scholarly journals Multiperiod Telser’s Safety-First Portfolio Selection with Regime Switching

2018 ◽  
Vol 2018 ◽  
pp. 1-18
Author(s):  
Chuangwei Lin ◽  
Huiling Wu
Keyword(s):  
Markov Chain ◽  
Portfolio Selection ◽  
Optimal Strategy ◽  
Regime Switching ◽  
Risk Control ◽  
Control Level ◽  
Terminal Wealth ◽  
Lagrange Multiplier Technique ◽  
Portfolio Selection Model ◽  
Safety First

This paper investigates a multiperiod Telser’s safety-first portfolio selection model with regime switching where the returns of the assets are assumed to depend on the market states modulated by a discrete-time Markov chain. The investor aims to maximize the expected terminal wealth and does not want the probability of the terminal wealth to fall short of a disaster level to exceed a predetermined number called the risk control level. Referring to Tchebycheff inequality, we modify Telser’s safety-first model to the case that aims to maximize the expected terminal wealth subject to a constraint where the upper bound of the disaster probability is less than the risk control level. By the Lagrange multiplier technique and the embedding method, we study in detail the existence of the optimal strategy and derive the closed-form optimal strategy. Finally, by mathematical and numerical analysis, we analyze the effects of the disaster level, the risk control level, the transition matrix of the Markov chain, the expected excess return, and the variance of the risky return.

scholarly journals Portfolio Selection Based on Bayesian Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Daping Zhao ◽  
Yong Fang ◽  
Chaoliang Zhang ◽  
Zongrun Wang
Keyword(s):  
Markov Chain ◽  
Stock Market ◽  
Portfolio Selection ◽  
Regime Switching ◽  
Numerical Experiments ◽  
Bayesian Theory ◽  
Selection Model ◽  
Portfolio Performance ◽  
State Transfer ◽  
Portfolio Selection Model

The traditional portfolio selection model seriously overestimates its theoretic optimal return. Aiming at this problem, two portfolio selection models are proposed to modify the parameters and enhance portfolio performance based on Bayesian theory. Firstly, a Bayesian-GARCH(1,1) model is built. Secondly, Markov Chain is applied to curve the parameters’ state transfer, and a Bayesian Markov regime-Switching-GARCH(1,1) model is constructed. Both the two models can handle the overestimation problem and can obtain self-financing portfolios. In the numerical experiments, both the models are examined with data from China stock market, and their performances are compared and analyzed. The results show that BMS-GARCH(1,1) model is superior to the Bayesian-GARCH(1,1) model.

scholarly journals Portfolio Selection with Jumps under Regime Switching

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Lin Zhao
Keyword(s):  
Markov Chain ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Regime Switching ◽  
Jump Processes ◽  
Bank Account ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Portfolio Selection Model ◽  
Mean Variance

We investigate a continuous-time version of the mean-variance portfolio selection model with jumps under regime switching. The portfolio selection is proposed and analyzed for a market consisting of one bank account and multiple stocks. The random regime switching is assumed to be independent of the underlying Brownian motion and jump processes. A Markov chain modulated diffusion formulation is employed to model the problem.

CONTINUOUS-TIME MEAN–VARIANCE OPTIMIZATION FOR DEFINED CONTRIBUTION PENSION FUNDS WITH REGIME-SWITCHING

2019 ◽  
Vol 22 (06) ◽  
pp. 1950029
Author(s):  
ZHIPING CHEN ◽  
LIYUAN WANG ◽  
PING CHEN ◽  
HAIXIANG YAO
Keyword(s):  
Brownian Motion ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Regime Switching ◽  
Efficient Frontier ◽  
Defined Contribution ◽  
Risky Assets ◽  
Mean Variance Portfolio ◽  
Mean Variance

Using mean–variance (MV) criterion, this paper investigates a continuous-time defined contribution (DC) pension fund investment problem. The framework is constructed under a Markovian regime-switching market consisting of one bank account and multiple risky assets. The prices of the risky assets are governed by geometric Brownian motion while the accumulative contribution evolves according to a Brownian motion with drift and their correlation is considered. The market state is modeled by a Markovian chain and the random regime-switching is assumed to be independent of the underlying Brownian motions. The incorporation of the stochastic accumulative contribution and the correlations between the contribution and the prices of risky assets makes our problem harder to tackle. Luckily, based on appropriate Riccati-type equations and using the techniques of Lagrange multiplier and stochastic linear quadratic control, we derive the explicit expressions of the optimal strategy and efficient frontier. Further, two special cases with no contribution and no regime-switching, respectively, are discussed and the corresponding results are consistent with those results of Zhou & Yin [(2003) Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model, SIAM Journal on Control and Optimization 42 (4), 1466–1482] and Zhou & Li [(2000) Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization 42 (1), 19–33]. Finally, some numerical analyses based on real data from the American market are provided to illustrate the property of the optimal strategy and the effects of model parameters on the efficient frontier, which sheds light on our theoretical results.

scholarly journals Multi-Period Mean-Absolute Deviation Fuzzy Portfolio Selection Model with Entropy Constraints

2016 ◽  
Vol 4 (5) ◽  
pp. 428-443 ◽  
Author(s):  
Peng Zhang ◽  
Heshan Gong ◽  
Weiting Lan
Keyword(s):  
Transaction Costs ◽  
Portfolio Selection ◽  
Path Dependence ◽  
Risk Control ◽  
Selection Model ◽  
Programming Approach ◽  
Absolute Deviation ◽  
Fuzzy Portfolio Selection ◽  
Proposed Model ◽  
Portfolio Selection Model

AbstractThis paper considers a multi-period fuzzy portfolio selection problem maximizing the terminal wealth imposed by risk control, in which the returns of assets are characterized by fuzzy numbers. A fuzzy absolute deviation is originally defined as the risk control of portfolio. Entropy constraints and borrowing constraints are added in the portfolio selection model. Based on the theories of possibility measures, a new multi-period portfolio optimization model with transaction costs is proposed. And then, the proposed model is transformed into a crisp nonlinear programming problem by using fuzzy programming approach. Because of the transaction costs, the multi-period portfolio selection is the dynamic optimization problem with path dependence. Through changing the cost function into a variable, the multi-period portfolio selection is approximately turned into the dynamic programming. Furthermore, the discrete approximate iteration method is designed to obtain the optimal portfolio strategy. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

scholarly journals Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

2021 ◽  
Vol 58 (2) ◽  
pp. 372-393
Author(s):  
H. M. Jansen
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
The State ◽  
Stochastic Integrals ◽  
Occupation Measure ◽  
Generator Matrix ◽  
Markov Modulated ◽  
Erlang Loss

AbstractOur aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox–Ingersoll–Ross process.

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.

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