scholarly journals MEAN-VARIANCE PORTFOLIO OPTIMIZATION WITH STATE-DEPENDENT RISK AVERSION

2012 ◽  
Vol 24 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Tomas Björk ◽  
Agatha Murgoci ◽  
Xun Yu Zhou
Keyword(s):  
Risk Aversion ◽  
Portfolio Optimization ◽  
State Dependent ◽  
Mean Variance Portfolio ◽  
Mean Variance

PRACTICAL INVESTMENT CONSEQUENCES OF THE SCALARIZATION PARAMETER FORMULATION IN DYNAMIC MEAN–VARIANCE PORTFOLIO OPTIMIZATION

2021 ◽  
Vol 24 (05) ◽  
pp. 2150029
Author(s):  
PIETER M. VAN STADEN ◽  
DUY-MINH DANG ◽  
PETER A. FORSYTH
Keyword(s):  
Risk Aversion ◽  
Portfolio Optimization ◽  
Optimization Problem ◽  
Jump Diffusion ◽  
Investment Strategies ◽  
Institutional Settings ◽  
Portfolio Optimization Problem ◽  
Mean Variance Portfolio ◽  
Mean Variance ◽  
Theoretical Risk

We consider the practical investment consequences of implementing the two most popular formulations of the scalarization (or risk-aversion) parameter in the time-consistent dynamic mean–variance (MV) portfolio optimization problem. Specifically, we compare results using a scalarization parameter assumed to be (i) constant and (ii) inversely proportional to the investor’s wealth. Since the link between the scalarization parameter formulation and risk preferences is known to be nontrivial (even in the case where a constant scalarization parameter is used), the comparison is viewed from the perspective of an investor who is otherwise agnostic regarding the philosophical motivations underlying the different formulations and their relation to theoretical risk-aversion considerations, and instead simply wishes to compare investment outcomes of the different strategies. In order to consider the investment problem in a realistic setting, we extend some known results to allow for the case where the risky asset follows a jump-diffusion process, and examine multiple sets of plausible investment constraints that are applied simultaneously. We show that the investment strategies obtained using a scalarization parameter that is inversely proportional to wealth, which enjoys widespread popularity in the literature applying MV optimization in institutional settings, can exhibit some undesirable and impractical characteristics.

Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishak Alia ◽  
Farid Chighoub
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Optimal Time ◽  
Uniqueness Results ◽  
State Dependent ◽  
Consistent Solution ◽  
Game Theoretic ◽  
Markov Modulated ◽  
Mean Variance Portfolio ◽  
Mean Variance

Abstract This paper studies optimal time-consistent strategies for the mean-variance portfolio selection problem. Especially, we assume that the price processes of risky stocks are described by regime-switching SDEs. We consider a Markov-modulated state-dependent risk aversion and we formulate the problem in the game theoretic framework. Then, by solving a flow of forward-backward stochastic differential equations, an explicit representation as well as uniqueness results of an equilibrium solution are obtained.

scholarly journals An Improvement of Stochastic Gradient Descent Approach for Mean-Variance Portfolio Optimization Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Stephanie S. W. Su ◽  
Sie Long Kek
Keyword(s):  
Portfolio Optimization ◽  
Standard Error ◽  
Gradient Descent ◽  
Optimization Problem ◽  
Stochastic Gradient Descent ◽  
Moment Estimation ◽  
The Mean ◽  
Portfolio Optimization Problem ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper, the current variant technique of the stochastic gradient descent (SGD) approach, namely, the adaptive moment estimation (Adam) approach, is improved by adding the standard error in the updating rule. The aim is to fasten the convergence rate of the Adam algorithm. This improvement is termed as Adam with standard error (AdamSE) algorithm. On the other hand, the mean-variance portfolio optimization model is formulated from the historical data of the rate of return of the S&P 500 stock, 10-year Treasury bond, and money market. The application of SGD, Adam, adaptive moment estimation with maximum (AdaMax), Nesterov-accelerated adaptive moment estimation (Nadam), AMSGrad, and AdamSE algorithms to solve the mean-variance portfolio optimization problem is further investigated. During the calculation procedure, the iterative solution converges to the optimal portfolio solution. It is noticed that the AdamSE algorithm has the smallest iteration number. The results show that the rate of convergence of the Adam algorithm is significantly enhanced by using the AdamSE algorithm. In conclusion, the efficiency of the improved Adam algorithm using the standard error has been expressed. Furthermore, the applicability of SGD, Adam, AdaMax, Nadam, AMSGrad, and AdamSE algorithms in solving the mean-variance portfolio optimization problem is validated.

Sign in / Sign up

Export Citation Format

Share Document