Dynamic Optimal Mean-Variance Investment with Mispricing in the Family of 4/2 Stochastic Volatility Models

This paper considers an optimal investment problem with mispricing in the family of 4/2 stochastic volatility models under mean–variance criterion. The financial market consists of a risk-free asset, a market index and a pair of mispriced stocks. By applying the linear–quadratic stochastic control theory and solving the corresponding Hamilton–Jacobi–Bellman equation, explicit expressions for the statically optimal (pre-commitment) strategy and the corresponding optimal value function are derived. Moreover, a necessary verification theorem was provided based on an assumption of the model parameters with the investment horizon. Due to the time-inconsistency under mean–variance criterion, we give a dynamic formulation of the problem and obtain the closed-form expression of the dynamically optimal (time-consistent) strategy. This strategy is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Results on the special case without mispricing are included. Finally, some numerical examples are given to illustrate the effects of model parameters on the efficient frontier and the difference between static and dynamic optimality.

Mean-Variance Portfolio Selection with Tracking Error Penalization

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in the case of misspecified parameters, by “fitting" it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean–Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

Otsu’s Thresholding Method Based on Plane Intercept Histogram and Geometric Analysis

The Three-Dimensional (3-D) Otsu’s method is an effective improvement on the traditional Otsu’s method. However, it not only has high computational complexity, but also needs to improve its anti-noise ability. This paper presents a new Otsu’s method based on 3-D histogram. This method transforms 3-D histogram into a 1-D histogram by a plane that is perpendicular to the main diagonal of the 3-D histogram, and designs a new maximum variance criterion for threshold selection. In order to enhance its anti-noise ability, a method based on geometric analysis, which can correct noise, is used for image segmentation. Simulation experiments show that this method has stronger anti-noise ability and less time consumption, comparing with the conventional 3-D Otsu’s method, the recursive 3-D Otsu’s method, the 3-D Otsu’s method with SFLA, the equivalent 3-D Otsu’s method and the improved 3-D Otsu’s method