Abstract: We are concerned with different properties of BSDE and their applications in finance. These equations, first introduced by Pardoux and Peng (1990) are useful for the theory of contingent claim valuation, especially cases with constraint and for the theorie of recursive utilities, introduced by Duffie and Epstein (1992)

Abstract:

Abstract: We combine the formulation of Mandelbaum [Mandelbaum, A. (1986) Probab. Theory Rel. Fields 71, 129-147] with ideas from Whittle [Whittle, P. (1980) J. R. Stat. Soc. B 42, 143-149] to obtain a simple and constructive proof for the optimality of Gittins index processes in the general, nonmarkovian dynamic allocation (or "multi-armed bandit") problem. Our approach also provides an explicit expression for the value of this problem.