Monoyios, Michael (2013) Malliavin calculus method for asymptotic expansion of dual control problems. SIAM Journal on Financial Mathematics, 4 . pp. 884915.

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Abstract
We develop a technique based on MalliavinBismut calculus ideas, for asymptotic expansion of dual control problems arising in connection with exponential indifference valuation of claims, and with minimisation of relative entropy, in incomplete markets. The problems involve optimisation of a functional of Brownian paths on Wiener
space, with the paths perturbed by a drift involving the control. In addition there is a penalty term in which the control features quadratically. The drift perturbation is interpreted as a measure change using the Girsanov theorem, leading to a form of the integration by parts formula in which a directional derivative on Wiener space is computed. This allows for asymptotic analysis of the control problem. Applications to incomplete Ito process markets are given, in which indifference prices are approximated in the low risk aversion limit. We also give an application to identifying the minimal entropy martingale measure as a perturbation to the minimal martingale measure in stochastic volatility models.
Item Type:  Article 

Subjects:  O  Z > Probability theory and stochastic processes 
Research Groups:  Mathematical and Computational Finance Group 
ID Code:  1877 
Deposited By:  Professor Michael Monoyios 
Deposited On:  26 Feb 2015 08:46 
Last Modified:  29 May 2015 19:34 
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