Mathematics – Probability
Scientific paper
2010-09-06
Mathematics
Probability
21 pages
Scientific paper
This paper first studies super linear G-expectation. Uniqueness and existence theorem for backward stochastic differential equations (BSDEs) under super linear expectation is established to provide probabilistic interpretation for the viscosity solution of a class of Hamilton-Jacobi-Bellman equations, including the well known Black-Scholes-Barrenblett equation, arising in the uncertainty volatility model in mathematical finance. We also show that BSDEs under super linear expectation could characterize a class of stochastic control problems. A direct connection between recursive super (sub) strategies with mutually singular probability measures and classical stochastic control problems is provided. By this result we give representation for solutions of Black-Scholes-Barrenblett equations and G-heat equations.
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