Robust optimal asset-liability management with penalization on ambiguity

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.

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The Role of Inflation-indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phrase

10.20944/preprints201801.0239.v1 ◽

2018 ◽

Author(s):

Xiaoyi Zhang ◽

Junyi Guo

Keyword(s):

Pension Plan ◽

Optimal Investment ◽

Investment Strategy ◽

Programming Approach ◽

Defined Contribution ◽

Inflation Risk ◽

Dynamic Programming Approach ◽

Optimal Investment Strategy ◽

Defined Contribution Pension Plan ◽

Hamilton Jacobi Bellman

In this paper we investigate the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phrase which is risk-averse and pays close attention to inflation risk. The plan aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal wealth by investing the wealth in a financial market consisting of an inflation-indexed bond, an ordinary zero coupon bond and a risk-free asset. We derive the optimal investment strategy in closed-form using the dynamic programming approach by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Our theoretical and numerical results reveal that under some rational assumptions, an inflation-indexed bond do has significant advantage to hedge inflation risk.

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Pricing strategy and product quality design with platform-investment

Journal of Industrial and Management Optimization ◽

10.3934/jimo.2021224 ◽

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

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.

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

Scientific Research and Development Economics of the Firm ◽

10.12737/2306-627x-2020-82-88 ◽

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.

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

Mathematics ◽

10.3390/math9091058 ◽

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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TheCEVModel and Its Application in a Study of Optimal Investment Strategy

Mathematical Problems in Engineering ◽

10.1155/2014/317071 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 2

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.

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Optimal investment strategies in a CIR framework

Journal of Applied Probability ◽

10.1239/jap/1014843074 ◽

2000 ◽

Vol 37 (4) ◽

pp. 936-946 ◽

Cited By ~ 42

Author(s):

Griselda Deelstra ◽

Martino Grasselli ◽

Pierre-François Koehl

Keyword(s):

Financial Markets ◽

Interest Rates ◽

Utility Function ◽

Closed Form ◽

Continuous Time ◽

Optimal Investment ◽

Investment Strategy ◽

Investment Strategies ◽

Optimal Investment Strategy ◽

Optimal Investment Problem

We study an optimal investment problem in a continuous-time framework where the interest rates follow Cox-Ingersoll-Ross dynamics. Closed form formulae for the optimal investment strategy are obtained by assuming the completeness of financial markets and the CRRA utility function. In particular, we study the behaviour of the solution when time approaches the terminal date.

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Optimal investment strategies in a CIR framework

Journal of Applied Probability ◽

10.1017/s0021900200018131 ◽

2000 ◽

Vol 37 (04) ◽

pp. 936-946 ◽

Cited By ~ 12

Author(s):

Griselda Deelstra ◽

Martino Grasselli ◽

Pierre-François Koehl

Keyword(s):

Financial Markets ◽

Interest Rates ◽

Utility Function ◽

Closed Form ◽

Continuous Time ◽

Optimal Investment ◽

Investment Strategy ◽

Investment Strategies ◽

Optimal Investment Strategy ◽

Optimal Investment Problem

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

Journal of Industrial & Management Optimization ◽

10.3934/jimo.2021138 ◽

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

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.

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