Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure

The discrete-time mean-variance portfolio selection formulation, a representative of general dynamic mean-risk portfolio selection problems, does not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated pre-committed efficient policy may become inefficient when considering the corresponding truncated problem, thus stimulating investors' irrational investment behavior. We investigate analytically effects of portfolio constraints on time consistency of efficiency for convex cone constrained markets. More specifically, we derive the semi-analytical expressions for the pre-committed efficient mean-variance policy and the minimum-variance signed supermartingale measure (VSSM) and reveal their close relationship. Our analysis shows that the pre-committed discrete-time efficient mean-variance policy satisfies TCIE if and only if the conditional expectation of VSSM's density (with respect to the original probability measure) is nonnegative, or once the conditional expectation becomes negative, it remains at the same negative value until the terminal time. Our findings indicate that the property of time consistency in efficiency only depends on the basic market setting, including portfolio constraints, and this fact motivates us to establish a general solution framework in constructing TCIE dynamic portfolio selection problem formulations by introducing suitable portfolio constraints

Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications *

We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are introduced, and following the dynamic programming approach in [32], we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations. We present several financial applications with explicit solutions, and revisit in particular optimal tracking problems with price impact, and the conditional mean-variance portfolio selection in incomplete market model.Comment: to appear in Probability, Uncertainty and Quantitative Ris

Asymmetry, Loss Aversion and Forecasting

Conditional volatility models, such as GARCH, have been used extensively in financial applications to capture predictable variation in the second moment of asset returns. However, with recent theoretical literature emphasising the loss averse nature of agents, this paper considers models which capture time variation in the second lower partial moment. Utility based evaluation is carried out on several approaches to modelling the conditional second order lower partial moment (or semi-variance), including distribution and regime based models. The findings show that when agents are loss averse, there are utility gains to be made from using models which explicitly capture this feature (rather than trying to approximate using symmetric volatility models). In general direct approaches to modelling the semi-variance are preferred to distribution based models. These results are relevant to risk management and help to link the theoretical discussion on loss aversion to emprical modellingAsymmetry, loss aversion, semi-variance, volatility models.