An Anticipative Stochastic Calculus Approach to Pricing in Markets Driven by Lévy Process
نویسنده
چکیده
We use the Itô-Ventzell formula for forward integrals and Malliavin calculus to study the stochastic control problem associated to utility indifference pricing in a market driven by Lévy processes. This approach allows us to consider general possibly non-Markovian systems, general utility functions and possibly partial information based portfolios. In the special case of the exponential utility function Uα = − exp(−αx) ; α > 0, we obtain asymptotics properties for vanishing α. In the special case of full information based portfolios and no jumps, we obtain a recursive formula for the optimal portfolio in a non-Markovian setting.
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