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
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
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 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 question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probabili...The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure （martingale measure） if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.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 papcr investigates a Parcto optimal insurancc contract design problcm within a behavioral finance framework.In this context,the insured evaluates contracts using the rank-dependent utility(RDU,for short)theory,wh...This papcr investigates a Parcto optimal insurancc contract design problcm within a behavioral finance framework.In this context,the insured evaluates contracts using the rank-dependent utility(RDU,for short)theory,while the insurer applies the expected value premium principle.The analysis incorporates the incentive compatibility constraint,ensuring that the contracts,called moral-hazard-free,are free from the moral hazard issues identified in Bernard et al.[4].Initially,the problem is formulated as a nonconcave maximization problem involving Choquet expectation.It is then transformed into a quantile optimization problem and addrcssed using thc calculus of variations mcthod.The optimal contracts are characterized by a double-obstacle ordinary differential equation for a semi-linear second-order elliptic operator with nonlocal boundary conditions,which seems new in the financial economics literature.We present a straightforward numerical scheme and a numerical example to compute the optimal contracts.Let and mo represent the relative safety loading and the mass of the potential loss at O,respectively.We discover that every moral-hazard-free contract is optimal for infinitely many RDU-insured individuals if 0<θ<m_(0)/1-m_(0).Conversely,certain contracts,such as the full coverage contract,are never optimal for any RDU-insured individual ifθ>m_(0)/1-m_(0)Additionally,we derive all the Pareto optimal contracts when either the compensation or the retention violates the monotonicity constraint.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
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.
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 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 question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure （martingale measure） if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.
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.
基金support from the NSFC(Grant No.11471276,11971409)The Hong Kong RGC(GRF Grant No.15202817,15202421,15204622 and 15203423)+1 种基金the PolyU-SDU Joint Research Center on Financial Mathematics,the CAS AMSS-PolyU Joint Laboratory of Applied Mathematics,the Research Centre for Quantitative Finance(1-CE03)internal grants from The Hong Kong Polytechnic University.
文摘This papcr investigates a Parcto optimal insurancc contract design problcm within a behavioral finance framework.In this context,the insured evaluates contracts using the rank-dependent utility(RDU,for short)theory,while the insurer applies the expected value premium principle.The analysis incorporates the incentive compatibility constraint,ensuring that the contracts,called moral-hazard-free,are free from the moral hazard issues identified in Bernard et al.[4].Initially,the problem is formulated as a nonconcave maximization problem involving Choquet expectation.It is then transformed into a quantile optimization problem and addrcssed using thc calculus of variations mcthod.The optimal contracts are characterized by a double-obstacle ordinary differential equation for a semi-linear second-order elliptic operator with nonlocal boundary conditions,which seems new in the financial economics literature.We present a straightforward numerical scheme and a numerical example to compute the optimal contracts.Let and mo represent the relative safety loading and the mass of the potential loss at O,respectively.We discover that every moral-hazard-free contract is optimal for infinitely many RDU-insured individuals if 0<θ<m_(0)/1-m_(0).Conversely,certain contracts,such as the full coverage contract,are never optimal for any RDU-insured individual ifθ>m_(0)/1-m_(0)Additionally,we derive all the Pareto optimal contracts when either the compensation or the retention violates the monotonicity constraint.
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.
