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A variational approach to the financial problem with insolvencies and analysis of the contagion. (English) Zbl 1443.91317

Rassias, Themistocles M. (ed.) et al., Mathematical analysis and applications. Cham: Springer. Springer Optim. Appl. 154, 17-40 (2019).
Summary: In this chapter we improve some results in literature on the general financial equilibrium problem related to individual entities, called sectors, which invest in financial instruments as assets and as liabilities. Indeed the model, studied in the chapter, takes into account the insolvencies and we analyze how these insolvencies affect the financial problem. For this improved model we describe a variational inequality for which we provide an existence result. Moreover, we study the dual Lagrange problem, in which the Lagrange variables, which represent the deficit and the surplus per unit, appear and an economical indicator is provided. Finally, we perform the contagion by means of the deficit and surplus variables. As expected, the presence of the insolvencies makes it more difficult to reach the financial equilibrium and increases the risk of a negative contagion for all the systems.
For the entire collection see [Zbl 1432.65003].

MSC:

91G45 Financial networks (including contagion, systemic risk, regulation)
49J40 Variational inequalities
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[1] A. Barbagallo, P. Daniele, S. Giuffrè, A. Maugeri, Variational approach for a general financial equilibrium problem: The Deficit Formula, the Balance Law and the Liability Formula. A path to the economy recovery. Eur. J. Oper. Res. 237(1), 231-244 (2014) · Zbl 1304.91248 · doi:10.1016/j.ejor.2014.01.033
[2] J.M. Borwein, V. Jeyakumar, A.S. Lewis, M. Wolkowicz, Constrained approximation via convex programming, University of Waterloo (1988). Preprint
[3] R.I. Bot, E.R. Csetnek, A. Moldovan, Revisiting some duality theorems via the quasirelative interior in convex optimization. J. Optim. Theory Appl. 139(1), 67-84 (2008) · Zbl 1189.90117 · doi:10.1007/s10957-008-9412-4
[4] V. Caruso, P. Daniele, A network model for minimizing the total organ transplant costs. Eur. J. Oper. Res. 266(2), 652-662 (2018) · Zbl 1403.90667 · doi:10.1016/j.ejor.2017.09.040
[5] G. Colajanni, P. Daniele, S. Giuffrè, A. Nagurney, Cybersecurity investments with nonlinear budget constraints and conservation laws: variational equilibrium, marginal expected utilities, and Lagrange multipliers. Int. Trans. Oper. Res. 25(5), 1415-1714 (2018) · Zbl 1410.90008 · doi:10.1111/itor.12502
[6] G. Colajanni, P. Daniele, S. Giuffrè, A. Maugeri, Nonlinear duality in Banach spaces and applications to finance and elasticity, in Applications of Nonlinear Analysis, ed. by Th. M. Rassias. Springer Optimization and Its Applications, vol. 134 (Springer, New York, 2018), pp. 101-139 · Zbl 1405.49026 · doi:10.1007/978-3-319-89815-5_5
[7] P. Daniele, Dynamic Networks and Evolutionary Variational Inequalities (Edward Elgar Publishing, Cheltenham, 2006) · Zbl 1117.49002
[8] P. Daniele, Evolutionary variational inequalities and applications to complex dynamic multi-level models. Transport. Res. Part E 46, 855-880 (2010) · doi:10.1016/j.tre.2010.03.005
[9] P. Daniele, S. Giuffrè, General infinite dimensional duality and applications to evolutionary network equilibrium problems. Optim. Lett. 1, 227-243 (2007) · Zbl 1151.90577 · doi:10.1007/s11590-006-0028-z
[10] P. Daniele, S. Giuffrè, Random variational inequalities and the random traffic equilibrium problem. J. Optim. Theory Appl. 167(1), 363-381 (2015) · Zbl 1329.49015 · doi:10.1007/s10957-014-0655-y
[11] P. Daniele, S. Giuffrè, S. Pia, Competitive financial equilibrium problems with policy interventions. J. Ind. Manag. Optim. 1(1), 39-52 (2005) · Zbl 1140.91382 · doi:10.3934/jimo.2005.1.39
[12] P. Daniele, S. Giuffrè, G. Idone, A. Maugeri, Infinite dimensional duality and applications. Math. Ann. 339, 221-239 (2007) · Zbl 1356.49064 · doi:10.1007/s00208-007-0118-y
