Bargaining and Optimal Investments

We study a problem of optimal consumption and portfolio selection in a market where the logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve pure-jump Levy processes as driving noise instead of Brownian motion like in the Black and Scholes model. The state constrained optimization problem involves the notion of local substitution and is of singular type. The associated Hamilton-Jacobi-Bellman equation is a nonlinear first order integro-differential equation subject to gradient and state constraints. We characterize the value function of the singular stochastic control problem as the unique constrained viscosity solution of the associated Hamilton-Jacobi-Bellman equation. This characterization is obtained in two main steps. First, we prove that the value function is a constrained viscosity solution of an integro-differential variational inequality. Second, to ensure that the characterization of the value function is unique, we prove a new comparison (uniqueness) result for the state constraint problem for a class of integro-differential variational inequalities. In the case of HARA utility, it is possible to determine an explicit solution of our portfolio-consumption problem when the Levy process posseses only negative jumps. This is, however, the topic of a companion paper [7].

By this study, we want to provide tools for an economic agent who wants to maintain her maximized intertemporal consumption rate over time period regularly by trading activity in capital market. She would use the diversification principle to compose portfolio that is consisted of risky and risk free assets, with initial wealth by using principle of dynamic programming in stochastic control problem. While our target function is to maximize the discounted utility function over consumption rate, the agent may use this portion of wealth for hedonistic lifestyle without thinking the bequest aim. Motivated by observation that seminal work of Samuelson (1969)’s optimal investment on risky asset was independent of time and wealth process, we were replacing the source of uncertainty in the risky asset by binomial process in order to improve Samuelson's solution. The risky asset price evolution is determined to move in two possible directions of up and down in the next time instantly with certain probability, following binomial trees scheme. Working within this setting, we manage to obtain trading strategies as explicit solution for the optimal investment and consumption decisions which were being expressed as time-dependent functions as well as wealth process feedback form. This solution goes along with inter-temporal concept that our consumption and investment strategies tomorrow will be affected with our wealth today. We exemplify the results by numerical examples and perform Monte Carlo simulation.

Portfolio is the set of assets either real or financial owned by investor. One asset used by investor is stock because the stock has various price along the period time. Nowadays, stock investments have been done by investors. Stock price can be either profit or loss so that it is required portfolio selection. From the various price of stock, we can compute the return, expected return, and the risk of stock. In this research, we will make the optimal portfolio which can result maximum return and minimum risk of stock with the available investation. Goal programming is the mathematical programming techniques to solve the objectives subject to some constraints where the there are priorities for each objective. An application of goal programming is portfolio selection. Portfolio selection is determining some stocks optimizing maximum return and minimum risk of stock with the available investation. The novelty of this research is Goal Programming as portfolio selection method will be optimized by Particle Swarm Optimization (PSO) so that it is called Particle Swarm Optimization-Goal Programming (PSOGP). In PSO, there is initialization of particle i.e. proportion of investation on each stock as decision variable. Particle must be constructed so that it can satisfy the constraint investation of all stocks. In optimization process, the new particle is also modified so that satisfying the constraints. In multiobjective optimization, sort the fitness on the value of the first priority objective. If first fitness have the same value of the objective, then sort them on the second priority objective, and so forth. Based on simulation, PSOGP can be applied on the portfolio selection and can optimize priority of some objectives.

Dividends, taxes, and normative portfolio theory

Contents: Acknowledgements General Introduction PART I HARRY M. MARKOWITZ Introduction to Part I Howard R. Vane and Chris Mulhearn 1. Harry Markowitz (1952a), 'Portfolio Selection' 2. Harry Markowitz (1952b), 'The Utility of Wealth' 3. H. Levy and H.M. Markowitz (1979), 'Approximating Expected Utility by a Function of Mean and Variance' 4. Harry M. Markowitz and Eric L. van Dijk (2003), 'Single-Period Mean-Variance Analysis in a Changing World' PART II MERTON H. MILLER Introduction to Part II Howard R. Vane and Chris Mulhearn 5. Franco Modigliani and Merton H. Miller (1958), 'The Cost of Capital, Corporation Finance and the Theory of Investment' 6. Franco Modigliani and Merton H. Miller (1959), 'The Cost of Capital, Corporation Finance and the Theory of Investment: Reply' 7. Merton H. Miller and Franco Modigliani (1961), 'Dividend Policy, Growth, and the Valuation of Shares' 8. Franco Modigliani and Merton H. Miller (1963), 'Corporate Income Taxes and the Cost of Capital: A Correction' 9. Merton H. Miller and Franco Modigliani (1966), 'Some Estimates of the Cost of Capital to the Electric Utility Industry, 1954-57' 10. Merton H. Miller (1977), 'Debt and Taxes' PART III WILLIAM F. SHARPE Introduction to Part III Howard R. Vane and Chris Mulhearn 11. William F. Sharpe (1963), 'A Simplified Model For Portfolio Analysis' 12. William F. Sharpe (1964), 'Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk' 13. William F. Sharpe (1966), 'Mutual Fund Performance' 14. William F. Sharpe (1978), 'Bank Capital Adequacy, Deposit Insurance, and Security Values' PART IV ROBERT C. MERTON Introduction to Part IV Howard R. Vane and Chris Mulhearn 15. Robert C. Merton (1969), 'Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case' 16. Robert C. Merton (1971), 'Optimum Consumption and Portfolio Rules in a Continuous-Time Model' 17. Robert C. Merton (1973a), 'Theory of Rational Option Pricing' 18. Robert C. Merton (1973b), 'An Intertemporal Capital Asset Pricing Model' 19. Robert C. Merton (1974), 'On the Pricing of Corporate Debt: The Risk Structure of Interest Rates' 20. Robert C. Merton (1977), 'On the Pricing of Contingent Claims and the Modigliani-Miller Theorem' PART V MYRON S. SCHOLES Introduction to Part V Howard R. Vane and Chris Mulhearn 21. Fischer Black and Myron Scholes (1972), 'The Valuation of Option Contracts and a Test of Market Efficiency' 22. Fischer Black and Myron Scholes (1973), 'The Pricing of Options and Corporate Liabilities' 23. Fischer Black and Myron Scholes (1974), 'The Effects of Dividend Yield and Dividend Policy on Common Stock Prices and Returns' 24. Myron Scholes and Joseph Williams (1977), 'Estimating Betas from Nonsynchronous Data' 25. Merton H. Miller and Myron S. Scholes (1978), 'Dividends and Taxes' Name Index

