Fuzzy portfolio selection with prospect consistency constraint based on possibility theory

2020 ◽  
pp. 1-24
Author(s):  
Xue Deng ◽  
Chuangjie Chen
Keyword(s):  
Value Function ◽  
Mathematical Proof ◽  
Optimal Strategies ◽  
Possibility Theory ◽  
Mean Value ◽  
Fuzzy Portfolio Selection ◽  
Portfolio Strategy ◽  
Consistency Constraint ◽  
Reduce Risk ◽  
Rigorous Mathematical Proof

Considering that most studies have taken the investors’ preference for risk into account but ignored the investors’ preference for assets, in this paper, we combine the prospect theory and possibility theory to provide investors with a portfolio strategy that meets investors’ preference for assets. Firstly, a novel reference point is proposed to give investors a comprehensive impression of assets. Secondly, the prospect return rate of assets is quantified as trapezoidal fuzzy number, and its possibilistic mean value and variance are regarded as prospect return and risk and then used to define the fuzzy prospect value. This new definition is presented to denote the score of an asset in investors’ subjective cognition. And then, a prospect asset filtering frame is proposed to help investors select assets according to their preference. When assets are selected, another new definition called prospect consistency coefficient is proposed to measure the deviation of a portfolio strategy from investors’ preference. Some properties of the definition are presented by rigorous mathematical proof. Based on the definition and its properties, a possibilistic model is constructed, which can not only provide investors optimal strategies to make profit and reduce risk as much as possible, but also ensure that the deviation between the strategies and investors’ preference is tolerable. Finally, a numerical example is given to validate the proposed method, and the sensitivity analysis of parameters in prospect value function and prospect consistency constraint is conducted to help investors choose appropriate values according to their preferences. The results show that compared with the general M-V model, our model can not only better satisfy investors’ preference for assets, but also disperse risk effectively.

scholarly journals Optimal Portfolios for Financial Markets with Wishart Volatility

2013 ◽  
Vol 50 (4) ◽  
pp. 1025-1043 ◽  
Author(s):  
Nicole Bäuerle ◽  
Zejing Li
Keyword(s):  
Value Function ◽  
Numerical Study ◽  
Heston Model ◽  
Hard Part ◽  
Control Approach ◽  
Portfolio Strategy ◽  
Hamilton Jacobi Bellman ◽  
The One ◽  
Hedging Demand ◽  
The Value Function

We consider a multi asset financial market with stochastic volatility modeled by a Wishart process. This is an extension of the one-dimensional Heston model. Within this framework we study the problem of maximizing the expected utility of terminal wealth for power and logarithmic utility. We apply the usual stochastic control approach and obtain, explicitly, the optimal portfolio strategy and the value function in some parameter settings. In particular, we do this when the drift of the assets is a linear function of the volatility matrix. In this case the affine structure of the model can be exploited. In some cases we obtain a Feynman-Kac representation of the candidate value function. Though the approach we use is quite standard, the hard part is to identify when the solution of the Hamilton-Jacobi-Bellman equation is finite. This involves a couple of matrix analytic arguments. In a numerical study we discuss the influence of the investors' risk aversion on the hedging demand.

Realisation of the mean-value function

1973 ◽  
Vol 9 (22) ◽  
pp. 528
Author(s):  
E. Ball
Keyword(s):  
Value Function ◽  
Mean Value ◽  
The Mean

A New Method for Evaluating Stochastic Models of Brand Choice

1970 ◽  
Vol 7 (3) ◽  
pp. 300-306 ◽  
Author(s):  
David A. Aaker
Keyword(s):  
Stochastic Models ◽  
Goodness Of Fit ◽  
Value Function ◽  
Choice Model ◽  
Brand Choice ◽  
Mean Value ◽  
Model Fit ◽  
New Method ◽  
Structural Comparison ◽  
Goodness Of Fit Test

This article explores the use of a brand choice stochastic model's mean value function in evaluating two models empirically, using a common set of purchase data. The linear learning model fit the data well, but its mean value function was not capable of making reasonable predictions of successive, aggregate purchasing statistics. Another brand choice model, the new trier model, was found to perform much better. The results suggest that model tests should not be restricted to the usual goodness-of-fit test, especially in situations of non-stationarity. A structural comparison of the two models focuses on their different approaches to nonstationarity.

