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Register a new userSub- and Super-solution Approach to Accuracy Analysis of Portfolio Optimization Asymptotics in Multiscale Stochastic Factor Market
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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 accuracy analysis for cases with general utility functions and two timescale factors by constructing sub- and super-solutions to the fully nonlinear problem such that their difference is at the desired level of accuracy. This approach will be valuable in various related stochastic control problems.
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This paper studies a robust portfolio optimization problem under the multi-factor volatility model introduced by Christoffersen et al. (2009). The optimal strategy is derived analytically under the worst-case scenario with or without derivative trading. To illustrate the effects of ambiguity, we compare our optimal robust strategy with some strategies that ignore the information of uncertainty, and provide the corresponding welfare analysis. The effects of derivative trading to the optimal portfolio selection are also discussed by considering alternative strategies. Our study is further extended to the cases with jump risks in asset price and correlated volatility factors, respectively. Numerical experiments are provided to demonstrate the behavior of the optimal portfolio and utility loss.
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Fractional stochastic volatility models have been widely used to capture the non-Markovian structure revealed from financial time series of realized volatility. On the other hand, empirical studies have identified scales in stock price volatility: both fast-time scale on the order of days and slow-scale on the order of months. So, it is natural to study the portfolio optimization problem under the effects of dependence behavior which we will model by fractional Brownian motions with Hurst index $H$, and in the fast or slow regimes characterized by small parameters $eps$ or $delta$. For the slowly varying volatility with $H in (0,1)$, it was shown that the first order correction to the problem value contains two terms of order $delta^H$, one random component and one deterministic function of state processes, while for the fast varying case with $H > half$, the same form holds at order $eps^{1-H}$. This paper is dedicated to the remaining case of a fast-varying rough environment ($H < half$) which exhibits a different behavior. We show that, in the expansion, only one deterministic term of order $sqrt{eps}$ appears in the first order correction.
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