By Kwok-Chung Ivan, Lam
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Extra info for Indifference Pricing in a Basis Risk Model with Stochastic Volatility
E. H. Karlsen, A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets, Stochastics, 77(2), 109-137, (2005)  F. Black, M. A. H. R. A. Davis, Option hedging with basis risk, in Y. Kabanov, R. Liptser and J. Stoyanov, eds, ‘From Stochastic Calculus to Mathematical Finance’, Springer, pp. 169-187 (2006)  F. Delbaen, P. Grandits, T. Rheinl¨ainder, D. Sampieri, M. Schweizer, Ch. Stricker, Exponential hedging and entropic penalties, Mathematical Finance, 12:99-124, (2002)  F.
McWalter, Quadratic hedging of basis risk, Quantitative Finance Research Centre, Research paper 225 (2008)  J. Kallsen, T. Rheinl¨ander, Asymptotic utility-based pricing and hedging for exponential utility, Statistics & Decisions, 28, 17-36, (2011)  I. P. E. Shreve, G-L. Xu, Martingale and duality methods for utility maximization in an incomplete market, SIAM Journal of Control and Optimisation, 29:702-730 (1991)  D. Kramkov, M. C. Merton, Lifetime portfolio selection under uncertainty: the continuous-time case, Rev.
Although it is a common practice to look at exponential utility due to its ability to simplify problem in computing indiﬀerence price, it is worth noting that using such utility function removes the initial wealth dependence from the indiﬀerence price that is a desirable feature to have. As a result, it would be a good idea to consider power utility, but one can imagine the computational complexity that arose when we are considering a 4 dimensional indiﬀerence price. Also, the use of power utility in the maximization problem might pose diﬃculties in pricing short position claims.
Indifference Pricing in a Basis Risk Model with Stochastic Volatility by Kwok-Chung Ivan, Lam