Optimal strategies for a non-linear premium-reserve model in a competitive insurance market

2016 ◽  
Vol 11 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Athanasios A. Pantelous ◽  
Eudokia Passalidou
Keyword(s):  
Linear Models ◽  
Quadratic Function ◽  
Optimal Strategies ◽  
Mean Value ◽  
Performance Criterion ◽  
The State ◽  
Numerical Application ◽  
Income Insurance ◽  
Non Linear ◽  
Quadratic Performance

AbstractThe calculation of a fair premium is always a challenging topic in the real-world insurance applications. In this paper, a non-linear premium-reserve (P-R) model is presented and the premium is derived by minimising a quadratic performance criterion. The reserve is a stochastic equation, which includes an additive random non-linear function of the state, premium and not necessarily Gaussian noise, which is, however, independently distributed in time, provided only that the mean value and the covariance of the random function is 0 and a quadratic function of the state, premium and other parameters, respectively. In this quadratic representation of the covariance function, new parameters are implemented and enriched further by the previous linear models, such as the income insurance elasticity of demand, the number of insured and the inflation in addition to the company’s reputation. The quadratic utility function concerns the present value of the reserve. Interestingly, for the very first time, the derived optimal premium in a competitive market environment is also dependent on the company’s reserve among the other parameters. Finally, a numerical application illustrates the main findings of the paper.

scholarly journals Monitoring Pareto Type IV SRGM using SPC

2013 ◽  
Vol 11 (1) ◽  
pp. 2161-2168
Author(s):  
Sridevi Gutta ◽  
Satya R Prasad
Keyword(s):  
Value Function ◽  
Failure Process ◽  
Likelihood Estimation ◽  
Mean Value ◽  
Data Sets ◽  
Unknown Parameters ◽  
Statistical Process ◽  
Software Failure ◽  
Failure Data ◽  
Type Iv

The Reliability of the Software Process can be monitored efficiently using Statistical Process Control (SPC). SPC is the application of statistical techniques to control a process. SPC is a study of the best ways of describing and analyzing the data and then drawing conclusion or inferences based on available data. With the help of SPC the software development team can identify software failure process and find out actions to be taken which assures better software reliability. This paper provides a control mechanism based on the cumulative observations of Interval domain data using mean value function of Pareto type IV distribution, which is based on Non-Homogenous Poisson Process (NHPP). The unknown parameters of the model are estimated using maximum likelihood estimation approach. Besides it also presents an analysis of failure data sets at a particular point and compares Pareto Type II and Pareto Type IV models.

scholarly journals Asymptotic Properties of Solutions of Two-Dimensional Differential-Difference Elliptic Problems

2017 ◽  
Vol 63 (4) ◽  
pp. 678-688 ◽  
Author(s):  
A B Muravnik
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Value Function ◽  
Boundary Value ◽  
Asymptotic Properties ◽  
Nonlocal Problem ◽  
Mean Value ◽  
Boundary Line ◽  
Strong Ellipticity Condition ◽  
Nonlocal Terms

In the half-plane {−∞<x<+∞}×{0<y<+∞}, the Dirichlet problem is considered for m differential-difference equations of the kind uxx+∑mk=1akuxx(x+hk,y)+uyy=0, where the amount of nonlocal terms of the equation is arbitrary and no commensurability conditions are imposed on their coefficients a1,..., am and the parameters h1,..., hm determining the translations of the independent variable x. The only condition imposed on the coefficients and parameters of the studied equation is the nonpositivity of the real part of the symbol of the operator acting with respect to the variable x. Earlier, it was proved that the specified condition (i. e., the strong ellipticity condition for the corresponding differential-difference operator) guarantees the solvability of the considered problem in the sense of generalized functions (according to the Gel’fand-Shilov definition), a Poisson integral representation of a solution was constructed, and it was proved that the constructed solution is smooth outside the boundary line. In the present paper, the behavior of the specified solution as y → +∞ is investigated. We prove the asymptotic closedness between the investigated solution and the classical Dirichlet problem for the differential elliptic equation (with the same boundary-value function as in the original nonlocal problem) determined as follows: all parameters h1,..., hm of the original differential-difference elliptic equation are assigned to be equal to zero. As a corollary, we prove that the investigated solutions obey the classical Repnikov-Eidel’man stabilization condition: the solution stabilizes as y → +∞ if and only if the mean value of the boundary-value function over the interval (-R, +R) has a limit as R → +∞.

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