Optimal Portfolio Selection in Ex Ante Stock Price Bubble and Furthermore Bubble Burst Scenario from Dhaka Stock Exchange with Relevance to Sharpe’s Single Index Model

The question how to optimize consumption and portfolio choice over the life cycle has been widely discussed in the literature so far. In this paper we concentrate on a retiree's optimal consumption and portfolio selection over his remaining years of life. We apply the logistic model of mortality thus modeling the empirically observed increase of mortality during the retirement period. The optimal consumption strategy and portfolio choice are established by reducing the Hamilton-Jacobi-Bellmann equation to the explicit solution of an ordinary differential function (ODF) that includes the mortality rate. A general finding is that the Merton-Samuelson result of constant portfolio choice for a constant mortality is confirmed for arbitrary mortality. The portfolio choice is only influenced by risk and return of assets and the retirees’ risk aversion. To get the specific optimal consumption strategy in a realistic situation the logistic model of mortality has been fitted to the data of the Statistical Yearbook for the Federal Republic of Germany 2006/2008. The optimal initial value for the ODF is obtained by numerical methods. The solution provides a large increase in the ratio of optimal consumption to wealth up to about 92 years followed by a sharp decrease. A bequest motive dampens the magnitudes of the ups and downs of the consumption ratio but does not change the basic shape.

In a typical capital rationing problem, a project portfolio is selected to maximize expected return on investment while adhering to the capital budget constraint. Sometimes projects may be delayed and they have to be funded beyond their planned completion time. This type of ‘unplanned carryovers’ represents a financial obligation to the company. If future years' capital budgets cannot be expanded to cover such obligations, future projects may be cancelled or postponed to fund the unplanned carryover. In this paper, we develop a methodology based on multi-attribute utility theory and chance-constrained programming to optimize portfolio selection subject to the constraints that the selected portfolio does not exceed the available budget and that the carryover of the unspent funds to the next fiscal year does not exceed predetermined limits. We use this technique to select an optimal project portfolio for Lockheed Martin Space Systems' infrastructure investments.

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Mean-variance portfolio optimization is widely used by financial professionals as a fundamental strategy for constructing portfolios that achieve the highest returns for a given degree of risk tolerance. This traditional approach suffers from computational instability issues, which are often solved by integrating regularization-based methods. However, regularized mean-variance models overlook sector considerations, emphasizing a need for market-informed portfolio optimization. In this paper, we propose an extended mean-variance portfolio selection framework that incorporates a new adaptive sparse-group least absolute shrinkage and selection operator (LASSO) regularization as a penalty parameter. In the proposed model, the sparse optimal portfolio is selected considering both sectors and assets simultaneously. Moreover, the inclusion of adaptive weights in the regularization, estimated based on chosen criteria, enables the use of more market data in a Markowitz portfolio model. We also develop an efficient alternating direction method of multipliers (ADMM) algorithm that guarantees convergence, for finding the optimal sparse portfolio. The effectiveness of the suggested portfolio selection model is validated by numerical results derived from the constituents of the Standard and Poor’s 500. These results demonstrate superior performance over our selected benchmark models across various evaluation measurements.

