scholarly journals Time-Consistent Strategies for Multi-Period Portfolio Optimization with/without the Risk-Free Asset

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Zhongbao Zhou ◽  
Xianghui Liu ◽  
Helu Xiao ◽  
TianTian Ren ◽  
Wenbin Liu
Keyword(s):  
Empirical Studies ◽  
Lagrange Function ◽  
Investment Strategy ◽  
Open Loop ◽  
Investment Strategies ◽  
Variance Model ◽  
Risky Assets ◽  
Consistent Solution ◽  
Mean Variance Portfolio ◽  
Mean Variance

The pre-commitment and time-consistent strategies are the two most representative investment strategies for the classic multi-period mean-variance portfolio selection problem. In this paper, we revisit the case in which there exists one risk-free asset in the market and prove that the time-consistent solution is equivalent to the optimal open-loop solution for the classic multi-period mean-variance model. Then, we further derive the explicit time-consistent solution for the classic multi-period mean-variance model only with risky assets, by constructing a novel Lagrange function and using backward induction. Also, we prove that the Sharpe ratio with both risky and risk-free assets strictly dominates that of only with risky assets under the time-consistent strategy setting. After the theoretical investigation, we perform extensive numerical simulations and out-of-sample tests to compare the performance of pre-commitment and time-consistent strategies. The empirical studies shed light on the important question: what is the primary motivation of using the time-consistent investment strategy.

scholarly journals Open-loop equilibrium mean-variance reinsurance, new business and investment strategies with constraints

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Liming Zhang ◽  
Rongming Wang ◽  
Jiaqin Wei
Keyword(s):  
Convex Set ◽  
Investment Strategy ◽  
Open Loop ◽  
Equilibrium Strategy ◽  
Investment Strategies ◽  
Risky Investment ◽  
New Business ◽  
New Policies ◽  
Risk Processes ◽  
Mean Variance

<p style='text-indent:20px;'>In this paper, we study a general mean-variance reinsurance, new business and investment problem, where the claim processes of original and new businesses are modeled by two different risk processes and the safety loadings of reinsurance and new business are different. The retention level of the insurer is constrained in <inline-formula><tex-math id="M1">\begin{document}$ [0,1] $\end{document}</tex-math></inline-formula> and the controls of new business and risky investment are required to be non-negative. This model relaxes the limitations of those in existing research. By using the projection onto the convex set controls valued in, we obtain an open-loop equilibrium reinsurance-new business-investment strategy explicitly. We also show that the obtained equilibrium strategy is the optimal one among all deterministic strategies in the sense that it yields the smallest mean-variance cost. In the case where original and new businesses are the same, the equilibrium strategy is given in closed-form and its sensitivities to safety loadings are shown by numerical examples. At last, by comparing with the case where acquiring new business is prohibited, we show that allowing writing new policies indeed improves the performance of the insurer's risk management.</p>

OPTIMAL CONSTANT-REBALANCED PORTFOLIO INVESTMENT STRATEGIES FOR DYNAMIC PORTFOLIO SELECTION

2006 ◽  
Vol 09 (06) ◽  
pp. 951-966 ◽  
Author(s):  
ZHONG-FEI LI ◽  
KAI W. NG ◽  
KEN SENG TAN ◽  
HAILIANG YANG
Keyword(s):  
Risk Measure ◽  
Efficient Frontier ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Variance Model ◽  
Optimal Constant ◽  
Black Scholes ◽  
Dynamic Portfolio ◽  
Portfolio Optimization Problem ◽  
Mean Variance

In this paper we propose a variant of the continuous-time Markowitz mean-variance model by incorporating the Earnings-at-Risk measure in the portfolio optimization problem. Under the Black-Scholes framework, we obtain closed-form expressions for the optimal constant-rebalanced portfolio (CRP) investment strategy. We also derive explicitly the corresponding mean-EaR efficient portfolio frontier, which is a generalization of the Markowitz mean-variance efficient frontier.

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 Optimal Reinsurance-Investment Problem under Mean-Variance Criterion with n Risky Assets

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Peng Yang
Keyword(s):  
Financial Market ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Risky Assets ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Mean Variance ◽  
Variance Criterion

Based on the mean-variance criterion, this paper investigates the continuous-time reinsurance and investment problem. The insurer’s surplus process is assumed to follow Cramér–Lundberg model. The insurer is allowed to purchase reinsurance for reducing claim risk. The reinsurance pattern that the insurer adopts is combining proportional and excess of loss reinsurance. In addition, the insurer can invest in financial market to increase his wealth. The financial market consists of one risk-free asset and n correlated risky assets. The objective is to minimize the variance of the terminal wealth under the given expected value of the terminal wealth. By applying the principle of dynamic programming, we establish a Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, we derive the explicit solutions for the optimal reinsurance-investment strategy and the corresponding efficient frontier by solving the HJB equation. Finally, numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes with model parameters.

Mean-variance portfolio selection with an uncertain exit-time in a regime-switching market

2019 ◽  
Vol 53 (4) ◽  
pp. 1171-1186
Author(s):  
Reza Keykhaei
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Exit Time ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Homogeneous Markov Chain ◽  
Investment Strategies ◽  
Special Cases ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper, we deal with multi-period mean-variance portfolio selection problems with an exogenous uncertain exit-time in a regime-switching market. The market is modelled by a non-homogeneous Markov chain in which the random returns of assets depend on the states of the market and investment time periods. Applying the Lagrange duality method, we derive explicit closed-form expressions for the optimal investment strategies and the efficient frontier. Also, we show that some known results in the literature can be obtained as special cases of our results. A numerical example is provided to illustrate the results.

THE IMPACT OF SAVINGS WITHDRAWALS ON A BANKER’S CAPITAL HOLDINGS SUBJECT TO BASEL III ACCORD

2020 ◽  
Vol 15 (02) ◽  
pp. 2050006
Author(s):  
RYLE S. PERERA ◽  
KIMITOSHI SATO
Keyword(s):  
Stock Returns ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Short Selling ◽  
Terminal Condition ◽  
Capital Regulation ◽  
Basel Iii ◽  
Investment Strategies ◽  
The Impact ◽  
Mean Variance

In this paper, we analyze the impact of savings withdrawals on a bank’s capital holdings under Basel III capital regulation. We examine the interplay between savings withdrawals and the investment strategies of a bank, by extending the classical mean–variance paradigm to investigate the bankers optimal investment strategy. We solve this via an optimization problem under a mean–variance paradigm, subject to a quadratic optimization function which incorporates a running penalization cost alongside the terminal condition. By solving the Hamilton–Jacobi–Bellman (HJB) equation, we derive the closed-form expressions for the value function as well as the banker’s optimal investment strategies. Our study provides a novel insight into the way banks allocate their capital holdings by showing that in the presence of savings withdrawals, banks will increase their risk-free asset holdings to hedge against the forthcoming deposit withdrawals whilst facing short-selling constraints. Moreover, we show that if the savings depositors of the bank are more stock-active, an economic expansion will imply a greater reduction in bank savings. As a result, the banker will reduce his/her loan portfolio and will depend on high stock returns with short-selling constraints to conform to Basel III capital regulation.

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