# Portfolio Optimization under Local-Stochastic Volatility: Coefficient Taylor Series Approximations & Implied Sharpe Ratio

*Matthew Lorig* and
*Ronnie Sircar*

Papers from arXiv.org

**Abstract:**
We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the `implied Sharpe ratio' and derive a series approximation for this quantity. The zeroth-order approximation of the value function and optimal investment strategy correspond to those obtained by Merton (1969) 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. 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.

**New Economics Papers:** this item is included in nep-upt

**Date:** 2015-06

**References:** View references in EconPapers View complete reference list from CitEc

**Citations** View citations in EconPapers (1) Track citations by RSS feed

**Downloads:** (external link)

http://arxiv.org/pdf/1506.06180 Latest version (application/pdf)

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:arx:papers:1506.06180

Access Statistics for this paper

More papers in Papers from arXiv.org

Series data maintained by arXiv administrators ().