The Mathematical Institute, University of Oxford, Eprints Archive

Malliavin calculus method for asymptotic expansion of dual control problems

Monoyios, Michael (2013) Malliavin calculus method for asymptotic expansion of dual control problems. SIAM Journal on Financial Mathematics, 4 . pp. 884-915.

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Abstract

We develop a technique based on Malliavin-Bismut 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 It\^o 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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