[13] P. Daniele, S. Giuffrè, A. Maugeri, Remarks on general infinite dimensional duality with cone and equality constraints. Commun. Appl. Anal. 13(4), 567-578 (2009) · Zbl 1209.90289
[14] P. Daniele, S. Giuffrè, M. Lorino, A. Maugeri, C. Mirabella, Functional inequalities and analysis of contagion in the financial networks, in Handbook of Functional Equations - Functional Inequalities, ed. by Th.M. Rassias. Optimization and Its Applications, vol. 95 (Springer, New York, 2014), pp. 129-146 · Zbl 1315.39015
[15] P. Daniele, S. Giuffrè, A. Maugeri, F. Raciti, Duality theory and applications to unilateral problems. J. Optim. Theory Appl. 162(3), 718-734 (2014) · Zbl 1322.90111 · doi:10.1007/s10957-013-0512-4
[16] P. Daniele, S. Giuffrè, M. Lorino, Functional inequalities, regularity and computation of the deficit and surplus variables in the financial equilibrium problem. J. Glob. Optim. 65, 575-596 (2016) · Zbl 1343.91047 · doi:10.1007/s10898-015-0382-4
[17] P. Daniele, M. Lorino, C. Mirabella, The financial equilibrium problem with a Markowitz-type memory term and adaptive, constraints. J. Optim. Theory Appl. 171, 276-296 (2016) · Zbl 1351.90061 · doi:10.1007/s10957-016-0973-3
[18] K. Forbes, The “Big C”: Identifying contagion. NBER Working Paper No. 18465, 2012
[19] S. Giuffrè, Strong solvability of boundary value contact problems. Appl. Math. Optim. 51(3), 361-372 (2005) · Zbl 1125.35045 · doi:10.1007/s00245-004-0817-7
[20] S. Giuffrè, A. Maugeri, New results on infinite dimensional duality in elastic-plastic torsion. Filomat 26(5), 1029-1036 (2012) · Zbl 1289.74042 · doi:10.2298/FIL1205029G
[21] S. Giuffrè, A. Maugeri, Lagrange multipliers in elastic-plastic torsion, in AIP Conference Proceedings, Rodi, September 2013, vol. 1558, pp. 1801-1804
[22] S. Giuffrè, A. Maugeri, A measure-type Lagrange multiplier for the elastic-plastic torsion. Nonlinear Anal. 102, 23-29 (2014) · Zbl 1511.35342 · doi:10.1016/j.na.2014.01.023
[23] S. Giuffrè, S. Pia, Weighted traffic equilibrium problem in non pivot Hilbert spaces with long term memory, in AIP Conference Proceedings, Rodi, September 2010, vol. 1281, 2010, pp. 282-285
[24] S. Giuffrè, G. Idone, A. Maugeri, Duality theory and optimality conditions for generalized complementary problems. Nonlinear Anal. 63, e1655-e1664 (2005) · Zbl 1224.90194 · doi:10.1016/j.na.2004.12.019
[25] S. Giuffrè, A. Maugeri, D. Puglisi, Lagrange multipliers in elastic-plastic torsion problem for nonlinear monotone operators. J. Differ. Equ. 259(3), 817-837 (2015) · Zbl 1319.35258 · doi:10.1016/j.jde.2015.02.019
[26] S. Giuffrè, A. Pratelli, D. Puglisi, Radial solutions and free boundary of the elastic-plastic torsion problem. J. Convex Anal. 25(2), 529-543 (2018) · Zbl 1465.35416
[27] R.B. Holmes, Geometric Functional Analysis (Springer, Berlin, 1975) · Zbl 0336.46001
[28] G. Idone, A. Maugeri, Generalized constraints qualification and infinite dimensional duality. Taiwan. J. Math. 13, 1711-1722 (2009) · Zbl 1223.90040 · doi:10.11650/twjm/1500405610
[29] V. Jeyakumar, H. Wolkowicz, Generalizations of slater constraint qualification for infinite convex programs. Math. Program. 57, 85-101 (1992) · Zbl 0771.90078 · doi:10.1007/BF01581074
[30] A. Maugeri, D. Puglisi, On nonlinear strong duality and the infinite dimensional Lagrange multiplier rule. J. Nonlinear Convex Anal. 18(3), 369-378 (2017) · Zbl 1392.49038
[31] H.M. Markowitz, Portfolio selection. J. Finan. 7, 77-91 (1952)
[32] H.M. Markowitz, Portfolio Selection: Efficient Diversification of Investments (Wiley, New York, 1959)
[33] A. Maugeri, F. Raciti, Remarks on infinite dimensional duality. J. Global Optim. 46, 581-588 (2010) · Zbl 1198.90390 · doi:10.1007/s10898-009-9442-y
[34] A. Maugeri, L. Scrimali, New approach to solve convex infinite-dimensional bilevel problems: application to the pollution emission price problem. J. Optim. Theory Appl. 169(2), 370-387 (2016) · Zbl 1339.49009 · doi:10.1007/s10957-016-0894-1
[35] A. Nagurney, J. Dong, M. Hughes, Formulation and computation of general financial equilibrium. Optimization 26, 339-354 (1992) · Zbl 0817.90005 · doi:10.1080/02331939208843862
[36] R.
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