Jensen's inequality connected with a double random good

In this paper, we define a multiple random good of order 2 denoted by X12 whose possible values are of a monetary nature. A two-risky asset portfolio is a multiple random good of order 2. It is firstly possible to establish its expected return by using a linear and quadratic metric. We secondly establish the expected return on X12 denoted by P(X12) by using a multilinear and quadratic metric. An extension of the notion of mathematical expectation of X12 is carried out by using the notion of α-norm of an antisymmetric tensor of order 2. An extension of the notion of variance of X12 denoted by Var(X12) is shown by using the notion of α-norm of an antisymmetric tensor of order 2 based on changes of origin. An extension of the notion of expected utility connected with X12 is considered. An extension of Jensen’s inequality is shown as well. We focus on how the decision-maker maximizes the expected utility connected with multiple random goods of order 2 being chosen by her under conditions of uncertainty and riskiness