Aug 2026· International Journal of Computer Science and Mathematical Theory· 0 citations
Abstract
This paper investigates optimal portfolio choice for a risk-averse investor who is operating in a
financial market characterized by continuous time usage and with explicit attention being paid to
the investor's sensitivity to market movements. The investor's preferences are described by a
power utility function of constant relative risk aversion, which promotes economically interesting
behavior over wealth levels. The market consists of a risk-free asset and many risky assets,
evolving under stochastic differential equations. By allowing the investor to adjust portfolio
positions according to the changes in the processes of risky assets, the model can extend
traditional portfolio optimization frameworks. Aiming to self-assemble against dynamic
programming and the Hamilton-Jacobi-Bellman equation, exploiting Itô's calculus, we got
analytical representations of the optimal portfolio strategy and its expected terminal utility. The
quantification of the explicit sensitivity effect parameter allowed the activation of market
responsiveness to additional advantage. Numerical simulations, with Python, demonstrate the
role of market signals on a market-responsive portfolio. Two- and three-dimensional numerical
figure analyses also depict the behavior, in terms of the optimal investment decisions, of risk
aversion, asset volatility, and sensitivity parameters.
With the increasing power of institutional investors, in order to compete for more investment agency business, the competition among institutional investors has become increasingly fierce. This paper studies a non-zero-sum game between two competing institutional investors who adopt mean–variance preferences and account for model uncertainty in order to derive robust optimal portfolios. The ambiguity-averse institutional investors can invest in a financial market with one risk-free bond and one individual stock. The objective of each institutional investor is to maximize the mean–variance utility of his terminal wealth relative to that of his competitor under the worst-case scenario of the alternative measures. By means of stochastic dynamic programming, we obtain closed-form expressions for the robust Nash equilibrium strategies and prove a verification theorem. Numerical simulations are finally presented to examine how model parameters influence the equilibrium strategies and to extract associated economic interpretations.
Market timing models aim to anticipate short-term market movements according to a given source of information. Such information could be extracted from an analysis of history or a forecast of the future. In fact, the financial markets are driven mainly by the expectations of market investors and by exogenous sources. An explicit way for market investors to make clear their expectations about a certain asset is to define the implied volatility of the options that are written on that asset. Moreover, the literature proposed tools that generate the state price density of the underlying by observing the implied volatility of the options. The combination of the implied volatilities and the state price density can give deep insight into investors’ expectations about the short-term movements of the underlying and, thus, can represent a reliable source of information to perform a market timing strategy or to select a portfolio for a risk-neutral investor with a short-term horizon. To avoid adjusting the procedure for dividend-paying assets, we develop our approach considering market price indexes. This approach constitutes a completely new technique to establish both a market timing strategy and a ranking among the considered indexes. In the empirical analysis, we considered both the market timing problem for a single index and the portfolio selection problem when multiple indexes are available.
S. Vitali, Miloš Kopa, R. Domínguez et al.· Annals of Operations Researc...· 0 citations
To measure the wealth of a portfolio of investments refers to assessing the overall financial health
and values of a collection of investments held by individual or organization; which allows
investors to track the performance of their investments over time and understand the wealth on
their investment. Therefore, this paper considered two system of second order Differential
Equations (ODE) with appropriate stock quantities for variation of portfolios of investments. The
problems were analytically solved by adopting the series solution approaches of Frobenius and
method of undetermined coefficient; closed form solutions are derived for wealth of portfolios of
investments. More so, capital market were effectively analyzed which demonstrated the impact
analysis on the wealth of portfolios of investments and other capital market variables were
presented graphically. Secondly, we state and prove theorem to show that our proposed model
under-goes rate of change property which is informative to investors. To this end, the governing
equations are reliable as it realistically addresses the principles of capital market investments.
P. E. Brown-Ikiri· World Journal of Finance and...· 0 citations
Portfolio management has consistently faced the fundamental challenge of uncertainty in estimating asset returns and risks, which has limited the practical effectiveness of classical optimization approaches, particularly the Markowitz mean–variance model. In this context, the Black–Litterman model, as a Bayesian framework, enables the derivation of more stable estimates that are consistent with market economic logic by combining market equilibrium returns with investor views. The primary objective of the present study is to propose a structured framework for portfolio management using the Black–Litterman model with the systematic incorporation of investor views grounded in fundamental analysis and asset pricing factors. From a methodological perspective, this research is applied–developmental and quantitative, and it is empirically conducted using daily stock data of manufacturing firms listed on the Tehran Stock Exchange over the period 2015 to 2023. Rather than relying on subjective judgments, investor views are extracted based on the results of regressions from the Fama–French three-factor model and are incorporated into the Black–Litterman framework in the form of relative views. After computing the implied equilibrium returns and incorporating the views, posterior Black–Litterman returns are derived, and optimal portfolio weights are determined through mean–variance optimization. The performance of the resulting portfolio is compared with that of the classical Markowitz portfolio and the baseline Black–Litterman model using return, risk, and risk-adjusted performance measures. The findings indicate that the implied equilibrium returns obtained from the Black–Litterman model are generally more conservative than historical averages and help prevent overfitting to past data. The empirical results show that incorporating Fama–French–based views leads to a significant increase in cumulative returns, improvements in the Sharpe and Sortino ratios, and reductions in the standard deviation and maximum drawdown of the portfolio compared with both the Markowitz approach and the Black–Litterman model without views. Moreover, sensitivity analysis with respect to the τ parameter demonstrates that selecting intermediate values of this parameter can establish an appropriate balance between market information and investor views. Overall, the results confirm that the structured integration of Fama–French factor analysis with the Bayesian Black–Litterman framework enhances the stability of asset allocation and improves the risk-adjusted performance of portfolios, and can therefore serve as a practical and reliable framework for investment managers in volatile and emerging markets.
Amirhossein Soltanabadi, Ahmad Yarahmadi, H. Mohseni· Journal of Management and Bu...· 0 citations
Portfolio optimization is a fundamental aspect of investment management that focuses on constructing a portfolio capable of delivering the highest possible return while minimizing investment risk. Modern Portfolio Theory (MPT), introduced by Harry Markowitz, provides a quantitative framework for selecting an optimal combination of assets based on their expected returns, variances, and correlations. This study examines the application of Modern Portfolio Theory in optimizing investment portfolios by evaluating the trade-off between risk and return across different asset classes. Historical financial data are analyzed to estimate expected returns, standard deviations, and covariance among selected securities. The efficient frontier is generated to identify portfolios that maximize returns for a given level of risk, while diversification is employed to reduce unsystematic risk. The findings demonstrate that a well-diversified portfolio designed using MPT can significantly improve investment performance compared to investing in individual assets. The study also highlights the practical significance of portfolio optimization in assisting investors, financial analysts, and portfolio managers in making informed investment decisions aligned with their financial objectives and risk tolerance. Overall, the research emphasizes that Modern Portfolio Theory remains a valuable and effective approach for achieving efficient asset allocation and enhancing long-term portfolio performance in dynamic financial markets. Keywords: Portfolio Optimization, Modern Portfolio Theory (MPT), Investment Management, Risk-Return Trade-off, Asset Allocation, Portfolio Diversification, Efficient Frontier.
K. Naveen, Amita Johar, T. Meghana· International Journal of Dat...· 0 citations
This work exploits the auxiliary-threshold representation of CVaR to establish the existence of an optimal strategy and strong duality without requiring market completeness, and proves that the resulting strategies converge to the optimal control as the number of iterations tends to infinity.
Anran Hu, Silvana M. Pesenti, Xiaofei Shi· 0 citations
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