetic approach

Trimborn, Torsten; Pareschi, Lorenzo; Frank, Martin

doi:10.3934/dcdsb.2019136

Cited by 13 publications

(16 citation statements)

References 48 publications

(77 reference statements)

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“…Dombrovskii and Obedko [88] consider optimum portfolio selection issues subject to investment, trade, and various borrowing and lending rates limitations, use MPC for designing optimization feedback portfolio strategies, and further test the approach on real data of the Russian Stock Exchange, Moscow Interbank Currency Exchange, and New York Stock Exchange. Conversely, to gain insights into the stock market and allocation of capital, Trimborn et al [112] employ MPC to approximate and solve the optimization of the utility function. To predict shifts in the term interest rate structure, Zantedeschi et al [113] propose a dynamic product partition model (PPM) that relates macrovariables to term structures and indicate major economic disruptions, including recessions.…”

Section: Stock Returnsmentioning

confidence: 99%

Sailing through the COVID-19 Crisis by Using AI for Financial Market Predictions

Sharma

Erkut

Jain

et al. 2020

Mathematical Problems in Engineering

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The outbreak of COVID-19 has brought the world to an unprecedented position where financial and mental resources are drying up. Livelihoods are being lost, and it is becoming tough to save lives. These are the times to think of unprecedented solutions to the financial challenges being faced. Artificial intelligence (AI) has provided a fresh approach to finance through its implementation in the prediction of financial market prices by promising more generalizable results for stock market forecasting. Immense literature has attempted to apply AI and machine learning for predicting stock market returns and volatilities. The research on the applications of AI in finance lacks a consolidated overview of different research directions, findings, methodological approaches, and contributions. Therefore, there is a need to consolidate the extant literature in this upcoming field to consolidate the findings, identify the research gaps in the existing literature, and set a research agenda for future researchers. This paper addresses this need by synthesizing the extant literature in the form of a systematic review for addressing the use of AI in stock market predictions and interpreting the results in a narrative review. The gap formed through this article is the use of a combination of AI as a subject with the neural network as another area and stock market forecasting as another theme, and it will pave the way for future research studies. The analyses help highlight four important gaps in the existing literature on the subject.

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Section: Stock Returnsmentioning

confidence: 99%

Sailing through the COVID-19 Crisis by Using AI for Financial Market Predictions

Sharma

Erkut

Jain

et al. 2020

Mathematical Problems in Engineering

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show abstract

“…A rigorous derivation of the macroscopic portfolio model can be performed by the use of mean field theory. We refer to [46] for details.…”

Section: Macroscopic Portfolio Modelmentioning

confidence: 99%

“…In the case of random fundamental prices the model is even able to reproduce fat tails in logarithmic stock price return data. Mathematically, the model can be regarded as the moment model of the recently introduced mesoscopic kinetic portfolio model [46].…”

mentioning

confidence: 99%

A macroscopic portfolio model: from rational agents to bounded rationality

Trimborn

2019

Math Finan Econ

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We introduce a microscopic model of interacting financial agents, where each agent is characterized by two portfolios; money invested in bonds and money invested in stocks. Furthermore, each agent is faced with an optimization problem in order to determine the optimal asset allocation. The stock price evolution is driven by the aggregated investment decision of all agents. In fact, we are faced with a differential game since all agents aim to invest optimal. Mathematically such a problem is ill posed and we introduce the concept of Nash equilibrium solutions to ensure the existence of a solution. Especially, we denote an agent who solves this Nash equilibrium exactly a rational agent. As next step we use model predictive control to approximate the control problem. This enables us to derive a precise mathematical characterization of the degree of rationality of a financial agent. This is a novel concept in portfolio optimization and can be regarded as a general approach. In a second step we consider the case of a fully myopic agent, where we can solve the optimal investment decision of investors analytically. We select the running cost to be the expected missed revenue of an agent and we assume quadratic transaction costs. More precisely the expected revenues are determined by a combination of a fundamentalist or chartist strategy. Then we derive the mean field limit of the microscopic model in order to obtain a macroscopic portfolio model. The novelty in comparison to existent macroeconomic models in literature is that our model is derived from microeconomic dynamics. The resulting portfolio model is a three dimensional ODE system which enables us to derive analytical results. The conducted simulations reveal that the model shares many dynamical properties with existing models in literature. Thus, our model is able to replicate the most prominent features of financial markets, namely booms and crashes. In the case of random fundamental prices the model is even able to reproduce fat tails in logarithmic stock price return data. Mathematically, the model can be regarded as the moment model of the recently introduced mesoscopic kinetic portfolio model [46].

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“…Cordier et al [21] employ the kinetic theory to analyse the behaviour of agents in the financial market and derive a linear mesoscopic dynamic model describing the wealth growth of agents, in which agents choose their own investment portfolio in stocks and bonds. Trimborn et al [22] investigate the relationship between the agent's investment strategies and the stock price in the financial market by using the kinetic theory and model predictive control method.…”

Section: Introductionmentioning

confidence: 99%

The influence of knowledge level on the proportion of wealth in the stock market

Lai

2022

Proc. R. Soc. A.

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The kinetic theory is applied to investigate the impact of knowledge level on the proportion of wealth in the stock market. Assume that each agent’s wealth is non-negative in the financial market and agents are allowed to choose their own portfolios in the stock and bond. The nonlinear Boltzmann models describing the investment proportion of wealth between the two assets and knowledge formation are discussed. In the models, the agent’s knowledge level and psychological factors affect their investment strategies and risk prediction. A value function containing the current price and intrinsic value of the stock is used to depict the agent’s psychological factors. The asymptotic procedure is employed to obtain the Fokker–Planck equation relating to the Boltzmann model. The numerical simulation experiments illustrate that knowledge has the potential to increase the proportion of wealth invested in the stock and improve the wealth status of agents.

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Portfolio optimization and model predictive control: A kinetic approach

Cited by 13 publications

References 48 publications

Sailing through the COVID-19 Crisis by Using AI for Financial Market Predictions

Sailing through the COVID-19 Crisis by Using AI for Financial Market Predictions

A macroscopic portfolio model: from rational agents to bounded rationality

The influence of knowledge level on the proportion of wealth in the stock market

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