Growth Optimal Investment Strategy: The Impact of Reallocation Frequency and Heavy Tails

2012 ◽  
Vol 13 (2) ◽  
pp. 228-240 ◽  
Author(s):  
G. Bamberg ◽  
A. Neuhierl
Keyword(s):  
Heavy Tails ◽  
Geometric Mean ◽  
Asymptotic Optimality ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Optimal Investment Strategy ◽  
Optimality Properties ◽  
Heavy Tailed ◽  
The Impact

Abstract The strategy to maximize the long-term growth rate of final wealth (maximum expected log strategy, maximum geometric mean strategy, Kelly criterion) is based on probability theoretic underpinnings and has asymptotic optimality properties. This article reviews the allocation of wealth in a two-asset economy with one risky asset and a risk-free asset. It is also shown that the optimal fraction to be invested in the risky asset (i) depends on the length of the basic return period and (ii) is lower for heavy-tailed log returns than for light-tailed log returns.

scholarly journals Optimal Investment Strategy under the CEV Model with Stochastic Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yong He ◽  
Peimin Chen
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Stochastic Interest Rate ◽  
Model Parameters ◽  
Optimal Investment Strategy ◽  
Stochastic Interest ◽  
Cev Process ◽  
The Interest Rate

Interest rate is an important macrofactor that affects asset prices in the financial market. As the interest rate in the real market has the property of fluctuation, it might lead to a great bias in asset allocation if we only view the interest rate as a constant in portfolio management. In this paper, we mainly study an optimal investment strategy problem by employing a constant elasticity of variance (CEV) process and stochastic interest rate. The assets of investment for individuals are supposed to be composed of one risk-free asset and one risky asset. The interest rate for risk-free asset is assumed to follow the Cox–Ingersoll–Ross (CIR) process, and the price of risky asset follows the CEV process. The objective is to maximize the expected utility of terminal wealth. By applying the dual method, Legendre transformation, and asymptotic expansion approach, we successfully obtain an asymptotic solution for the optimal investment strategy under constant absolute risk aversion (CARA) utility function. In the end, some numerical examples are provided to support our theoretical results and to illustrate the effect of stochastic interest rates and some other model parameters on the optimal investment strategy.

scholarly journals Robust Time-Consistent Portfolio Selection for an Investor under CEV Model with Inflation Influence

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Peng Yang
Keyword(s):  
Probability Measure ◽  
Financial Market ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Control Technique ◽  
Model Parameters ◽  
Cev Model ◽  
Terminal Wealth ◽  
Optimal Investment Strategy

A robust time-consistent optimal investment strategy selection problem under inflation influence is investigated in this article. The investor may invest his wealth in a financial market, with the aim of increasing wealth. The financial market includes one risk-free asset, one risky asset, and one inflation-indexed bond. The price process of the risky asset is governed by a constant elasticity of variance (CEV) model. The investor is ambiguity-averse; he doubts about the model setting under the original probability measure. To dispel this concern, he seeks a set of alternative probability measures, which are absolutely continuous to the original probability measure. The objective of the investor is to seek a time-consistent strategy so as to maximize his expected terminal wealth meanwhile minimizing his variance of the terminal wealth in the worst-case scenario. By using the stochastic optimal control technique, we derive closed-form solutions for the optimal time-consistent investment strategy, the probability scenario, and the value function. Finally, the influences of model parameters on the optimal investment strategy and utility loss function are examined through numerical experiments.

scholarly journals Optimal Investment Strategy for DC Pension Plan with Stochastic Income and Inflation Risk under the Ornstein–Uhlenbeck Model

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1756
Author(s):  
Yang Wang ◽  
Xiao Xu ◽  
Jizhou Zhang
Keyword(s):  
Control Method ◽  
Closed Form Solution ◽  
Pension Plan ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Legendre Transform ◽  
Defined Contribution ◽  
Inflation Risk ◽  
Optimal Investment Strategy

This paper is concerned with the optimal investment strategy for a defined contribution (DC) pension plan. We assumed that the financial market consists of a risk-free asset and a risky asset, where the risky asset is subject to the Ornstein–Uhlenbeck (O-U) process, and stochastic income and inflation risk were also considered in the model. We firstly derived the Hamilton–Jacobi–Bellman (HJB) equation through the stochastic control method. Secondly, under the logarithmic utility function, the closed-form solution of optimal asset allocation was obtained by using the Legendre transform method. Finally, we give several numerical examples and a financial analysis.

scholarly journals Asset allocation for a DC pension plan with learning about stock return predictability

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Pei Wang ◽  
Ling Zhang ◽  
Zhongfei Li
Keyword(s):  
Stock Return ◽  
Pension Plan ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Return Predictability ◽  
Programming Approach ◽  
Model Parameters ◽  
Stock Return Predictability ◽  
Optimal Investment Strategy ◽  
The Impact

<p style='text-indent:20px;'>This paper investigates an optimal investment problem for a defined contribution pension plan member who receives a stochastic salary, and considers inflation risk and stock return predictability. The member aims to maximize the expected power utility from her terminal real wealth by investing her pension account wealth in a financial market consisting of a risk-free asset, an inflation-indexed bond and a stock. The expected excess return on the stock can be predicted by both an observable predictor and an unobservable predictor, and the member has to estimate the unobservable predictor by learning the history information. By using the filtering techniques and dynamic programming approach, the closed-form optimal investment strategy and the corresponding value function are derived. Finally, with the help of numerical analysis, we explore the impact of model parameters on the optimal investment strategy, and analyze the welfare benefits from leaning and using inflation-indexed bond to hedge the stock return predictors.</p>

scholarly journals Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Huiling Wu
Keyword(s):  
Regime Switching ◽  
Stock Price ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Power Utility ◽  
Optimal Investment Strategy ◽  
Admissible Strategies ◽  
Definition Of ◽  
Markovian Regime Switching ◽  
Optimal Investment And Consumption

This paper studies an investment-consumption problem under inflation. The consumption price level, the prices of the available assets, and the coefficient of the power utility are assumed to be sensitive to the states of underlying economy modulated by a continuous-time Markovian chain. The definition of admissible strategies and the verification theory corresponding to this stochastic control problem are presented. The analytical expression of the optimal investment strategy is derived. The existence, boundedness, and feasibility of the optimal consumption are proven. Finally, we analyze in detail by mathematical and numerical analysis how the risk aversion, the correlation coefficient between the inflation and the stock price, the inflation parameters, and the coefficient of utility affect the optimal investment and consumption strategy.

scholarly journals Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1610
Author(s):  
Katia Colaneri ◽  
Alessandra Cretarola ◽  
Benedetta Salterini
Keyword(s):  
Stock Prices ◽  
Regime Switching ◽  
Common Factor ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Market Model ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Insurance Company ◽  
Optimal Investment Strategy

In this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the optimal investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters.

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