Portfolio benchmarking under drawdown constraint and stochastic sharpe ratio

We consider an investor who seeks to maximize her expected utility of wealth relative to a benchmark, or target over a finite time horizon, and under a portfolio drawdown constraint, in a market with local stochastic volatility. We propose a new investor objective paradigm which allows the investor to target the portfolio benchmark while obeying the constraint, both of which can be characterized in terms of the running maximum wealth process. In the absence of closed-form formulas for the value function and optimal portfolio strategy in the incomplete market models we consider, we obtain approximations for these quantities through the use of a coefficient expansion technique and nonlinear transformations. We utilize regularity properties of the risk tolerance function to numerically compute the estimates for our approximations. In order to achieve similar utility, compared to a constant volatility model, we illustrate that the investor must deploy a quite different portfolio strategy which depends on the current level of volatility

Using Rough logic for predicting price movements on financial markets

Financial markets and especially their movements are very difficult to predict. For this reason, it cannot be clearly concluded what market will do. We cannot use basic logical operators such as if A happens, then comes B. Since we cannot use simple decision rules and we work in high uncertainty we cannot easily build classical mathematical model because of uncertainty of each and every result. However to analyze this type of data we can used Rough logic which is design to work with uncertainty. The aim of this thesis is use of Rough logic to create a mathematical model, which will be able to some extent to understand and eventually predict individual market movements. Market uncertainty Purpose of the article: Using Rough logic for predicting price movements. Scientific aim: Rough Set. Conclusions: Methodology for using Rough set in financial markets

The Variance-Covariance model as a decision support for chartered financial analysts in portfolio optimization: O modelo de Variance-Covariance como suporte à decisão para analistas financeiros certificados na otimização de portfólio

This study proposes the Variance-Covariance model to improve decision-making regarding the creation and optimization of an investment portfolio made by Chartered Financial Analysts. To optimize an investment portfolio, these specialists must find, given some profitability, how much they should invest in each of the selected stocks to minimize risk. This is typically achieved using the Mean-Variance model proposed by Harry Markowitz. However, it is observed that the use of the Mean-Variance model does not always lead to an expedited selection of shares that make up an investment portfolio. This is because the behaviour of the portfolio components cannot often be assessed with sufficient confidence in their trends. Financial analysts regularly prefer to compose their portfolios so that not all stocks follow the same direction to achieve greater peace of mind in bearish markets. Thus, in this work, the Variance-Covariance mathematical model is proposed as a complement to charting to support the decision criteria regarding portfolio diversification due to adverse conditions in the stock markets. We elaborate on the hypothesis that financial analysts using the Variance-Covariance matrix will achieve better financial decisions in less time-consuming