The study proposes to include the financial analysis (FA) in optimal portfolio selection. The role of FA in investment decisions is well recognized. While comparing two stocks on FA of their companies it is important to have both drawn from the same sector of economy. This reason motivated us to propose a sectoral portfolio optimization (SPO) which, instead of looking to optimize among all stocks together, focuses on optimizing stocks within each sector on the basis of FA. These stocks are then pooled together and an optimal portfolio is formed from them with their FA weights and mean returns. In context of FA, the four financial ratios included in present study are return on asset (profitable ratio), debt-assets ratio (solvency ratio), current ratio (liquidity ratio), and price-to-earning ratio (valuation ratio). The risk in a portfolio is quantified using the second order stochastic dominance and to this effect constraints are added in the selection process to generate optimal portfolios for rational risk averse investors. The performance of the optimal portfolios from the proposed model is tested against the portfolios from the traditional second order stochastic dominance model [named (SSDP) in this work], the benchmark index and four 5-star rated mutual funds of India from diversified equity. The out-of-sample analysis is carried on mean returns, Sharpe ratio, Sortino ratio, and also their ability to dominate the benchmark index in almost second order stochastic dominance sense over the tolerable violation regions. The stock price data for the period April 2004 to November 2014 of S&P BSE 500 index is used for testing the models. The optimal portfolios generated from the SPO perform better than the portfolios generated from the (SSDP), the benchmark index and the MFs, indicating effectiveness of FA in SPO framework.

The purpose of this study was to examine Mean-Gini strategy (MG) and Mean-Extended Gini strategy (MEG) for optimum portfolio selection, in terms of the monthly Rate of Return, Standard Deviation, Sharpe Ratio, Treynor Ratio and Jensen’s Alpha. This paper compared different optimum portfolio strategies, based on Moroccan financial market data taken from turbulent market periods between the years 2007 to 2015. Two distinct sub-periods were studied: (1) crisis period: 2007-2009; (2) post-crisis period: 2010-2015. The results show that both strategies were profitable for investors, but that the MEG strategy is the more appropriate and secure strategy for an individual investor.

We present a new urban transit investment model, integrating transport economic theory regarding optimal investment with transport modeling, planning, and network design. The model expands on the theory of optimal transit network planning and investment, accounting for the effects of the investment on accessibility, level of service, and speed. The model seeks long-term optimal transit investment and optimal road pricing simultaneously in an integrated, unified model. To illustrate the advantages of our approach, we applied our empirical model to two case studies, Tel Aviv and Toronto, integrating our theoretical contribution into practice. Our results demonstrate the model’s ability to indicate the optimal transit mode and investment on a corridor level and the total investment required for the city transit network. The model results were compared to the actual and planned transit networks of Tel Aviv and Toronto and showed the model’s capability to produce a good balance of strategic design and network details. The research concludes that applying the right toll with the applicable transit investment is crucial for obtaining an efficient network and performance. This research can direct planners and policymakers in planning urban transport and provide a comprehensive set of guidelines for optimizing the simultaneous investment in mass transit and the congestion toll toward more sustainable cities and transportation systems.

Because the investment market in real life is complex and mobile, there are many other factors to consider when meeting the risk and income equilibrium, such as transaction cost, diversification degree and so on. To simulate the real transactions in financial market, multiple decision criteria in portfolio selection should be considered to provide investors with additional choices. This paper discusses a multi-objective portfolio optimization problem for practical portfolio selection in fuzzy environment, in which the return rates and the turnover rates are characterized by fuzzy variables. Under the premise of meeting the two wishes level of investors’ maximum and minimum risk, we assume that the rate of return is a fuzzy variable, and get the corresponding fuzzy portfolio optimization model. What’s more, we apply a particle swarm optimization algorithm to solve the proposed multi-period fuzzy portfolio selection models. To reflect investor’s aspiration levels for the two objectives, a fuzzy decision technique is employed to transform the proposed model into a single objective mixed-integer nonlinear programming problem. Finally, a numerical example is given to illustrate the application of our models. Comparative results show that the designed algorithm is effective for solving the proposed models.

The main objective of this research is to form an optimal investment portfolio consisting of a number of stocks selected according to specific criteria in Amman Stock Exchange and to test the ability of a various economic models to predict the performance of this portfolio in the foreseeable future. A time series for the return of the selected portfolio and for the return of a market index are formed. A set of tests were conducted to reach a stationary time series return and, then, to follow the Box-Jenkins methodology in order to build predictive models (ARMA) and to examine the residuals of models and to model them using ARCH and GARCH models to reach the best prediction of the performance of the portfolio and the market index in the forecasted periods. The data were tracked on a daily basis for the study sample and the market index simultaneously for a period of three years. Twenty-one companies were selected in the investment portfolio distributed among several sectors. The study concluded that the formed portfolio achieved a good diversification and gave a high return in relation to the lowest possible risk according to the Sharpe scale. Also, it is concluded that the model ARMA (1,1) is the most suitable for estimating market portfolio returns and forecasting risks for the market index return, and ARMA (2,1) and the model ARMA - GARCH are the most capable one of achieving good results that can be relied upon in tracking the performance of the studied investment portfolio.