Risk Management in Hierarchical Games with Random Factors
A game-theoretic model of the Principal-agent type is considered, in which the result of an agent’s activity depends not only on his/her choice but also on some random factor. The Principal is assumed to choose the total probability of all negative events that he/she will exclude from consideration; in the other respects, he/she is cautious. The structure of the Principal’s optimal strategies is found. Two models differing by the Principal’s awareness of the partner’s actions are studied.
Keywordstheory of decision making hierarchical systems risk management games with random factors Value at Risk
Unable to display preview. Download preview PDF.
- 1.Markowitz, H.M., Portfolio Selection, J. Finance, 1952, vol. 7, no. 1, pp. 77–91.Google Scholar
- 2.Sharpe, W., Alexander, G.J., and Bailey, J.W., Investments, Upper Saddle River: Prentice Hall, 1994, 5th ed. Translated under the title Investitsii, Moscow: Infra-M, 1997.Google Scholar
- 3.Agasandyan, G.A., Primenenie kontinual’nogo kriteriya VAR na finansovykh rynkakh (Application of Continual Value at Risk in Financial Markets), Moscow: Vychisl. Tsentr Ross. Akad. Nauk, 2011.Google Scholar
- 4.Jorion, P., Value at Risk: The New Benchmark for Managing Financial Risk, New York: McGraw-Hill, 2006.Google Scholar
- 10.Bolton, P. and Dewatripont, M., Contract Theory, Cambridge: MIT Press, 2004.Google Scholar
- 11.Laffont, J.-J. and Martimort, D., The Theory of Incentives: The Principal-Agent Model, Cambridge: MIT Press, 2002.Google Scholar
- 17.Burkov, V.N. and Novikov, D.A., Optimal Incentive Mechanisms in Active Systems under Stochastic Uncertainty, Autom. Remote Control, 1995, vol. 56, no. 10, pp. 121–126.Google Scholar
- 19.Gorelov, M.A., The Principle of Value at Risk in a Hierarchical Game, Upravl. Bol’sh. Sist., 2018, no. 72, pp. 6–26.Google Scholar
- 20.Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional’nogo analiza (Elements of the Theory of Functions and Functional Analysis), Moscow: Nauka, 1981.Google Scholar