In this paper,we present a brief version of de Finetti-Ramsey’s subjective probability theory and provide a rigorous yet intuitively plausible explanation of expected utility using elementary mathematics.In a final s...In this paper,we present a brief version of de Finetti-Ramsey’s subjective probability theory and provide a rigorous yet intuitively plausible explanation of expected utility using elementary mathematics.In a final section,we take up the case of some“Paradoxes in Expected Utility Theory”and try to reconcile them with the help of subjective probabilities.展开更多
This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by a-maxmin expected CES utility which is to differentiate ambiguity ...This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by a-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiple- priors utility and the technique of backward stochastic differential equations （BSDEs）, we transform the （^-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor＇s uncertainty. Our model investi- gates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flex- ibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.展开更多
This paper investigates testable restrictions on the time-series behavior of consumption and asset returns implied by a representative agent model with the spirit of capitalism in which intertemporal preference is rep...This paper investigates testable restrictions on the time-series behavior of consumption and asset returns implied by a representative agent model with the spirit of capitalism in which intertemporal preference is represented by a utility function that generalizes conventional, time-additive, expected utility. In the recursive structure of preference, the author examines the implication for cosumptions, portfolio holdings, and stock-market prices when investors accumulate wealth not only for the sake of consumption but also for wealth-induced social status. When investors care about relative social status, the propensity to consume and risk-taking behavior will depend on social standards, and stock prices will be volatible. Hence, the spirit of capitalism seems to be a driving force behind stock-market volatility and economic growth. Because the elasticity df substitution and the coefficient of relative risk aversion are independent and the spirit of capitalism is introduced, the equity premium puzzle can be partially explained in the model.展开更多
In this paper, it is discussed a framework combining traditional expected utility and weighted entropy (EU-WE)—also named mean contributive value index—which may be conceived as a decision aiding procedure, or a heu...In this paper, it is discussed a framework combining traditional expected utility and weighted entropy (EU-WE)—also named mean contributive value index—which may be conceived as a decision aiding procedure, or a heuristic device generating compositional scenarios, based on information theory concepts, namely weighted entropy. New proofs concerning the maximum value of the index and the evaluation of optimal proportions are outlined, with emphasis on the optimal value of the Lagrange multiplier and its meaning. The rationale is a procedure of maximizing the combined value of a system expressed as a mosaic, denoted by characteristic values of the states and their proportions. Other perspectives of application of this EU-WE framework are suggested.展开更多
This article analyzes the Pareto optimal allocations,agreeable trades and agreeable bets under the maxmin Choquet expected utility(MCEU)model.We provide several useful characterizations for Pareto optimal allocations ...This article analyzes the Pareto optimal allocations,agreeable trades and agreeable bets under the maxmin Choquet expected utility(MCEU)model.We provide several useful characterizations for Pareto optimal allocations for risk averse agents.We derive the formulation descriptions for non-existence agreeable trades or agreeable bets for risk neutral agents.We build some relationships between ex-ante stage and interim stage on agreeable trades or bets when new information arrives.展开更多
This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor's subjective vi...This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor's subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets' prices are discussed. Some properties of the maximal utility function with respect to the endowment are given.展开更多
The likelihood function plays a central role in statistical analysis in relation to information, from both frequentist and Bayesian perspectives. In large samples several new properties of the likelihood in relation t...The likelihood function plays a central role in statistical analysis in relation to information, from both frequentist and Bayesian perspectives. In large samples several new properties of the likelihood in relation to information are developed here. The Arrow-Pratt absolute risk aversion measure is shown to be related to the Cramer-Rao Information bound. The derivative of the log-likelihood function is seen to provide a measure of information related stability for the Bayesian posterior density. As well, information similar prior densities can be defined reflecting the central role of likelihood in the Bayes learning paradigm.展开更多
This paper discusses a method for identifying states in a multistage Decision Making Problem in which an Indifferent Event is either predetermined or can be automatically derived after the fact. First, when they are p...This paper discusses a method for identifying states in a multistage Decision Making Problem in which an Indifferent Event is either predetermined or can be automatically derived after the fact. First, when they are pre-set, the amount of possible information about Indifferent Event tends to be large. Therefore, since the decision is risk tolerant, the Max-Product method of Tanaka et al. is used to calculate the expected utility possibility. Next, in the case of automatic derivation after the fact, the amount of information on the possibility of Indifferent Event is relatively small, so the expected utility possibility is derived using Zadeh’s Fuzzy Event Possibility Measure. Here, it is assumed that the setting of the utility function is independent of the information on the occurrence of the Indifferent Event and is identified by the decision maker by lot drawing using the certainty equivalence method. As a concrete example, we focus on the pass/fail decision of a recommendation test, which is a two choice question in the No-Data Problem, and illustrate the multistage state identification method. .展开更多
文摘In this paper,we present a brief version of de Finetti-Ramsey’s subjective probability theory and provide a rigorous yet intuitively plausible explanation of expected utility using elementary mathematics.In a final section,we take up the case of some“Paradoxes in Expected Utility Theory”and try to reconcile them with the help of subjective probabilities.
