scholarly journals TheCEVModel and Its Application in a Study of Optimal Investment Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Aiyin Wang ◽  
Ls Yong ◽  
Yang Wang ◽  
Xuanjun Luo
Keyword(s):  
Optimal Investment ◽  
Investment Strategy ◽  
Legendre Transform ◽  
Investment Strategies ◽  
Approximation Solution ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Optimal Investment Strategy ◽  
Hamilton Jacobi Bellman ◽  
Exponential Utility Function

The constant elasticity of variance (CEV) model is used to describe the price of the risky asset. Maximizing the expected utility relating to the Hamilton-Jacobi-Bellman (HJB) equation which describes the optimal investment strategies, we obtain a partial differential equation. Applying the Legendre transform, we transform the equation into a dual problem and obtain an approximation solution and an optimal investment strategies for the exponential utility function.

scholarly journals Robust optimal asset-liability management with penalization on ambiguity

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yu Yuan ◽  
Hui Mi
Keyword(s):  
Reference Model ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Programming Approach ◽  
Stochastic Dynamic ◽  
Economic Implication ◽  
Investment Strategies ◽  
Dynamic Programming Approach ◽  
Optimal Investment Strategy ◽  
Special Cases

<p style='text-indent:20px;'>In this paper, we study the robust optimal asset- problems for an ambiguity-averse investor, who does not have perfect information in the drift terms of the risky asset and liability processes. Two different kinds of objectives are considered: <inline-formula><tex-math id="M1">\begin{document}$ (i) $\end{document}</tex-math></inline-formula> Maximizing the minimal expected utility of the terminal wealth; <inline-formula><tex-math id="M2">\begin{document}$ (ii) $\end{document}</tex-math></inline-formula> Minimizing the maximal cumulative deviation. The ambiguity in both problems is described by a set of equivalent measures to the reference model. By the stochastic dynamic programming approach and Hamilton-Jacobi-Bellman (HJB) equation, we derive closed-form expressions for the value function and corresponding robust optimal investment strategy in each problem. Furthermore, some special cases are provided to investigate the effect of model uncertainty on the optimal investment strategy. Finally, the economic implication and parameter sensitivity are analyzed by some numerical examples. We also compare the robust optimal investment strategies in two different problems.</p>

scholarly journals Pricing strategy and product quality design with platform-investment

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xiujing Dang ◽  
Yang Xu ◽  
Gongbing Bi ◽  
Lei Qin
Keyword(s):  
Product Quality ◽  
Value Added ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Profit Sharing ◽  
Investment Strategies ◽  
Contract Term ◽  
Optimal Investment Strategy ◽  
Sustainable Value ◽  
Quality Design

<p style='text-indent:20px;'>With the development of business, more consumers are quality sensitive and improving the product quality becomes particularly important. We mainly discuss two investment strategies: retailer-investment and platform-investment. Compared with non-investment case, only if consumer sensitivity is not too high, it is profitable for the retailer to select retailer-investment. When both retailer-investment and platform-investment are viable, the choice of investment mechanism depends on the profit-sharing ratio. Particularly, if the ratio is within a certain range, the optimal investment strategy is platform-investment, achieving a triple-win outcome. Besides, to effectively alleviate the contradiction between the retailer's moral hazard problem and the sustainable value-added effect of platform-investment, we further research the contract term. These results give us some meaningful management inspirations in investment mechanism.</p>

Analysis of the Possibilities of Using the Wald-Savage Test for the Study of Game Models

2021 ◽  
Vol 9 (4) ◽  
pp. 82-88
Author(s):  
Dmitriy Vlasov
Keyword(s):  
Optimality Criterion ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Optimality Criteria ◽  
Advanced Training ◽  
Investment Strategies ◽  
Optimal Investment Strategy ◽  
Game Matrix ◽  
States Of Nature ◽  
Savage Criterion

Within the framework of this article, the mechanisms for constructing and researching the game model for choosing the investor's optimal investment strategy in various information conditions are disclosed: building many players, building many players' strategies, the option of formalizing the payment function in the form of a game matrix, many optimality criteria, methods of justifying the choice of the strategy optimality criterion. Against the background of the application of classical criteria (Savage criterion, Wald criterion, Hodge-Lehman criterion, Hermeyer criterion), special attention is paid to the analysis of the possibilities of using the integrated Wald-Savage criterion for the study of game models, which allows to smooth the shortcomings of classical criteria and take into account the investor's appetite for risk. Attention is focused on the need to justify the choice of the criterion for the optimality of investment strategies, as well as the need of the researcher to clarify the states of nature and the probabilities of their implementations. The mechanisms for constructing and researching game models presented in this article can be used to improve methodological systems for teaching applied mathematical disciplines at an economic university, to build new variable educational disciplines on modern issues of decision theory, as well as within the framework of the system of advanced training in economics.

scholarly journals Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong
Keyword(s):  
Stock Price ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Dynamic Programming Principle ◽  
Legendre Transform ◽  
Order Partial Differential Equation ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Time Dynamic ◽  
Mean Variance

This paper studies a continuous-time dynamic mean-variance portfolio selection problem with the constraint of a higher borrowing rate, in which stock price is governed by a constant elasticity of variance (CEV) process. Firstly, we apply Lagrange duality theorem to change an original mean-variance problem into an equivalent optimization one. Secondly, we use dynamic programming principle to get the Hamilton-Jacobi-Bellman (HJB) equation for the value function, which is a more sophisticated nonlinear second-order partial differential equation. Furthermore, we use Legendre transform and dual theory to transform the HJB equation into its dual one. Finally, the closed-form solutions to the optimal investment strategy and efficient frontier are derived by applying variable change technique.

scholarly journals Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chubing Zhang ◽  
Ximing Rong
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Legendre Transform ◽  
Investment Strategies ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Plan Member ◽  
Cara Utility ◽  
Hamilton Jacobi Bellman ◽  
Coupon Bond

We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model) and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.

scholarly journals A Model for the Optimal Investment Strategy in the Context of Pandemic Regional Lockdown

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1058
Author(s):  
Antoine Tonnoir ◽  
Ioana Ciotir ◽  
Adrian-Liviu Scutariu ◽  
Octavian Dospinescu
Keyword(s):  
Mathematical Model ◽  
Negative Impact ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Economic Consequences ◽  
Decision Makers ◽  
Investment Strategies ◽  
Negative Consequences ◽  
Optimal Investment Strategy ◽  
Proposed Model

The Covid-19 pandemic has generated major changes in society, most of them having a negative impact on the quality of life and income obtained by the population and businesses. The negative consequences have been highlighted in the decrease of the GPD level for regions, countries and even continents. Returning to pre-pandemic levels is a considerable effort for both economic and political decision-makers. This article deals with the construction of a mathematical model for economic aspects in the context of variable productivity in time. Through this mathematical model, we propose to maximize revenues in pandemic conditions, in order to limit the economic consequences of the lockdown. One advantage of the proposed model consists in the fact that it is based on units that can be regions, economic branches, economic units or fields of investment. Another strength of the model is determined by the fact that it offers the possibility to choose between two different investment strategies, based on the specific options of the decision makers: the consistent increase of the state revenues or the amelioration of the disparity phenomenon. Furthermore, our model extends previous approaches from the literature by adding some generalization options and the proposed model can be applied in lockdown cases and seasonal situations.

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