A Stochastic Differential Game in the Orthrant

Abstract

We study a zero-sum stochastic differential game in the nonnegative orthrant. The state of the system is governed by controlled reflecting diffusions in the nonnegative orthrant. We consider discounted and average payoff evaluation criteria. We prove the existence of values and optimal strategies for both payoff criteria.  2002 Elsevier Science

Dynamic asset management with risk-sensitive criterion and non-negative factor constraints: a differential game approach

“…where C(l 0 ,T,D l ) is independent of m. Now using the standard approximation procedure see for example [10], we can show that (4.7) has a solution in…”

“…For a specific construction of D m see [10]. We assume that (A1) The function g is bounded continuous and there exists d .…”

A nonzero-sum risk-sensitive stochastic differential game in the orthant

“…x is the probability measure on the space over which X(•) is a weak solution of (1) corresponding to a strategy pair (v 1 , v 2 ) and initial state x. We refer [23], [24], [37] for sufficient conditions ensuring (A2).…”

“…The process ξ(•) changes only when X(•) hits ∂D. Such processes arise in many applications including the heavy traffic analysis of queuing networks coming from problems in manufacturing systems and communications (see [13], [15], [23], [31]). Since except for a few special cases, the direct analysis of problems in queuing network are very difficult to analyze, one tries to find a continuous approximation of it which can provide a tractable solution.…”

“…It is known that (see [23], [22]) in a typical communication network there are several users, and different users may have different objectives leading to conflicts. In view of this, the analysis of such problems is often carried out using game theoretic framework.…”