Recent results on a general financial equilibrium problem

The Financial Equilibrium Problem with a Markowitz-Type Memory Term and Adaptive Constraints

“…In order to determine the equilibrium prices, we establish the equilibrium condition which expresses the equilibration of the total assets, the total liabilities and the portion of financial transactions per unit F j employed to cover the expenses of the financial institutions including possible dividends, as in [1][2][3]. Hence, the equilibrium condition for the price r j of instrument j is the following:…”

“…To each financial volume s i and l i held by sector i, we associate the functions μ (1) i (t), μ (2) i (t), related, respectively, to the assets and to the liabilities and which represent the "equilibrium disutilities" per unit of sector i. Then, (6) and (8) mean that the financial volume invested in instrument j as assets x * i j is greater than or equal to zero if the jth component…”

“…In the previous papers [1][2][3], where the authors deal with the financial equilibrium problem, they assume that significant utility functions there exist and provide the properties they need to have in order to ensure the existence of solutions to the financial equilibrium problem. This paper aims at covering a lack providing the existence of a significant evolutionary measure of the risk, which satisfies all the assumptions This evolutionary financial measure of the risk is obtained by generalizing the celebrated measure of the financial risk introduced by Markowitz in [4,5] in the stationary setting.…”

“…Then, such a concrete example of evolutionary risk measure of Markowitz type allows us to be sure that in the previous papers [1][2][3], we are not working on empty sets. Of course, the evolutionary measure is interesting in itself because we can see how to pass from the stationary to the evolutionary case.…”