Reflected backward stochastic differential equations and a class of non linear dynamic pricing rule

Details Reflected backward stochastic differential equations and a class of non linear dynamic pricing rule Reflected backward stochastic differential equations and a class of non linear dynamic pricing rule

2008-02-15

arxiv.org/abs/0802.2172v2

Economy

Quantitative Finance

Pricing of Securities

20 pages, partial modification of the content

Scientific paper

In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver $g$ is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of $g$-Snell enveloppe. Then, in a second step, we relate this representation to a specific class of dynamic monetary concave functionals already introduced in a discrete time setting. This connection implies that the solution, characterized by means of non linear expectations, has again the time consistency property.

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