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|Abstract:||© 2016 Society for Industrial and Applied Mathematics. We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expan sion techniques, we derive approximations for both the value function and the optimal investment s trategy. We also analyze the "implied Sharpe ratio" and derive a series approximation for this quan tity. The zeroth order approximation of the value function and optimal investment strategy correspond to those obtained by [Merton, Rev. Econ. Statist., 51, pp. 247-257] when the risky asset follows a geometric Brownian motion. The first order correction of the value function can, for general utility functions, be expressed as a differential operator acting on the zeroth order term. For power utility functions, higher order terms can also be computed as a differential operator acting on the zeroth order term. While our approximations are derived formally, we give a rigorous accuracy bound for the higher order approximations in this case in pure stochastic volatility models. a number of examples are provided in order to demonstrate numerically the accuracy of our approximations.|
|Citation:||Lorigt, M, Sircar, R. (2016). Portfolio optimization under local-stochastic volatility: Coefficient taylor series approximations and implied sharpe ratio. SIAM Journal on Financial Mathematics, 7 (1), 418 - 447. doi:10.1137/15M1027073|
|Pages:||418 - 447|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||SIAM Journal on Financial Mathematics|
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