Abstract
The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal strategies in the regime where these factors are running on both slow and fast timescales. However, the rigorous justification of the accuracy of these approximations has been limited to power utilities and a single factor. In this paper, we provide an accurate analysis for cases with general utility functions and two timescale factors by constructing sub- and supersolutions to the fully nonlinear problem so that their difference is at the desired level of accuracy. This approach will be valuable in various related stochastic control problems.
Original language | English (US) |
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Pages (from-to) | 109-128 |
Number of pages | 20 |
Journal | SIAM Journal on Financial Mathematics |
Volume | 13 |
Issue number | 1 |
DOIs | |
State | Published - 2022 |
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Finance
- Applied Mathematics
Keywords
- portfolio optimization
- rigorous asymptotics
- stochastic volatility
- subsolution
- supersolution
- utility maximization