A stochastic target approach for P&L matching problems
Bouchard, Bruno; Vu, Thanh Nam (2012), A stochastic target approach for P&L matching problems, Mathematics of Operations Research, 37, 3, p. 526-558. http://dx.doi.org/10.1287/moor.1120.0549
TypeArticle accepté pour publication ou publié
Journal nameMathematics of Operations Research
Institute of Management Sciences
MetadataShow full item record
Abstract (EN)Within a Brownian diffusion Markovian framework, we provide a direct PDE characterization of the minimal initial endowment required so that the terminal wealth of a financial agent (possibly diminished by the payoff of a random claim) can match a set of constraints in probability. Such constraints should be interpreted as a rough description of a targeted profit and loss (P&L) distri- bution. This allows to give a price to options under a P&L constraint, or to provide a description of the discrete P&L profiles that can be achieved given an initial capital. This approach provides an alternative to the standard utility indifference (or marginal) pricing rules which is better adapted to market practices. From the mathematical point of view, this is an extension of the stochastic target problem under controlled loss, studied in Bouchard, Elie and Touzi (2009), to the case of multiple constraints. Although the associated Hamilton-Jacobi-Bellman operator is fully discontinuous, and the terminal condition is irregular, we are able to construct a numerical scheme that converges at any continuity points of the pricing function.
Subjects / KeywordsQuantile Hedging; Discontinuous viscosity solutions; Stochastic target problem
Showing items related by title and author.
Generalized stochastic target problems for pricing and partial hedging under loss constraints - Application in optimal book liquidation Bouchard, Bruno; Dang, Ngoc Minh (2013) Article accepté pour publication ou publié