Conditional Risk Premiums and the Value Function of Prospect Theory

2020 ◽  
pp. 1-10
Author(s):  
Martin Walther ◽  
Markus Münster
Keyword(s):  
Prospect Theory ◽  
Value Function ◽  
Risk Premiums ◽  
Conditional Risk ◽  
The Value Function

scholarly journals A DECISION-MAKING FRAMEWORK BASED ON THE PROSPECT THEORY UNDER AN INTUITIONISTIC FUZZY ENVIRONMENT

2018 ◽  
Vol 24 (6) ◽  
pp. 2374-2396 ◽  
Author(s):  
Jing Gu ◽  
Zijian Wang ◽  
Zeshui Xu ◽  
Xuezheng Chen
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Value Function ◽  
Behavior Pattern ◽  
Weighting Function ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Framework ◽  
Decision Making Behavior ◽  
The Value Function

Uncertainty and ambiguity are frequently involved in the decision-making process in our daily life. This paper develops a generalized decision-making framework based on the prospect theory under an intuitionistic fuzzy environment, by closely integrating the prospect theory and the intuitionistic fuzzy sets into our framework. We demonstrate how to compute the intuitionistic fuzzy prospect values as the reference values for decision-making and elaborate a four-step editing phase and a valuation phase with two key functions: the value function and the weighting function. We then conduct experiments to test our decision- making methodology and the key features of our framework. The experimental results show that the shapes of the value function and the weighting function in our framework are in line with those of prospect theory. The methodology proposed in this paper to elicit prospects that are not only under uncertainty but also under ambiguity. We reveal the decision-making behavior pattern through comparing the parameters. People are less risk averse when making decisions under an intuitionistic fuzzy environment than under uncertainty. People still underestimate the probability of the events in our experiment. Further, the choices of participants in the experiments are consistent with the addition and multiplication principles of our framework.

The Relationship Between Numeracy and the Value Function and Probability Weighting in Prospect Theory

2012 ◽  
Author(s):  
Mona Gauth ◽  
Maria Henriksson ◽  
Peter Juslin ◽  
Neda Kerimi ◽  
Marcus Lindskog ◽  
...  
Keyword(s):  
Prospect Theory ◽  
Value Function ◽  
Probability Weighting ◽  
The Relationship ◽  
The Value Function

An Empirical Study on Value Functions of Stock Markets

2011 ◽  
Vol 204-210 ◽  
pp. 899-906
Author(s):  
Feng Hua Wen ◽  
Gui Tian Rao ◽  
Xiao Guang Yang
Keyword(s):  
Prospect Theory ◽  
Stock Markets ◽  
Subjective Experience ◽  
Value Function ◽  
Empirical Studies ◽  
Value Functions ◽  
A Value ◽  
Egarch Model ◽  
The Value Function ◽  
Psychological Experiments

As a core component of the prospect theory, a value function is employed to characterize the subjective experience of a decision-maker’s gain or loss. Previous empirical studies of the prospect theory were largely carried out through psychological experiments on individual decision-makers. In this paper, taking the whole stock market as an entity, we use the flow of information extracted by EGARCH Model as the proxy variable of change in wealth, and then use a two-stage power function as the representation of the value function to study the daily return data from the stock markets of 10 countries or regions. Empirical results show that the value functions of all the 10 stock markets present the shape of inverse-S, instead of the S-Shape of the value function generated by most psychological experiments on individuals.

Can prospect theory explain the disposition effect? An analysis based on value function

2018 ◽  
Vol 8 (3) ◽  
pp. 235-255
Author(s):  
Xiaotian Liu ◽  
Huayue Zhang ◽  
Shengmin Zhao
Keyword(s):  
Prospect Theory ◽  
Portfolio Choice ◽  
Crucial Role ◽  
Value Function ◽  
Disposition Effect ◽  
Dynamic Programming Method ◽  
Prediction Ability ◽  
Content Type ◽  
The Impact ◽  
The Value Function

Purpose The prospect theory is potentially an essential ingredient in modeling the disposition effect. However, many scholars have tried to explain the disposition effect with the help of prospect theory and they came to opposite conclusions. The purpose of this paper is to examine the impact of value function of the prospect theory on predicting the disposition effect. Design/methodology/approach Lagrange multiplier optimization and dynamic programming method are used to solve the representative investor’s optimal portfolio choice problem. Furthermore, numerical simulation is used to compare the prediction ability of different types of value function. Findings The authors support that the value function has a crucial role in predicting the disposition effect with prospect theory, i.e. the curvature and boundedness of the value function may influence the performance of applying the prospect theory in the disposition effect. They conclude that a piecewise negative exponential value function can predict the disposition effect, while others like the piecewise power value function may not. Originality/value Extant literature about modeling the disposition effect with the prospect theory mostly focus on the time when gain-loss utility occurs or the selection of reference point. This paper based on the value function properties provides a new perspective in analyzing the crucial role that value function has in predicting financial market anomalies.

The value function for time-related decisions

2011 ◽  
Author(s):  
Anouk Festjens ◽  
Siegfried Dewitte ◽  
Enrico Diecidue ◽  
Sabrina Bruyneel
Keyword(s):  
Value Function ◽  
The Value Function

scholarly journals Pricing Perpetual American Put Options with Asset-Dependent Discounting

2021 ◽  
Vol 14 (3) ◽  
pp. 130
Author(s):  
Jonas Al-Hadad ◽  
Zbigniew Palmowski
Keyword(s):  
Value Function ◽  
Asset Price ◽  
Stopping Times ◽  
Martingale Measure ◽  
Put Options ◽  
American Put Options ◽  
Exact Calculations ◽  
Negative Exponential ◽  
American Put ◽  
The Value Function

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VAPutω(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process St is a geometric Lévy process with negative exponential jumps, i.e., St=seζt+σBt−∑i=1NtYi. The asset-dependent discounting is reflected in the ω function, so this approach is a generalisation of the classic case when ω is constant. It turns out that under certain conditions on the ω function, the value function VAPutω(s) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ω such that VAPutω(s) takes a simplified form.

scholarly journals Robo-Advising: Learning Investors’ Risk Preferences via Portfolio Choices*

2020 ◽  
Author(s):  
Humoud Alsabah ◽  
Agostino Capponi ◽  
Octavio Ruiz Lacedelli ◽  
Matt Stern
Keyword(s):  
Opportunity Cost ◽  
Value Function ◽  
Risk Preference ◽  
Portfolio Decisions ◽  
Learning Framework ◽  
Portfolio Choices ◽  
Trading Decisions ◽  
Exploration Exploitation ◽  
The Value Function ◽  
Over Time

Abstract We introduce a reinforcement learning framework for retail robo-advising. The robo-advisor does not know the investor’s risk preference but learns it over time by observing her portfolio choices in different market environments. We develop an exploration–exploitation algorithm that trades off costly solicitations of portfolio choices by the investor with autonomous trading decisions based on stale estimates of investor’s risk aversion. We show that the approximate value function constructed by the algorithm converges to the value function of an omniscient robo-advisor over a number of periods that is polynomial in the state and action space. By correcting for the investor’s mistakes, the robo-advisor may outperform a stand-alone investor, regardless of the investor’s opportunity cost for making portfolio decisions.

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