On Imprecise Investment Recommendations

Abstract

Abstract. The return rate is considered here as a fuzzy probabilistic set. Then the expected return is obtained as a fuzzy subset in the real line. This result is a theoretical foundation for new investment strategies. All considered strategies result of comparison profit fuzzy index and limit value. In this way we obtain an imprecise investment recommendation. Financial equilibrium criteria are a special case of comparison of the profit index and the limit value. The following criteria are generalized here: the Sharpe's Ratio, the Jensen's Alpha and the Treynor's Ratio. Moreover, the safety-first criteria are generalized here for the fuzzy case. The Roy Criterion, the Kataoka Criterion and the Telser Criterion are also generalized. Obtained results show that proposed theory is useful for the investment applications.

Catastrophe bond pricing for the two-factor Vasicek interest rate model with automatized fuzzy decision making

“…We apply an approach similar to the one used in Piasecki (2014) in another context. We obtain a fuzzy set of possible decisions.…”

Representation of Japanese Candlesticks by Oriented Fuzzy Numbers

“…. Different methods of determining numbers S 1 , S 2 and estimating the probabilities (31) and (32) are discussed in (Marszałek and Burczyński 2013a, 2013b, 2014. However, in all the examples given there we observe that:…”

“…Let fixed security be given as Y quoted in the assumed time period [0, T], Marszałek and Burczyński (2013a, 2013b, 2014 consider the observed quotation trend Q : [0, T] → R + as a realization of random variable. Considered security, Y, can be represented by the following parameters: the open price P o , the close price P c , the high price P h , and the low price P l .…”

“…In our opinion, OFCs are an excellent short record of quotation volatility. In (Marszałek and Burczyński 2013a, 2013b, 2014, it is shown that OFC is very useful for financial decision making. Unfortunately, OFC does not save information about the low price P l and high price P h .…”

“…Using the disorientation map (34), we can convert any oriented expected rate to fuzzy return rate. Then, JCs may be applied in fuzzy portfolio analysis (Fang et al 2008;Gupta et al 2014) or in (Piasecki 2014). (6.17, 6.18, 6.38, 6.47).…”