Robust time-consistent mean–variance portfolio selection problem with multivariate stochastic volatility

Robust equilibrium strategy for mean-variance-skewness portfolio selection problem

“…Pun [29] establishes a general analytical framework for continuous-time stochastic control problems for an ambiguity-averse agent with time-inconsistent preference. Similar investigations and results of robust portfolio selection can be also found in [7,8,32,34,35,36].…”

“…Recall that there exists a state variable Z in the financial market, which can be used to describe the dynamics of stochastic volatility, stochastic interest rate, regime switching and so on [34,41]. Therefore, it would be interesting to consider some specific cases with additional state variable Z and attempt to derive the (semi-)closed form solutions.…”

“…First, wealth-dependent risk aversion, skewness preference with wealth-dependent coefficient and model uncertainty are introduced into the mean-variance portfolio problem and then a new robust investment model is established, which extends the models investigated in [27,29]. Specially, the wealth-dependent risk aversion, wealth-dependent skewness preference and ambiguity-aversion could be dependent, while some studies (see, for example, [34,38]) only consider the independent case of risk aversion and ambiguity-aversion for simplic-ity. Second, the detailed verification of the admissibility of our newly derived robust equilibrium investment strategy is given, which makes our paper more complete from a mathematical point of view, whereas neither [27] nor [29] verifies it.…”

Robust Consumption Portfolio Optimization with Stochastic Differential Utility

“…Recently, several extensions about robustness were made in different aspects: (i) optimal investment under correlation, equicorrelation, variance-covariance or volatility ambiguity, such as Fouque, Pun and Wong [14], Han and Wong [15], Ismail and Pham [18], Pun [33]; (ii) an economy modelled by a multivariate stochastic volatility model, especially the principle component stochastic volatility (PCSV) model, which nests Heston's model as a special case (in one dimension, i.e., one risky-asset case). PCSV was initiated in Escobar, Gotz, Seco and Zagst [13] and investigated in Bergen, Escobar, Rubtsov and Zagst [3] and Yan, Han, Pun and Wong [38]. However, aforementioned works about consumption-investment problems were not investigated under SDU preference.…”

Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility

“…A lot of empirical evidence show that the volatilities of risky assets prices are not constant or deterministic; Heston et al (1993) [22] introduced a stochastic volatility model, which is still popular for option pricing or asset pricing. Additionally, several papers also used this model or its extension in portfolio selection problems, for example, Li et al (2012) [23], Liu (2007) [24], and Yan et al (2020) [25]. Additionally, it is generally accepted that the interest rate is stochastic, and popular models describing interest rate include the CIR model and Vasicek model.…”