基金Supported by National Natural Science Foundation of China (71171003, 71271003)Programming Fund Project of the Humanities and Social Sciences Research of the Ministry of Education of China (12YJA790041)+1 种基金Anhui Natural Science Foundation (090416225, 1208085MG116)Anhui Natural Science Foundation of Universities (KJ2010A037, KJ2010B026)
文摘This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by a-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiple- priors utility and the technique of backward stochastic differential equations （BSDEs）, we transform the （^-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor＇s uncertainty. Our model investi- gates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flex- ibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.
文摘This paper investigates testable restrictions on the time-series behavior of consumption and asset returns implied by a representative agent model with the spirit of capitalism in which intertemporal preference is represented by a utility function that generalizes conventional, time-additive, expected utility. In the recursive structure of preference, the author examines the implication for cosumptions, portfolio holdings, and stock-market prices when investors accumulate wealth not only for the sake of consumption but also for wealth-induced social status. When investors care about relative social status, the propensity to consume and risk-taking behavior will depend on social standards, and stock prices will be volatible. Hence, the spirit of capitalism seems to be a driving force behind stock-market volatility and economic growth. Because the elasticity df substitution and the coefficient of relative risk aversion are independent and the spirit of capitalism is introduced, the equity premium puzzle can be partially explained in the model.
文摘In this paper, it is discussed a framework combining traditional expected utility and weighted entropy (EU-WE)—also named mean contributive value index—which may be conceived as a decision aiding procedure, or a heuristic device generating compositional scenarios, based on information theory concepts, namely weighted entropy. New proofs concerning the maximum value of the index and the evaluation of optimal proportions are outlined, with emphasis on the optimal value of the Lagrange multiplier and its meaning. The rationale is a procedure of maximizing the combined value of a system expressed as a mosaic, denoted by characteristic values of the states and their proportions. Other perspectives of application of this EU-WE framework are suggested.
基金supported by the National Natural Science Foundation of China(No.12171471)Natural Science Foundation of Jiangsu Province(No.BK20221543).
文摘This article analyzes the Pareto optimal allocations,agreeable trades and agreeable bets under the maxmin Choquet expected utility(MCEU)model.We provide several useful characterizations for Pareto optimal allocations for risk averse agents.We derive the formulation descriptions for non-existence agreeable trades or agreeable bets for risk neutral agents.We build some relationships between ex-ante stage and interim stage on agreeable trades or bets when new information arrives.
基金Supported by the Fundamental Research Funds for the Central University(10D10909)
文摘This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor's subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets' prices are discussed. Some properties of the maximal utility function with respect to the endowment are given.
文摘The likelihood function plays a central role in statistical analysis in relation to information, from both frequentist and Bayesian perspectives. In large samples several new properties of the likelihood in relation to information are developed here. The Arrow-Pratt absolute risk aversion measure is shown to be related to the Cramer-Rao Information bound. The derivative of the log-likelihood function is seen to provide a measure of information related stability for the Bayesian posterior density. As well, information similar prior densities can be defined reflecting the central role of likelihood in the Bayes learning paradigm.
文摘This paper discusses a method for identifying states in a multistage Decision Making Problem in which an Indifferent Event is either predetermined or can be automatically derived after the fact. First, when they are pre-set, the amount of possible information about Indifferent Event tends to be large. Therefore, since the decision is risk tolerant, the Max-Product method of Tanaka et al. is used to calculate the expected utility possibility. Next, in the case of automatic derivation after the fact, the amount of information on the possibility of Indifferent Event is relatively small, so the expected utility possibility is derived using Zadeh’s Fuzzy Event Possibility Measure. Here, it is assumed that the setting of the utility function is independent of the information on the occurrence of the Indifferent Event and is identified by the decision maker by lot drawing using the certainty equivalence method. As a concrete example, we focus on the pass/fail decision of a recommendation test, which is a two choice question in the No-Data Problem, and illustrate the multistage state identification method. .
