A d-person differential game with state space constraints

Ramasubramanian, S. (2007) A d-person differential game with state space constraints Applied Mathematics & Optimization, 56 (3). pp. 312-342. ISSN 0095-4616

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Official URL: http://www.springerlink.com/content/t6164036717271...

Related URL: http://dx.doi.org/10.1007/s00245-007-9011-z

Abstract

We consider a network of d companies (insurance companies, for example) operating under a treaty to diversify risk. Internal and external borrowing are allowed to avert ruin of any member of the network. The amount borrowed to prevent ruin is viewed upon as control. Repayment of these loans entails a control cost in addition to the usual costs. Each company tries to minimize its repayment liability. This leads to a d-person differential game with state space constraints. If the companies are also in possible competition a Nash equilibrium is sought. Otherwise a utopian equilibrium is more appropriate. The corresponding systems of HJB equations and boundary conditions are derived. In the case of Nash equilibrium, the Hamiltonian can be discontinuous; there are d interlinked control problems with state constraints; each value function is a constrained viscosity solution to the appropriate discontinuous HJB equation. Uniqueness does not hold in general in this case. In the case of utopian equilibrium, each value function turns out to be the unique constrained viscosity solution to the appropriate HJB equation. Connection with Skorokhod problem is briefly discussed.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:d-Person Differential Game; State Space Constraints; Nash Equilibrium; Utopian Equilibrium; Dynamic Programming Principle; System Of Hjb Equations; Constrained Viscosity Solution; Semicontinuous Envelope; Deterministic Skorokhod Problem; Drift; Reflection
ID Code:52181
Deposited On:03 Aug 2011 06:45
Last Modified:03 Aug 2011 06:45

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